- Typically, debentures have higher interest rates than mortgage bonds primarily because the mortgage bonds are backed by assets while debentures are unsecured.
ANS: T DIF: Easy TOP: Mortgage bonds
- A call provision gives bondholders the right to demand, or “call for,” repayment of a bond. Typically, calls are exercised if interest rates rise, because when rates rise the bondholder can get the principal amount back and reinvest it elsewhere at higher rates.
ANS: F DIF: Easy TOP: Call provision
- Issuing zero coupon bonds might appeal to a company that is considering investing in a long-term project that will not generate positive cash flows for several years.
ANS: T DIF: Easy TOP: Zero coupon bonds
- The motivation for floating rate bonds arose out of the costly experience of the early 1980s when inflation pushed interest rates to very high levels causing sharp declines in the prices of long-term bonds.
ANS: T DIF: Easy TOP: Floating rate debt
- Because junk bonds are such high-risk instruments, the returns on such bonds aren’t very high and the existence of this market detracts from social welfare.
ANS: F DIF: Easy TOP: Junk bonds and social welfare
- There is an inverse relationship between bond ratings and the required return on a bond. The required return is lowest for AAA rated bonds, and required returns increase as the ratings get lower (worse).
ANS: T DIF: Easy TOP: Bond ratings and required returns
- LIBOR is an acronym for London Interbank Offer Rate, which is an average of interest rates offered by London banks to S. corporations.
ANS: F DIF: Easy TOP: LIBOR
- In general, long-term unsecured debt is less costly than long-term secured for a particular firm.
ANS: F DIF: Easy TOP: Types of debt
- Foreign debt is a debt instrument sold by a foreign borrower but denominated in the currency of the country in which it is sold.
ANS: T DIF: Easy TOP: Foreign debt
- Foreign debt is debt sold in a country other than the one in whose currency the debt is denominated.
ANS: F DIF: Easy TOP: Foreign debt
- Eurobonds have a higher level of required disclosure than normally is found for bonds issued in domestic markets, particularly the United States.
ANS: F DIF: Easy TOP: Foreign debt
- Eurobonds are typically issued as registered bonds rather than bearer bonds.
ANS: F DIF: Easy TOP: Foreign debt
- Eurocredits are bank loans that are denominated in the currency of a country other than where the lending bank is located.
ANS: T DIF: Easy TOP: Foreign debt
- Although common stock represents a riskier investment to an individual than do bonds, in the sense of exposing the firm to the risk of bankruptcy, bonds represent a riskier method of financing to a corporation than does common stock.
ANS: T DIF: Medium TOP: Types of financing
- Restrictive covenants are designed so as to protect both the bondholder and the issuer even though they may constrain the actions of the firm’s managers. Such covenants are contained in the bond’s indenture.
ANS: T DIF: Medium TOP: Restrictive covenants
- One of the disadvantages to a firm in issuing zero coupon bonds is that the tax shield associated with the bonds’ appreciation cannot be claimed until the bond matures.
ANS: F DIF: Medium TOP: Zero coupon interest
- Floating rate debt is advantageous to investors because the interest rate moves up if market rates rise. Floating rate debt shifts interest rate risk to companies and thus has no advantages for issuers.
ANS: F DIF: Medium TOP: Floating rate debt
- If a firm raises capital by selling new bonds, the buyer is called the “issuing firm,” and the coupon rate is generally set equal to the required rate.
ANS: F DIF: Easy TOP: Issuing bonds
- A 20-year original maturity bond with 1 year left to maturity has more interest rate price risk than a 10-year original maturity bond with 1 year left to maturity. (Assume that the bonds have equal default risk and equal coupon rates.)
ANS: F DIF: Easy TOP: Interest rate risk
- Regardless of the size of the coupon payment, the price of a bond moves in the opposite direction from interest rate movements. For example, if interest rates rise, bond prices fall.
ANS: T DIF: Easy TOP: Prices and interest rates
- Because short-term interest rates are much more volatile than long-term rates, you would, in the real world, be subject to much more interest rate price risk if you purchased a 30-day bond than if you bought a 30-year bond.
ANS: F DIF: Easy TOP: Interest rate risk
- A bond’s value will increase as interest rates rise over time.
ANS: F DIF: Easy TOP: Bond value
- You have just noticed in the financial pages of the local newspaper that you can buy a bond ($1,000 par) for $800. If the coupon rate is 10 percent, with annual interest payments, and there are 10 years to maturity, should you make the purchase if your required return on investments of this type is 12 percent?
ANS: T
Tabular solution:
V_{d} | = $100 (PVIFA_{12%, 10}) + $1,000 (PVIF_{12%, 10}) |
| = $100 (5.6502) + $1,000 (0.3220) = $877.02. |
Thus, the value is significantly higher than the market price and the bond should be purchased.
Financial calculator solution:
Inputs: N = 10; I = 12; PMT = 100; FV = 1,000.
Output: PV = -$887.00.
DIF: Medium TOP: Bond value
- If two bonds have the same maturity and the same expected rate of return, but one has a higher coupon, the price of the low coupon bond will be more affected by a given change in interest rates.
ANS: T DIF: Medium TOP: Prices and interest rates
- A bond with a $100 annual interest payment and $1,000 face value with five years to maturity (not expected to default) would sell for a premium if interest rates were below 9% and would sell for a discount if interest rates were greater than 11%.
ANS: T DIF: Medium TOP: Bond premium and discounts
- Call provisions on corporate bonds are generally included to protect the issuer against large declines in interest rates. They affect the actual maturity of the bond but not its price.
ANS: F DIF: Medium TOP: Callable bonds
- Bonds issued by BB&C Communications that have a coupon rate of interest equal to 10 percent currently have a yield to maturity (YTM) equal to 8 percent. Based on this information, BB&C’s bonds must currently be selling at a premium in the financial markets.
ANS: F DIF: Medium TOP: Bond premium and discounts
- If a bond is callable, and if interest rates in the economy decline, then the company can sell a new issue of low-interest-rate bonds and use the proceeds to “call” the old bonds in and have effectively refinanced at a lower rate.
ANS: T DIF: Medium TOP: Call provision
- If the yield to maturity (the market rate of return) of a bond is less than its coupon rate, the bond should be selling at a discount; i.e., the bond’s market price should be less than its face (maturity) value.
ANS: F DIF: Medium TOP: Bond premium and discounts
- If you buy a bond that is selling for less than its face, or maturity, value then the price (value) of the bond will increase the maturity date nears if market interest rates do not change during the life of the bond.
ANS: T DIF: Medium TOP: Bond value
- The longer the maturity of a bond, the more its price will change in response to a given change in interest rates; this is called interest rate price risk.
ANS: T DIF: Medium TOP: Bond prices and interest rates
- Bonds with long maturities expose the investor to high interest rate reinvestment risk, which is the risk that income will differ from what is expected because the cash flows received from bonds will have to be reinvested at different interest rates.
ANS: F DIF: Medium TOP: Bond prices and interest rates
- If we have two bonds with a simple interest rate yield of 9% where one bond is compounded quarterly and the other bond is compounded monthly, the bond compounded quarterly will have a higher effective annual yield.
ANS: F DIF: Medium TOP: Bond yields
- All else equal, a zero-coupon bond’s price is more sensitive to changes interest rates than a bond with a 10% annual coupon.
ANS: T DIF: Medium TOP: Bond prices and interest rates
MULTIPLE CHOICE
- Which of the following are generally considered advantages of term loans over publicly issued bonds?
a. | Lower flotation costs. |
b. | Speed, or how long it takes to bring the issue to market. |
c. | Flexibility, or the ability to adjust the bond’s terms after it has been issued. |
d. | All of the above. |
e. | Only answers b and c above. |
ANS: D DIF: Easy OBJ: TYPE: Conceptual TOP: Term loans
- Other things held constant, if a bond indenture contains a call provision, the yield to maturity that would exist without such a call provision will generally be __________ the YTM with it.
a. | Higher than |
b. | Lower than |
c. | The same as |
d. | Either higher or lower, depending on the level of call premium, than |
e. | Unrelated to |
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: Call provision
- The terms and conditions to which a bond is subject are set forth in its
a. | Debenture. |
b. | Underwriting agreement. |
c. | Indenture. |
d. | Restrictive covenants. |
e. | Call provision. |
ANS: C DIF: Easy OBJ: TYPE: Conceptual TOP: Bond indenture
- A contract negotiated directly with a bank in which the borrower agrees to make a series of interest and principal payments on specific dates to the bank is called
a. | preferred stock. |
b. | commercial paper. |
c. | convertible debt. |
d. | a term loan. |
e. | a bond issue. |
ANS: D DIF: Easy OBJ: TYPE: Conceptual TOP: Term loans
- A bond differs from term in loans in that
a. | a bond issue is generally advertised. |
b. | a bond is sold to many investors. |
c. | a bond is offered to the public. |
d. | All of the above. |
e. | None of the above. |
ANS: D DIF: Easy OBJ: TYPE: Conceptual TOP: Bonds
- Which of the following types of debt are backed by some form of specific property?
a. | Debenture. |
b. | Mortgage bond. |
c. | Subordinated debt. |
d. | All of the above. |
e. | None of the above. |
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: Types of debt
- A bond that has a claim on assets only after the senior debt has been paid off in the event of liquidation is called what?
a. | Debenture. |
b. | Income bond. |
c. | Indenture. |
d. | Subordinated debenture. |
e. | Mortgage bond. |
ANS: D DIF: Easy OBJ: TYPE: Conceptual TOP: Types of debt
- Bonds that can be exchanged for shares of equity at the owner’s discretion are called what?
a. | Debenture. |
b. | Indenture. |
c. | Callable bond |
d. | Convertible bond. |
e. | Putable bond. |
ANS: D DIF: Easy OBJ: TYPE: Conceptual TOP: Types of debt
- A bond that only pays interest if the firm has sufficient earnings to cover the interest payments is called what?
a. | Callable bond. |
b. | Putable bond. |
c. | Convertible bond. |
d. | Income bond. |
e. | Indexed bond. |
ANS: D DIF: Easy OBJ: TYPE: Conceptual TOP: Types of debt
- A bond that can be redeemed for cash at the bondholder’s option is called what?
a. | Convertible bond. |
b. | Putable bond. |
c. | Callable bond. |
d. | Debenture. |
e. | Income bond. |
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: Types of debt
- Which of the following events would make it less likely that a company would choose to call its outstanding callable bonds?
a. | Increase in interest rates. |
b. | Decrease in interest rates. |
c. | Increase in price of outstanding convertible bonds. |
d. | A decrease in call premium. |
e. | Answers b and c only. |
ANS: A DIF: Easy OBJ: TYPE: Conceptual TOP: Callable bonds
- A bond that pays no annual interest but is sold at a discount below its par value is called what?
a. | Mortgage bond. |
b. | Callable bond. |
c. | Convertible bond. |
d. | Putable bond. |
e. | Zero coupon bond. |
ANS: E DIF: Easy OBJ: TYPE: Conceptual
TOP: Zero coupon bonds
- __________ are high-risk, high-yield bonds used to finance mergers, leveraged buyouts, and troubled companies.
a. | Callable bonds |
b. | Junk bonds |
c. | Convertible bonds |
d. | Floating rate bonds |
e. | Putable bonds |
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: Junk bond
- Which of the following ratings by Moody’s represent bonds that are at least investment grade?
a. | Caa |
b. | Baa |
c. | B |
d. | Ba |
e. | None of the above. |
ANS: B DIF: Easy OBJ: TYPE: Conceptual TOP: Bond ratings
- Which of the following ratings by Standard & Poor’s represent speculative grade debt?
a. | A |
b. | B |
c. | BB |
d. | BBB |
e. | None of the above. |
ANS: E DIF: Easy OBJ: TYPE: Conceptual TOP: Bond ratings
- Which of the following types of debt protect a bondholder against an increase in interest rates?
a. | Floating rate debt. |
b. | Bonds that are redeemable (“putable”) at par at the bondholders’ option. |
c. | Bonds with call provisions. |
d. | All of the above. |
e. | Only answers a and b above. |
ANS: E DIF: Medium OBJ: TYPE: Conceptual TOP: Types of debt
- Which of the following statements is correct?
a. | A zero coupon bond provides no interest payments during the life of the bond, but it provides its owner with a capital gain when the bond matures. In the United States, these bonds appeal to high-income investors because the tax on capital gains income is deferred until the bond matures or is sold. |
b. | The “penalty” for having a low bond rating is more severe when the Security Market Line (SML) is relatively steep than when it is not so steep. |
c. | A bond that is callable has a chance of being retired earlier than its stated term to maturity. Therefore, if the yield curve is upward sloping, an outstanding callable bond should have a lower yield to maturity than an otherwise identical noncallable bond. |
d. | A zero coupon bond is a bond that pays no interest and is offered (and subsequently sells) at par, therefore providing compensation to investors in the form of capital appreciation. |
e. | None of the above is a correct statement. |
ANS: B DIF: Medium OBJ: TYPE: Conceptual
TOP: Miscellaneous concepts
- Which of the following statements is false?
a. | Any bond sold outside the country of the borrower is called an international bond. |
b. | Foreign bonds and Eurobonds are two important types of international bonds. |
c. | Foreign bonds are bonds sold by a foreign borrower but denominated in the currency of the country in which the issue is sold. |
d. | The term Eurobond specifically applies to any foreign bonds denominated in U.S. currency. |
e. | None of the above. |
ANS: D DIF: Medium OBJ: TYPE: Conceptual
TOP: International bond markets
- Which type of investor would be most likely to purchase zero coupon bonds?
a. | Retired individuals seeking income for current consumption. |
b. | Individuals in high tax brackets. |
c. | Tax free investors such as pension funds. |
d. | Risk averse individuals anticipating increases in interest rates. |
e. | None of the above. |
ANS: C DIF: Medium OBJ: TYPE: Conceptual
TOP: Zero coupon bonds
- Which of the following securities is the riskiest to investors?
a. | Floating rate notes. |
b. | Income bonds. |
c. | Treasury bills. |
d. | First mortgage bonds. |
e. | Common stock. |
ANS: E DIF: Medium OBJ: TYPE: Conceptual
TOP: Types of securities
- Listed below are some provisions that are often contained in bond indentures:
1. | Fixed assets may be used as security. |
2. | The bond may be subordinated to other classes of debt. |
3. | The bond may be made convertible. |
4. | The bond may have a sinking fund. |
5. | The bond may have a call provision. |
6. | The bond may have restrictive covenants in its indenture. |
Which of the above provisions, each viewed alone, would tend to reduce the yield to maturity investors would otherwise require on a newly issued bond?
a. | 1, 2, 3, 4, 5, 6 |
b. | 1, 2, 3, 4, 6 |
c. | 1, 3, 4, 5, 6 |
d. | 1, 3, 4, 6 |
e. | 1, 4, 6 |
ANS: D DIF: Tough OBJ: TYPE: Conceptual TOP: Bond indenture
- Rollincoast Incorporated issued BBB bonds two years ago that provided a yield to maturity of 11.5 percent. Long-term risk-free government bonds were yielding 8.7 percent at that time. The current risk premium on BBB bonds versus government bonds is half what it was two years ago. If the risk-free long-term governments are currently yielding 7.8 percent, then at what rate should Rollincoast expect to issue new bonds?
a. | 7.8% |
b. | 8.7% |
c. | 9.2% |
d. | 10.2% |
e. | 12.9% |
ANS: C
Calculate the previous risk premium, RP_{BBB}, and new RP_{BBB}:
RP_{BBB} = 11.5% – 8.7% = 2.8%.
New RP_{BBB} = 2.8%/2 = 1.4%.
Calculate new YTM on BBB bonds: YTM_{BBB} = 7.8% + 1.4% = 9.2%.
DIF: Easy OBJ: TYPE: Problem TOP: Risk premium on bonds
- Claus & Company is planning a zero coupon bond issue. The bond has a par value of $1,000, matures in 2 years, and will be sold at a price of $826.45. The firm’s marginal tax rate is 40 percent. What is the annual after-tax cost of debt to the company on this issue?
a. | 4.0% |
b. | 6.0% |
c. | 8.0% |
d. | 10.0% |
e. | 12.0% |
ANS: B
Tabular solution:
First, find the value of r_{d} as the interest rate which will cause $826.45 to grow to $1,000 in 2 years.
$1,000 = $826.45(FVIF_{i,2})
FVIF_{i,2} = 1.2100
I = 0.10 = r_{d} = 10%.
r_{dT} = r_{d}(1 – T) = 0.10(0.6) = 0.06 = 6%.
Analysis of cash flows method using calculated r_{d} = 10% and financial calculator:
Year: | 0 | 1 | 2 |
Accrued value | $826.45 | $909.10 | $1,000.00 |
Interest ((V_{t} ´ 1.10) – V_{t}) | | 82.65 | 90.90 |
Tax saving (Interest ´ 0.40) | | 33.06 | 36.36 |
Cash flows | +826.45 | +33.06 | +36.36 |
| | | -1,000.00 |
| | | -$ 963.64 |
Financial calculator solution: (Using CFs from worksheet analysis)
Inputs: = 826.45; = 33.06; = -963.64.
Output: IRR% = 6.0%. r_{dT} = 6.0%.
DIF: Medium OBJ: TYPE: Problem TOP: Zero coupon bonds
- GP&L sold $1,000,000 of 12 percent, 30-year, semiannual payment bonds 15 years ago. The bonds are not callable, but they do have a sinking fund which requires GP&L to redeem 5 percent of the original face value of the issue each year ($50,000), beginning in Year 11. To date, 25 percent of the issue has been retired. The company can either call bonds at par for sinking fund purposes or purchase bonds on the open market, spending sufficient money to redeem 5 percent of the original face value each year. If the yield to maturity (15 years remaining) on the bonds is currently 14 percent, what is the least amount of money GP&L must put up to satisfy the sinking fund provision?
a. | $43,856 |
b. | $50,000 |
c. | $37,500 |
d. | $43,796 |
e. | $39,422 |
ANS: D
The company must call 5% or $50,000 face value each year. It could call at par and spend $50,000 or buy on the open market. Since the interest rate is higher than the coupon rate (14% vs. 12%), the bonds will sell at a discount, so open market purchases should be used.
Financial calculator solution:
Inputs: N = 30; I = 7; PMT = 60; FV = 1,000.
Output: PV = -875.91.
The company would have to buy 50 bonds at $875.91 each = $43,795.50 $43,796.
DIF: Tough OBJ: TYPE: Problem TOP: Bond sinking fund payments
- Bonds issued by BB&C Communications that have a coupon rate of interest equal to 10.65 percent currently have a yield to maturity (YTM) equal to 15.25 percent. Based on this information, BB&C’s bonds must currently be selling at __________ in the financial markets.
a. | par value |
b. | a discount |
c. | a premium |
d. | Not enough information is given to answer this question. |
e. | None of the above is a correct answer. |
ANS: B DIF: Easy OBJ: TYPE: Conceptual
TOP: Bond premium and discounts
- If the yield to maturity (the market rate of return) of a bond is less than its coupon rate, the bond should be
a. | selling at a discount; i.e., the bond’s market price should be less than its face (maturity) value. |
b. | selling at a premium; i.e., the bond’s market price should be greater than its face value. |
c. | selling at par; i.e., the bond’s market price should be the same as its face value. |
d. | purchased because it is a good deal. |
ANS: B DIF: Easy OBJ: TYPE: Conceptual
TOP: Bond premium and discounts
- A 12-year bond that has a 12 percent coupon rate is currently selling for $1,000, which equals the bond’s face value. If interest is paid semiannually, the bond’s yield to maturity is
a. | equal to 12 percent. |
b. | greater than 12 percent. |
c. | less than 12 percent. |
d. | More information is needed to answer this question. |
e. | None of the above is correct. |
ANS: A DIF: Easy OBJ: TYPE: Conceptual TOP: Bond yields
- Which of the following statements is correct?
a. | Other things held constant, a callable bond would have a lower required rate of return than a noncallable bond. |
b. | Other things held constant, a corporation would rather issue noncallable bonds than callable bonds. |
c. | Reinvestment rate risk is worse from a typical investor’s standpoint than interest rate price risk. |
d. | If a 10-year, $1,000 par, zero coupon bond were issued at a price which gave investors a 10 percent rate of return, and if interest rates then dropped to the point where r_{d} = YTM = 5%, we could be sure that the bond would sell at a premium over its $1,000 par value. |
e. | If a 10-year, $1,000 par, zero coupon bond were issued at a price which gave investors a 10 percent rate of return, and if interest rates then dropped to the point where r_{d} = YTM = 5%, we could be sure that the bond would sell at a discount below its $1,000 par value. |
ANS: E
A zero coupon bond will always sell at a discount below par, provided interest rates are above zero, which they always are.
DIF: Medium OBJ: TYPE: Conceptual TOP: Bonds
- Which of the following statements is correct?
a. | Rising inflation makes the actual yield to maturity on a bond greater than the quoted yield to maturity which is based on market prices. |
b. | The yield to maturity for a coupon bond that sells at its par value consists entirely of an interest yield; it has a zero expected capital gains yield. |
c. | On an expected yield basis, the expected capital gains yield will always be positive because an investor would not purchase a bond with an expected capital loss. |
d. | The market value of a bond will always approach its par value as its maturity date approaches. This holds true even if the firm enters bankruptcy. |
e. | All of the above statements are false. |
ANS: B DIF: Medium OBJ: TYPE: Conceptual TOP: Bond yields
- Which of the following statements is correct?
a. | The discount or premium on a bond can be expressed as the difference between the coupon payment on an old bond which originally sold at par and the coupon payment on a new bond, selling at par, where the difference in payments is discounted at the new market rate. |
b. | The price of a coupon bond is determined primarily by the number of years to maturity. |
c. | On a coupon paying bond, the final interest payment is made one period before maturity and then, at maturity, the bond’s face value is paid as the final payment. |
d. | The actual capital gains yield for a one-year holding period on a bond can never be greater than the current yield on the bond. |
e. | All of the above statements are false. |
ANS: A DIF: Medium OBJ: TYPE: Conceptual TOP: Bond concepts
- If you buy a bond that is selling for less than its face, or maturity, value what will happen to the price (value) of the bond as the maturity date nears if market interest rates do not change during the life of the bond?
a. | Because interest rates remain constant, nothing happens to the market value of the bond. |
b. | The price of the bond should decrease even further below the bond’s face value because the rates in the market are too high. |
c. | The price of the bond will increase as the bond gets closer to its maturity because the bond’s value has to equal its face value at maturity. |
d. | This question cannot be answered without additional information. |
e. | None of the above is a correct answer. |
ANS: C DIF: Medium OBJ: TYPE: Conceptual
TOP: Bond prices and interest rates
- Omega Software Corporation’s bond is currently selling at a discount in the financial markets. If the bond’s yield to maturity is 11.5 percent, what is its coupon rate of interest?
a. | greater than 11.5 percent |
b. | less than 11.5 percent |
c. | equal to 11.5 percent |
d. | There is not enough information to answer this question. |
e. | None of the above is a correct answer. |
ANS: D DIF: Medium OBJ: TYPE: Conceptual
TOP: Bond coupon rate
- Stephanie just purchased a corporate bond that matures in three years. The bond has a coupon interest rate equal to 9 percent and its yield to maturity is 6 percent. If market conditions do not change—that is market interest rates remain constant—and Stephanie sells the bond in 12 months, what will be her capital gain from holding the bond?
a. | Positive; because she bought the bond for a discount, which means its price has to increase as the maturity date nears. |
b. | Negative; because she bought the bond for a premium, which means its price has to decrease as the maturity date nears. |
c. | Zero, because she must have bought the bond for par, which means its price will not change as the maturity date nears. |
d. | This question cannot be answered, because the face (maturity) value of the bond is not given. |
e. | None of the above is correct. |
ANS: B DIF: Medium OBJ: TYPE: Conceptual TOP: Bond value
- Which of the following is not true about bonds? In all of the statements, assume other things are held constant?
a. | Price sensitivity, that is, the change in price due to a given change in the required rate of return, increases as a bond’s maturity increases. |
b. | For a given bond of any maturity, a given percentage point increase in the interest rate (r_{d}) causes a larger dollar capital loss than the capital gain stemming from an identical decrease in the interest rate. |
c. | For any given maturity, a given percentage point increase in the interest rate causes a smaller dollar capital loss than the capital gain stemming from an identical decrease in the interest rate. |
d. | From a borrower’s point of view, interest paid on bonds is tax-deductible. |
e. | A 20-year zero-coupon bond has less reinvestment rate risk than a 20-year coupon bond. |
ANS: B DIF: Tough OBJ: TYPE: Conceptual TOP: Bonds
- If interest rates fall from 8 percent to 7 percent, which of the following bonds will have the largest percentage increase in its value?
a. | A 10-year zero-coupon bond. |
b. | A 10-year bond with a 10 percent semiannual coupon. |
c. | A 10-year bond with a 10 percent annual coupon. |
d. | A 5-year zero-coupon bond. |
e. | A 5-year bond with a 12 percent annual coupon. |
ANS: A
Statement a is correct. The present value of the 10-year, zero-coupon bond at an 8 percent interest rate is $463.19, while its value at a 7 percent interest rate is $508.34. The percentage change is $45.15/$463.19 = 9.75%. If you work out the other percentage increases in values due to the change in interest rates, you’ll obtain the following results:
b. | 10-year, 10% semiannual coupon: 6.80%. |
c. | 10-year, 10% annual coupon: 6.75%. |
d. | 5-year, zero-coupon: 4.76%. |
e. | 5-year, 12% annual coupon: 3.91%. |
DIF: Tough OBJ: TYPE: Conceptual TOP: Bond value
- Which of the following statements is most correct?
a. | If a bond’s yield to maturity exceeds its coupon rate, the bond’s current yield must also exceed its coupon rate. |
b. | If a bond’s yield to maturity exceeds its coupon rate, the bond’s price must be less than its maturity value. |
c. | If two bonds have the same maturity, the same yield to maturity, and the same level of risk, the bonds should sell for the same price regardless of the bond’s coupon rate. |
d. | Answers b and c are both correct. |
e. | None of the above answers are correct. |
ANS: B
Statement b is correct. If a bond’s YTM exceeds its coupon rate, the n, by definition, the bond sells at a discount. Thus, the bond’s price is less than its maturity value. Statement a is false. Consider zero-coupon bonds. A zero-coupon bond’s YTM exceeds its coupon rate (which is equal to zero); however, its current yield is equal to zero which is equal to its coupon rate. Statement c is false; a bond’s value is determined by its cash flows: coupon payments plus principal. If the 2 bonds have different coupon payments, their prices would have to be different in order for them to have the same YTM.
DIF: Tough OBJ: TYPE: Conceptual TOP: Bond concepts
- Which of the following statements is most correct?
a. | All else equal, an increase in interest rates will have a greater effect on the prices of long-term bonds than it will on the prices of short-term bonds. |
b. | All else equal, and increase in interest rate will have a greater effect on higher-coupon bonds than it will have on lower-coupon bonds. |
c. | An increase in interest rates will have a greater effect on a zero-coupon bond with 10 years maturity than it will have on a 9-year bond with a 10 percent annual coupon. |
d. | All of the above are correct. |
e. | Answers a and c are both correct. |
ANS: E
Statements a and c are correct; therefore, statement e is the correct choice. The longer the maturity of a bond, the greater the impact an increase in interest rates will have on the bond’s price. Statement b is false. To see this, assume interest rates increase from 7 percent to 10 percent. Evaluate the change in the prices of a 10-year, 5 percent coupon bond and a 10-year, 12 percent coupon bond. The 5 percent coupon bond’s price decreases by 19.4 percent, while the 12 percent coupon bond’s price decreases by only 16.9 percent. Statement c is correct. To see this, evaluate a 10-year, zero-coupon bond and a 9-year, 10 percent annual coupon bond at 2 different interest rates, say 7 percent and 10 percent. The zero-coupon bond’s price decreases by 24.16 percent, while the 9-year, 10 percent coupon bond’s price decreases by only 16.33 percent.
DIF: Tough OBJ: TYPE: Conceptual TOP: Bond concepts
- Which of the following statements is correct?
a. | A 10-year bond would have more interest rate price risk than a 5-year bond, but all 10-year bonds have the same interest rate price risk. |
b. | A 10-year bond would have more reinvestment rate risk than a 5-year bond, but all 10-year bonds have the same reinvestment rate risk. |
c. | If their maturities were the same, a 5 percent coupon bond would have more interest rate price risk than a 10 percent coupon bond. |
d. | If their maturities were the same, a 5 percent coupon bond would have less interest rate price risk than a 10 percent coupon bond. |
e. | Zero-coupon bonds have more interest rate price risk than any other type bond, even perpetuities. |
ANS: C
Statement c is correct. For example, assume these coupon bonds have 10 years until maturity and the current interest rate is 12 percent. The 5 percent coupon bond’s value is $604.48, while the 10 percent coupon bond’s value is $887.00. Thus, the lower coupon bond has more price risk than the higher coupon bond. The lower the coupon, the greater the percentage of the cash flow that will come in the later years (from the maturity value), hence, the greater the impact of interest rate changes. Statement a is false—as we demonstrated above. Statement b is false—shorter-term bonds have more reinvestment rate risk than longer-term bonds because the principal payment must be reinvested sooner on the shorter-term bond. Statement d is false—as we demonstrated earlier. Statement e is false because perpetuities have no maturity date; therefore, they have more price risk than zero-coupon bonds. The longer a security’s maturity, the greater its price risk.
DIF: Tough OBJ: TYPE: Conceptual TOP: Price vs. reinvestment rate risk
- You have just purchased a 10-year, $1,000 par value bond. The coupon rate on this bond is 8 percent annually, with interest being paid each 6 months. If you expect to earn a 10 percent simple rate of return on this bond, how much did you pay for it?
a. | $1,122.87 |
b. | $1,003.42 |
c. | $875.38 |
d. | $950.75 |
e. | $812.15 |
ANS: C
Financial calculator solution:
Inputs: N = 20; I = 5; PMT = 40; FV = 1,000
Output: PV = -$875.38; V_{d} = $875.38.
DIF: Easy OBJ: TYPE: Problem TOP: Bond value—annual payment
- Assume that you wish to purchase a 20-year bond that has a maturity value of $1,000 and makes semiannual interest payments of $40. If you require a 10 percent simple yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?
a. | $619 |
b. | $674 |
c. | $761 |
d. | $828 |
e. | $902 |
ANS: D
Financial calculator solution:
Inputs: N = 40; I = 5; PMT = 40; FV = 1,000.
Outputs: PV = -$828.41; V_{d} = $828.
DIF: Easy OBJ: TYPE: Problem TOP: Bond value—semiannual payment
- A $1,000 par value bond pays interest of $35 each quarter and will mature in 10 years. If your simple annual required rate of return is 12 percent with quarterly compounding, how much should you be willing to pay for this bond?
a. | $941.36 |
b. | $1,051.25 |
c. | $1,115.57 |
d. | $1,391.00 |
e. | $825.49 |
ANS: C
Financial calculator solution:
Inputs: N = 40; I = 3; PMT = 35; FV = 1,000.
Outputs: PV = -$1,115.57; V_{d} = $1,115.57.
DIF: Easy OBJ: TYPE: Problem TOP: Bond value—quarterly payment
- Assume that a 15-year, $1,000 face value bond pays interest of $37.50 every 3 months. If you require a simple annual rate of return of 12 percent, with quarterly compounding, how much should you be willing to pay for this bond?
a. | $821.92 |
b. | $1,207.57 |
c. | $986.43 |
d. | $1,120.71 |
e. | $1,358.24 |
ANS: B
Financial calculator solution:
Inputs: N = 60; I = 3; PMT = 37.50; FV = 1,000
Output: PV = -$1,207.57; V_{d} = $1,207.57.
Note: Tabular solution differs from calculator solution due to interest factor rounding.
DIF: Medium OBJ: TYPE: Problem TOP: Bond value—quarterly payment
- Due to a number of lawsuits related to toxic wastes, a major chemical manufacturer has recently experienced a market reevaluation. The firm has a bond issue outstanding with 15 years to maturity and a coupon rate of 8 percent, with interest being paid semiannually. The required simple rate on this debt has now risen to 16 percent. What is the current value of this bond?
a. | $1,273 |
b. | $1,000 |
c. | $7,783 |
d. | $550 |
e. | $450 |
ANS: D
Financial calculator solution:
Inputs: N = 30; I = 8; PMT = 40; FV = 1,000.
Output: PV = -$549.69; V_{d} = $549.69 = $550.
DIF: Medium OBJ: TYPE: Problem TOP: Bond value—semiannual payment
- You are the owner of 100 bonds issued by Euler, Ltd. These bonds have 8 years remaining to maturity, an annual coupon payment of $80, and a par value of $1,000. Unfortunately, Euler is on the brink of bankruptcy. The creditors, including yourself, have agreed to a postponement of the next 4 interest payments (otherwise, the next interest payment would have been due in 1 year). The remaining interest payments, for Years 5 through 8, will be made as scheduled. The postponed payments will accrue interest at an annual rate of 6 percent, and they will then be paid as a lump sum at maturity 8 years hence. The required rate of return on these bonds, considering their substantial risk, is now 28 percent. What is the present value of each bond?
a. | $538.21 |
b. | $426.73 |
c. | $384.84 |
d. | $266.88 |
e. | $249.98 |
ANS: D
Numerical solution:
Find the compounded value at Year 8 of the postponed interest payments.
FV_{Deferred interest} | = $80(1.06)^{7} + $80(1.06)^{6} + $80(1.06)^{5} + $80(1.06)^{4} |
| = $441.83 payable at t = 8. |
Now find the value of the bond considering all cash flows
V_{d} | = $80(1/1.28)^{5} + $80(1/1.28)^{6} + $80(1/1.28)^{7} + $80(1/1.28)^{8} + $1,000(1/1.28)^{8} |
| + $441.83(1/1.28)^{8} = $266.86. |
Financial calculator solution:
Calculate FV of deferred interest
Inputs: = 0; = 80; N_{j} = 4; = 0; N_{j} = 4; I = 6.
Output: NFV = $441.828.
Calculate v_{B}, which is the PV of scheduled interest, deferred accrued interest, and maturity value
Inputs: = 0; = 0; N_{j} = 4; = 80; N_{j} = 3; = 1,521.83; I = 28.
Output: NPV = $266.88; V_{d} = $266.88.
Differences in tabular and financial calculator solutions are due to rounding of interest rate table figures.
DIF: Medium OBJ: TYPE: Problem TOP: Bond value
- You are contemplating the purchase of a 20-year bond that pays $50 in interest each six months. You plan to hold this bond for only 10 years, at which time you will sell it in the marketplace. You require a 12 percent annual return, but you believe the market will require only an 8 percent return when you sell the bond 10 years hence. Assuming you are a rational investor, how much should you be willing to pay for the bond today?
a. | $1,126.85 |
b. | $1,081.43 |
c. | $737.50 |
d. | $927.68 |
e. | $856.91 |
ANS: D
Financial calculator solution:
Calculate value of bond at Year 10
Inputs: N = 20; I = 4; PMT = 50; FB = 1,000.
Output: PV = -1,135.90.
Calculate value of bond at Year 0 using V_{10} as FV
Inputs: N = 20; I = 6; PMT = 50; FV = 1,135.90.
Output: PV = -$927.675 = $927.98; V_{d} = $927.68.
DIF: Medium OBJ: TYPE: Problem TOP: Bond value
- JRJ Corporation recently issued 10-year bonds at a price of $1,000. These bonds pay $60 in interest each six months. Their price has remained stable since they were issued, i.e., they still sell for $1,000. Due to additional financing needs, the firm wishes to issue new bonds that would have a maturity of 10 years, a par value of $1,000, and pay $40 in interest every six months. If both bonds have the same yield, how many new bonds must JRJ issue to raise $2,000,000 cash?
a. | 2,400 |
b. | 2,596 |
c. | 3,000 |
d. | 5,000 |
e. | 4,275 |
ANS: B
Number of bonds = $2,000,000 / $770.60 = 2,595.38 = 2,596.
Financial calculator solution:
Inputs: N = 20; I = 6; PMT = 40; FV = 1,000.
Output: PV = -$770.60; V_{d} = $770.60.
Number of bonds: $2,000,000 / $770.60 = 2,596 bonds.^{*}
* Rounded up to next whole bond.
DIF: Medium OBJ: TYPE: Problem TOP: Bond value
- Assume that you are considering the purchase of a $1,000 par value bond that pays interest of $70 each six months and has 10 years to go before it matures. If you buy this bond, you expect to hold it for 5 years and then to sell it in the market. You (and other investors) currently require a simple annual rate of 16 percent, but you expect the market to require a rate of only 12 percent when you sell the bond due to a general decline in interest rates. How much should you be willing to pay for this bond?
a. | $842.00 |
b. | $1,115.81 |
c. | $1,359.26 |
d. | $966.99 |
e. | $731.85 |
ANS: D
Financial calculator solution:
Solve for V_{d} at Time = 5 (V_{5}) with 5 years to maturity.
Inputs: N = 10; I = 6; PMT = 70; FV = 1,000.
Output: PV = $1,073.60.
Solve for V_{d} at Time = 0, assuming sale at V_{d} = $1,073.60.
Inputs: N = 10; I = 8: PMT = 70; FV = 1,073.60.
Output: PV = -$966.99; V_{d} = $966.99.
DIF: Medium OBJ: TYPE: Problem TOP: Bond value
- Cold Boxes Ltd. has 100 bonds outstanding (maturity value = $1,000). The required rate of return on these bonds is currently 10 percent, and interest is paid semiannually. The bonds mature in 5 years, and their current market value is $768 per bond. What is the annual coupon interest rate?
ANS: C
Tabular solution:
$768 = (PVIFA_{5%, 10}) + $1,000 (PVIF_{5%, 10}) = (7.7217) + $1,000 (0.6139)
154.10 = (7.7217)
= $19.96 = $20
PMT » $40 and coupon rate » 4%.
Financial calculator solution:
Inputs: N = 10; I = 5; PV = -768; FV = 1,000.
Output: PMT = $19,955 (semi-annual PMT).
Annual coupon rate = PMT ´ 2/M = $19,955 ´ 2/1,000 = 3.99% = 4%.
DIF: Medium OBJ: TYPE: Problem TOP: Bond coupon rate
- The current price of a 10-year, $1,000 par value bond is $1,158.91. Interest on this bond is paid every six months, and the simple annual yield is 14 percent. Given these facts, what is the annual coupon rate on this bond?
a. | 10% |
b. | 12% |
c. | 14% |
d. | 17% |
e. | 21% |
ANS: D
Financial calculator solution:
Inputs: N = 20; I = 7; PV = -1,158.91; FV = 1,000.
Output: PMT = $85.00 (Semiannual PMT).
Annual coupon rate = $85 (2) / $1,000 = 17.0%.
DIF: Medium OBJ: TYPE: Problem TOP: Bond coupon rate
- Rick bought a bond when it was issued by Macroflex Corporation 14 years ago. The bond, which has a $1,000 face value and a coupon rate equal to 10 percent, matures in six years. Interest is paid every six months; the next interest payment is scheduled for six months from today. If the yield on similar risk investments is 14 percent, what is the current market value (price) of the bond?
a. | $841.15 |
b. | $1,238.28 |
c. | $904.67 |
d. | $757.26 |
e. | $844.45 |
ANS: A DIF: Medium OBJ: TYPE: Problem
TOP: Bond value—semiannual payment
- Devine Divots issued a bond a few years ago that has a face value equal to $1,000 and pays investors $30 interest every six months. The bond has eight years remaining until maturity. If you require a 7 percent rate of return to invest in this bond, what is the maximum price you should be willing to pay to purchase the bond?
a. | $761.15 |
b. | $939.53 |
c. | $940.29 |
d. | $965.63 |
e. | $1,062.81 |
ANS: B DIF: Medium OBJ: TYPE: Problem
TOP: Bond value—semiannual payment
- Recently, Ohio Hospitals Inc. filed for bankruptcy. The firm was reorganized as American Hospitals Inc., and the court permitted a new indenture on an outstanding bond issue to be put into effect. The issue has 10 years to maturity and a coupon rate of 10 percent, paid annually. The new agreement allows the firm to pay no interest for 5 years. Then, interest payments will be resumed for the next 5 years. Finally, at maturity (Year 10), the principal plus the interest that was not paid during the first 5 years will be paid. However, no interest will be paid on the deferred interest. If the required return is 20 percent, what should the bonds sell for in the market today?
a. | $242.26 |
b. | $281.69 |
c. | $578.31 |
d. | $362.44 |
e. | $813.69 |
ANS: D
Financial calculator solution:
Method1. | Cash flows: |
| Inputs: CF_{0} = 1; CF_{1} = 0; N = 5; CF_{2} = 100; N_{j} = 4; CF_{5} = 1,600; I = 20. |
| Output: NPV = $362.44. V_{d} = $362.44. |
| |
Method2. | Time value discounting: (Calculate V_{d} as of Year 5, V_{5}) |
| Inputs: N = 5; I = 20; PMT = 100; FV = 1,500. |
| Output: PV_{5} = -$901.878. |
Calculate V_{d} or PV of V_{5}
Inputs: N = 5; I = 20; FV = 901.878.
Output: PV = -$362.44. V_{d} = $362.44.
DIF: Tough OBJ: TYPE: Problem TOP: Bond value
Financial Calculator Section
The following question(s) may require the use of a financial calculator.
- Trickle Corporation’s 12 percent coupon rate, semiannual payment, $1,000 par value bonds which mature in 25 years. The bonds currently sell for $1,230.51 in the market, and the yield curve is flat. Assuming that the yield curve is expected to remain flat, what is Trickle’s most likely before-tax cost of debt if it issues new bonds today?
a. | 4.78% |
b. | 6.46% |
c. | 7.70% |
d. | 9.56% |
e. | 12.92% |
ANS: D
Financial calculator solution:
Inputs: N = 50; PV = -1,230.51; PMT = 60; FV = 1,000
Outputs: I = 4.78 periodic rate (semiannual).
The simple annual rate equals 2 ´ 4.78% = 9.56%. Thus, the before-tax cost of debt is 9.56%.
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Bond valuation
- Leyland Enterprises has $5,000,000 in bonds outstanding. The bonds each have a maturity value of $1,000, an annual coupon of 12 percent, and 15 years left until maturity. The bonds can be called at any time at a call price of $1,100 per bond. If the bonds are called, the company must pay flotation costs of $50,000 ($10 for every $1,000 of bonds outstanding). Ignore tax considerations. Assume that the tax rate is zero. The company’s decision whether to call the bonds depends critically on the current interest rate it would pay on new bonds issued. What is the breakeven interest rate, below which it is profitable to call in the bonds?
a. | 10.51% |
b. | 11.21% |
c. | 12.57% |
d. | 13.33% |
e. | 14.89% |
ANS: A
Step 1: | Find present value of costs to call the issue: |
| |
| PV = Call Price + Flotation Costs |
| = $5,500,000 + $50,000 = $5,550,000 |
| |
Step 2: | Find the IRR which equates the PV of the calling costs to the PV of not calling. This is the breakeven interest rate. |
| |
| |
| |
| With a financial calculator input the following: |
| = -5,550,000 |
| = 600,000 |
| = 5,600,000 |
| Solve for IRR = 10.51%. |
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Refunding
- S. Delay Corporation, a subsidiary of the Postal Service, must decide whether to issue zero coupon bonds or quarterly payment bonds to fund construction of new facilities. The 1,000 par value quarterly payment bonds would sell at $795.54, have a 10 percent annual coupon rate, and mature in ten years. At what price would the zero coupon bonds with a maturity of 10 years have to sell to earn the same effective annual rate as the quarterly payment bonds?
a. | $274.50 |
b. | $271.99 |
c. | $198.89 |
d. | $257.52 |
e. | $254.84 |
ANS: D
Financial calculator solution:
Calculate simple periodic and annual interest rates
Inputs: N = 40; PV = -795.54; PMT = 25; FV = 1,000
Output: I = 3.45% per period
K_{nominal} = 4 ´ 3.45 = 13.80%
Calculate EAR using interest rate conversion feature
Inputs: P/YR = 4; NOM% = 13.80.
Output: EFF% = 14.53%
Calculate PV of zero coupon bond using EAR
Inputs: N = 10; I = 14.53; PMT = 0; FV = 1,000.
Output: PV = -257.518 -$257.52. V_{d} = $257.52.
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Zero coupon and EAR
- A 15-year zero coupon bond has a yield to maturity of 8 percent and a maturity value of $1,000. What is the amount of tax that an investor in the 30 percent tax bracket would pay during the first year of owning the bond?
a. | $7.57 |
b. | $10.41 |
c. | $15.89 |
d. | $20.44 |
e. | $25.22 |
ANS: A
Step 1: | Find PV of bond: |
| |
| N = 15 |
| I = 8 |
| PMT = 0 |
| FV = 1,000 |
| Solve for PV = -315.24. |
| |
Step 2: | Find interest for the first year: |
| | | |
| Value at t=0 | $315.24 | |
| Interest rate | ´ 0.08 | |
| Interest income | $ 25.22 | |
| |
Step 3: | Find tax due: |
| | | |
| Interest income | $25.22 | |
| Tax rate | ´ 0.30 | |
| Tax due | $ 7.57 | |
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Zero coupon bonds
- Two years ago, Targeau Corporation issued BBB rated bonds and the risk premium was 2.42 percentage points as marked up on long-term S. government bonds. The firm’s bonds had a 10-year maturity, were semiannual payment 9 percent coupon bonds with a $1,000 par value, and were originally priced at $973.17. Currently, Targeau’s BBB-rated bonds have 8 years to maturity and are priced at $1,070.43. The current risk premium on BBB rated bonds is 1.3 percentage points. By how many percentage points did the long-term government bond rates change in two years?
a. | -0.38% |
b. | -1.12% |
c. | -0.62% |
d. | -0.50% |
e. | -1.50% |
ANS: D
Financial calculator solution:
Calculate the YTM on the BBB bonds when they were issued:
Inputs: N = 20; PV = -973.17; PMT = 45; FV = 1,000.
Output: I = 4.71 semiannual; annual rate = 2(4.71%) = 9.42%.
Calculate the rate on U.S. government bonds:
U.S. government bond rate | = Targeau’s BBB bonds – RP_{BBB} |
| = 9.42% – 2.42% = 7.00%. |
Calculate the YTM today on the BBB bonds:
Inputs: N = 16; PV = -1,070.43; PMT = 45; FV = 1,000.
Output: I = 3.90 semiannual; annual rate = 2(3.90%) = 7.80%.
Calculate the current U.S. government bond rate and the change from two years ago:
Current U.S. government bond rate | = 7.80% – 1.3% = 6.50%. |
Change in U.S. government bond rate | = 6.50% – 7.00% |
| = -0.50 percentage points. |
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Changes in risk premiums
- Semiannual payment bonds with the same risk (Aaa) and maturity (20 years) as your company’s bonds have a simple (not EAR) yield of 9 percent. Your company’s treasurer is thinking of issuing at par some $1,000 par value, 20-year, quarterly payment She has asked you to determine what quarterly interest payment, in dollars, the company would have to set in order to provide the same effective annual rate (EAR) as those on the 20-year, semiannual payment bonds. What would the quarterly interest payment be, in dollars?
a. | $45.00 |
b. | $25.00 |
c. | $22.25 |
d. | $27.50 |
e. | $23.00 |
ANS: C
Cash flow time lines:
Numerical solution:
Step 1: | Solve for the EAR of 9% simple compounded semiannually. |
| |
| |
| |
Step 2: | Solve for k_{Simple} of 9.2025% EAR but with quarterly compounding. |
| |
| |
| k_{Simple}/4 = (1.092025)^{0.25} – 1 = 0.02225. |
| k_{Simple} = 0.02225 ´ 4 = 0.08901. |
| |
Step 3: | Calculate the quarterly payment using the periodic rate. |
| |
| Multiple 0.02225 ´ $1,000 = $22.25 = quarterly payment |
Financial calculator solution:
Step 1: | Calculate the EAR of 9% simple yield bond compounded semi-annually. Use interest rate conversion feature. |
| |
| Inputs: P/YR = 2; NOM% = 9. |
| Output: EFF% = 9.2025% |
| |
Step 2: | Calculate the simple rate, k_{Simple}, of a 9.2025% EAR but with quarterly compounding. |
| |
| Inputs: P/YR = 4; EFF% = 9.2025. |
| Output: NOM% = 8.90% |
| |
Step 3: | Calculate the quarterly periodic rate from k_{Simple} of 8.9% and calculate the quarterly payment. |
| |
| k_{Per} = k_{Simple}/4 = 8.90%/4 = 2.225% |
| Inputs: N = 80; I = 2.225; PV = -1,000; FV = 1,000. |
| Output: PMT = $22.25. |
DIF: Tough OBJ: TYPE: Financial Calculator
TOP: Bonds with differential payments
- Assume that the State of Florida sold tax-exempt, zero coupon bonds with a $1,000 maturity value 5 years ago. The bonds had a 25-year maturity when they were issued, and the interest rate built into the issue was 8 percent, compounded semiannually. The bonds are now callable at a premium of 4 percent over the accrued value. What effective annual rate of return would an investor who bought the bonds when they were issued and who still owns them earn if they were called today?
a. | 4.41% |
b. | 6.73% |
c. | 8.25% |
d. | 9.01% |
e. | 9.52% |
ANS: D
Calculate PV of zero coupon bond at Time 0:
N = 50; I = 4; PMT = 0; and FV = 1,000.
Solve for PV = $140.71.
Calculate accrued value at Year 5:
$140.71(1.04)^{2(5)} = $208.29.
Calculate EAR as follows:
N = 10; PV = -140.71; PMT = 0; and FV = 216.62.
Solve for I = 4.41%; however, this is a semiannual rate.
EAR = (1.0441)^{2} – 1 = 9.01%.
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Zero coupon bonds
Gargoyle Unlimited
Gargoyle Unlimited is planning to issue a zero coupon bond to fund a project that will yield its first positive cash flow in three years. That cash flow will be sufficient to pay off the entire debt issue. The bond’s par value will be $1,000, it will mature in 3 years, and it will sell in the market for $727.25. The firm’s marginal tax rate is 40 percent.
- Refer to Gargoyle Unlimited. What is the dollar value of the interest tax savings to the firm in the third year of the issue?
a. | $32.58 |
b. | $40.29 |
c. | $100.72 |
d. | $60.43 |
e. | $109.10 |
ANS: B
Cash flow time line:
Financial calculator solution:
Inputs: N = 3; PV = 727.25; FV = -1,000. Output: I = 11.20%.
| 0 | 1 | 2 | 3 |
1) Accrued value | 727.25 | 808.70 | 899.28 | 1,000.00 |
2) Interest expense | | 81.45 | 90.58 | 100.72 |
3) Tax savings (line 2 ´ 0.40) | | 32.58 | 36.23 | 40.29 |
| | | | +40.29 |
| | | | -1,000.00 |
4) Cash flows | +727.25 | +32.58 | +36.23 | -959.71 |
DIF: Tough OBJ: TYPE: Financial Calculator
TOP: Zero coupon interest tax shield
- Refer to Gargoyle Unlimited. What is the expected after-tax cost of this debt issue?
a. | 11.20% |
b. | 4.48% |
c. | 6.72% |
d. | 6.10% |
e. | 4.00% |
ANS: C
Financial calculator solution:
Solve for YTM using the information from the previous question
Inputs: N = 3; PV = +727.25; FV = -1,000
Output: I = 11.20.
Before-tax cost debt of this issue = 11.20%
k_{dT} = 11.20% (1-T) = 11.2% (0.6) = 6.72%
Alternate solution using cash flows
Inputs: = 727.25; = 32.58; = 36.23; = -959.71
Output: IRR% = 6.72%.
DIF: Medium OBJ: TYPE: Financial Calculator TOP: After-tax cost of debt
- You are offered a $1,000 par value bond which has a stepped-up coupon interest rate. The annual coupon rate is 10 percent coupon, payable semiannually ($50 each 6 months) for the first 15 years, and then the annual coupon increases to 13 percent, also payable semiannually, for the next 15 years. The first interest payment will be made 6 months from today, and the $1,000 principal amount will be returned at the end of Year 30. You currently have savings in an account which is earning a 9 percent simple rate, but with quarterly compounding; this is your opportunity cost for purposes of analyzing the bond. What is the value of the bond to you today?
a. | $1,614.53 |
b. | $1,419.18 |
c. | $1,306.21 |
d. | $1,250.25 |
e. | $1,155.98 |
ANS: E
Financial calculator solution:
Step 1 | Calculate the semiannual effective rate on the 9% account. We must discount the semiannual payment bond with a semiannual effective rate. Match the semiannual payment period with a semiannual rate, using the interest rate conversion feature: |
| |
| Inputs: NOM% = 9.0/2 = 4.5%; P/YR = 2. Output: EFF% = 4.55%. |
| |
Step 2 | Use the semiannual effective rate to discount the bond cash flows: |
| Inputs: = 0; = 50; N_{j} = 30; = 65; N_{j} = 29; = 1065; I = 4.55. |
| Output: NPV = $1,155.98 = V_{d}. |
| |
| The value of the stepped-up coupon bond is $1,155.98. |
DIF: Tough OBJ: TYPE: Problem TOP: Bond value
- Tony’s Pizzeria plans to issue bonds with a par value of $1,000 and 10 years to maturity. These bonds will pay $45 interest every 6 months. Current market conditions are such that the bonds will be sold to net $937.79. What is the YTM of the issue as a broker would quote it to an investor?
ANS: B
Financial calculator solution:
Inputs: N = 20; PV = -937.79; PMT = 45; FV = 1,000
Output: I = 5.0% per period. k_{d} = YTM = 5.0% ´ 2 periods = 10%
DIF: Easy OBJ: TYPE: Financial Calculator TOP: Yield to maturity
- The current market price of Smith Corporation’s 10 percent, 10-year bonds is $1,297.58. A 10 percent coupon interest rate is paid semiannually, and the par value is equal to $1,000. What is the YTM (stated on a simple, or annual, basis) if the bonds mature 10 years from today?
ANS: B
Financial calculator solution:
Inputs: N = 20; PV = -1,297.58; PMT = 50; FV = 1,000
Output: I = 3.0% per period. k_{d} = YTM = 3.0% ´ 2 periods = 6%
DIF: Easy OBJ: TYPE: Financial Calculator TOP: Yield to maturity
- A $1,000 par value bond sells for $1,216. It matures in 20 years, has a 14 percent coupon, pays interest semiannually, and can be called in 5 years at a price of $1,100. What is the bond’s YTM?
a. | 6.05% |
b. | 10.00% |
c. | 10.06% |
d. | 8.59% |
e. | 11.26% |
ANS: E
Financial calculator solution:
Inputs: N = 40; PV = -1,216; PMT = 70; FV = 1,000
Output: I = 5.6307 » 5.63% = k_{d/2}. YTM 5.63% ´ 2 = 11.26%
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Yield to maturity
- You have just been offered a $1,000 par value bond for $847.88. The coupon rate is 8 percent, payable annually, and interest rates on new issues of the same degree of risk are 10 percent. You want to know how many more interest payments you will receive, but the party selling the bond cannot remember. Can you determine how many interest payments remain?
ANS: B
Financial calculator solution:
Inputs: I = 10; PV = -$847.88; PMT = 80. FV = 1,000
Output: N = 15 Years.
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Interest payments remaining
- Assume that McDonald’s and Burger King have similar $1,000 par value bond issues outstanding. The bonds are equally risky. The Burger King bond has interest payments of $80 paid annually and matures 20 years from today. The McDonald’s bond has interest payments of $80 paid semiannually, and it also matures in 20 years. If the simple required rate of return, k_{d}, is 12 percent, semiannual basis, for both bonds, what is the difference in current market prices of the two bonds?
a. | No difference. |
b. | $2.20 |
c. | $3.77 |
d. | $17.53 |
e. | $6.28 |
ANS: D
Financial calculator section:
Burger King V_{d}
Calculate EAR to apply to Burger King bonds using interest rate conversion feature, and calculate the value V_{BK}, of Burger King bonds:
Inputs: P/YR = 2; NOM% = 12. Output: EFF% = EAR = 12.36%
Inputs: N = 20; I = 12.36; PMT = 80; FV = 1,000. Output: PV = -$681.54
McDonalds
Inputs: N = 40; I = 6; PMT = 40; FV = 1.000
Output: PV = $699.07
Calculate the difference between the two bonds’ PVs
Difference: V_{d(McD)} – V_{d(BK)} = 699.07 – 681.54 = $17.53
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Bond value
- An 8 percent annual coupon, noncallable bond has ten years until it matures and a yield to maturity of 9.1 percent. What should be the price of a 10-year bond of equal risk which pays an 8 percent semiannual coupon? Assume both bonds have a maturity value of $1,000.
a. | $898.64 |
b. | $736.86 |
c. | $854.27 |
d. | $941.08 |
e. | $964.23 |
ANS: D
Step 1: | Determine the interest rate to use in order to evaluate the semiannual bond’s price: |
| |
| In order for the 2 bonds to be of equal risk, their effective YTM must be equal. The annual bond’s nominal YTM = effective YTM = 9.1%. Thus, we need to calculate the semiannual bond’s nominal YTM. |
| |
| With a financial calculator: |
| EFF% = 9.1 |
| P/YR = 2 |
| Solve for NOM% = 8.9019%. |
| |
| Note that this is stated on an annual basis. To convert to a semiannual basis divide it by 2: |
| 8.9019%/2 = 4.451%. |
| |
Step 2: | Calculate the semiannual bond’s price: |
| |
| N = 20 |
| I = 4.451 |
| PMT = 40 |
| FV = 1,000 |
| Solve for PV = $941.08. |
DIF: Tough OBJ: TYPE: Financial Calculator
TOP: Bond value—semiannual payment
- Fish & Chips Inc. has two bond issues outstanding, and both sell for $701.22. The first issue has a coupon rate of 8 percent and 20 years to maturity. The second has an identical yield to maturity as the first bond, but only 5 years until maturity. Both issues pay interest annually. What is the annual interest payment on the second issue?
a. | $120.00 |
b. | $37.12 |
c. | $56.42 |
d. | $29.68 |
e. | $11.16 |
ANS: B
Financial calculator solution:
Calculate YTM or k_{d} for first issue
Inputs: N = 20; PV = -701.22; PMT = 80; FV = 1,000. Output: I = 12%
Calculate PMT on second issue using 12% = k_{d} = YTM
Inputs: N = 20; PV = -701.22; FV = 1,000
Output: PMT = $37.116 » $37.12
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Bond interest payments
- A two-year zero-coupon Treasury bond with a maturity value of $1,000 has a price of $873.4387. A one-year zero-coupon Treasury bond with a maturity value of $1,000 has a price of $938.9671. If the pure expectations theory is correct, for what price should one-year zero-coupon Treasury bonds sell one year from now?
a. | $798.89 |
b. | $824.66 |
c. | $852.28 |
d. | $930.23 |
e. | $989.11 |
ANS: D
First find the yields on one-year and two-year zero-coupon bonds, so you can find the implied rate on a one-year bond, one year from now. Then use this implied rate to find its price.
1-year | 2-year |
N = | 1 | N = | 2 |
PV = | -938.9671 | PV = | -873.4387 |
PMT = | 0 | PMT = | 0 |
FV = | 1,000 | FV = | 1,000 |
Solve for I = | 6.5% | Solve for I = | 7.0% |
Therefore, if the implied rate = ´
Now find the price of a 1-year zero, 1 year from now:
N | = 1 |
I | = 7.5 |
PMT | = 0 |
FV | = 1,000 |
Solve for PV | = $930.23. |
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Zeros and expectations theory
- A four-year, zero-coupon Treasury bond sells at a price of $762.8952. A three-year, zero-coupon Treasury bond sells at a price of $827.8491. Assuming the pure expectations theory is correct, what does the market believe the price of one-year, zero-coupon bonds will be in three years?
a. | $921.66 |
b. | $934.58 |
c. | $938.97 |
d. | $945.26 |
e. | $950.47 |
ANS: A
Step 1 | Calculate the YTM for the 3-year zero: |
| | | |
| N = | 3 | |
| PV = | -827.8491 | |
| PMT = | 0 | |
| FV = | 1,000 | |
| Solve for I = | 6.5% | |
| |
Step 2 | Calculate the YTM for the 4-year zero: |
| | | |
| N = | 4 | |
| PV = | -762.8952 | |
| PMT = | 0 | |
| FV = | 1,000 | |
| Solve for I = | 7% | |
| |
Step 3 | Calculate the interest rate on a 1-year zero, 3 years from now: |
| |
| |
| ´ = 8.5%. |
| |
Step 4 | Calculate the price of a 1-year zero 3 years from now: |
| | | |
| N = | 1 | |
| I = | 8.5 | |
| PMT = | 0 | |
| FV = | 1,000 | |
| Solve for PV = | $921.66. | |
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Zeros and expectations theory
Chapter 7— Stocks (Equity) —Characteristics and Valuation
TRUE/FALSE
- American depository receipts (ADRs) are foreign stocks listed on a domestic exchange.
ANS: F DIF: Easy TOP: American depository receipts
- Founders’ shares is a type of classified stock where the shares are owned by the firm’s founders and they retain the sole voting rights to those shares but have restricted dividends for a specified time period.
ANS: T DIF: Easy TOP: Founders shares
- A publicly owned corporation is simply a company whose shares are held by the investing public, which may include other corporations and institutions.
ANS: T DIF: Easy TOP: Public company
- After a new issue is brought to market it is the marginal investor who determines the price at which the stock will trade.
ANS: T DIF: Easy TOP: Marginal investor and price
- A stock’s par value is equal to the market value of the stock on the last day of the fiscal year for a firm.
ANS: F DIF: Easy TOP: Par value
- The book value per share is computed by taking the sum of common stock, additional paid in capital, and retained earnings and dividing the number by the number of shares outstanding.
ANS: T DIF: Easy TOP: Book value per share
- A proxy fight is an attempt by a group to gain control of a firm by convincing its stockholders to give the group the authority to vote their shares in order to elect a new management team.
ANS: T DIF: Easy TOP: Proxy fight
- A preemptive right is a provision in the corporate charter or by laws that gives common stockholders the right to purchase on a pro rata basis new issues of common stock.
ANS: T DIF: Easy TOP: Preemptive right
- Preemptive rights are important to stockholders because they provide protection against a dilution of value when new shares are issued.
ANS: T DIF: Easy TOP: Preemptive right
- One advantage of using common stock as a source of funds is that common stock does not legally obligate the firm to make payments to stockholders.
ANS: T DIF: Easy TOP: Common equity
- One advantage of common stock as a source of funds is that the underwriting and distribution costs of common stock are usually much lower than those for debt.
ANS: F DIF: Easy TOP: Common equity
- From a social welfare perspective, common stock is a desirable form of financing in part because it involves no fixed charge payments. Its inclusion in a firm’s capital structure makes the firm less vulnerable to the consequences of unanticipated declines in sales and earnings than if only debt were available.
ANS: T DIF: Medium TOP: Common stock and social welfare
- When a firm issues new equity, market pressure applies first to the new shares issued and then to existing shares. Subsequent to the new issue, the value of the new shares will rise to the equilibrium price of the old shares.
ANS: F DIF: Medium TOP: Market pressure
- When management controls more than 50% of the shares of the firm, they must be concerned with the potential of a proxy fights than can lead to takeovers of the firm and the replacement of management.
ANS: F DIF: Medium TOP: Takeover
- The constant growth model used for evaluating the price of a share of common stock can also be used to find the price of perpetual preferred stock or any other perpetuity.
ANS: T DIF: Easy TOP: Constant growth stock
- According to the textbook model, under conditions of nonconstant growth, the discount rate utilized to find the present value of the expected cash flows will be the same for the initial growth period as for the normal growth period.
ANS: T DIF: Easy TOP: Supernormal growth stock
- According to the basic stock valuation model, the value an investor assigns to a share of stock is dependent upon the length of time the investor plans to hold the stock.
ANS: F DIF: Easy TOP: Stock valuation
- Other things held constant, P/E ratios are higher for firms with high growth prospects. At the same time, P/E’s are lower for riskier firms, other things held constant. These two factors, growth prospects and riskiness, may either be offsetting or reinforcing as P/E determinants.
ANS: T DIF: Medium TOP: Risk and P/E ratios
MULTIPLE CHOICE
- The net income that firm earns can either be paid out to shareholders as __________ or can be reinvested in the company as __________.
a. | interest; additional paid-in capital |
b. | dividends; retained earnings |
c. | shares; capital stock. |
d. | capital gains; additional paid-in capital |
e. | interest; retained earnings |
ANS: B DIF: Easy OBJ: TYPE: Conceptual
TOP: Retained earnings
- In international markets, excluding stocks sold in the United States, what is any stock that is traded in a country other than the issuing company’s home country called?
a. | ADRs |
b. | Yankee stock |
c. | Euro stock |
d. | Class A stock |
e. | Preferred stock |
ANS: C DIF: Easy OBJ: TYPE: Conceptual
TOP: Euro stock
- Shareholders exert control of the management of the firm by
a. | electing board members who can replace management. |
b. | directly replacing management with themselves. |
c. | buying shares in an IPO at a discounted price. |
d. | running the daily operations of the firm. |
e. | None of the above. |
ANS: A DIF: Easy OBJ: TYPE: Conceptual
TOP: Control of the firm
- Stock owned by the organizers of the firm who have sole voting rights is
a. | preferred stock. |
b. | common equity. |
c. | founders’ shares. |
d. | convertible equity. |
e. | retained earnings. |
ANS: C DIF: Easy OBJ: TYPE: Conceptual TOP: Classes of stock
- Certificates representing ownership in stocks of foreign companies, which are held in a trust bank located in the country the stock is traded are called __________.
a. | Certificates of Ownership |
b. | Foreign Stock Funds |
c. | Mutual Funds |
d. | American Depository Receipts |
e. | Investment Bankers |
ANS: D DIF: Easy OBJ: TYPE: Conceptual TOP: ADRs
- Velcraft Company has 20,000,000 shares of common stock authorized, but to date, has only 12,000,000 shares outstanding, each with a $1.00 par value. The company has $24,000,000 in additional paid-in capital and retained earnings are $96,000,000. What is Velcraft’s current book value per share?
a. | $1.00 |
b. | $3.00 |
c. | $11.00 |
d. | $6.60 |
e. | $9.00 |
ANS: C
Construct a summary of the common stockholders’ equity accounts:
| Account balance |
Common stock (20 million authorized, 12 million | |
outstanding, $1.00 par value) | $ 12,000,000 |
Additional paid-in capital | 24,000,000 |
Retained earnings | 96,000,000 |
Total common stockholders’ equity | $132,000,000 |
Calculate the book value per share:
Book value per share = $132,000,000/12,000,000 = $11.00.
DIF: Easy OBJ: TYPE: Problem TOP: Book value per share
- Blow Glass Corporation has 100,000 shares of stock outstanding, each with a par value of $2.50 per share. Blow Glass also has another 400,000 shares of stock that are shelf registered. Blow Glass has retained earnings of $9,000,000 and additional paid-in capital of $1,000,000. What is Blow Glass’s book value per share?
a. | $90.00 |
b. | $100.00 |
c. | $27.50 |
d. | $102.50 |
e. | $92.50 |
ANS: D
Common stock | $ 250,000 |
Additional paid-in capital | 1,000,000 |
Retained earnings | 9,000,000 |
Total common stockholder’s equity | 10,250,000 |
Book value per share | $10,250,000/100,000 = $102.50 |
DIF: Easy OBJ: TYPE: Problem TOP: Book value per share
- Scubapro Corporation currently has 500,000 shares outstanding and plans to issue 200,000 more shares in a seasoned equity offering. The current shareholders have preemptive rights on any new issue of stock by Scubapro Corporation. An investor with 20,000 shares who exercises his preemptive rights on the new stock issue will have the right to buy how many stocks?
a. | 200,000 shares |
b. | 120,000 shares |
c. | 80,000 shares |
d. | 12,000 shares |
e. | 8,000 shares |
ANS: E
Percent ownership | 200,000/500,000 = 40% |
Preemptive right shares | 40%*(20,000) = 8,000 shares |
DIF: Easy OBJ: TYPE: Problem TOP: Preemptive right
- Micromain Company has 10,000,000 shares of common stock authorized and 8,000,000 shares outstanding, each with a $1.00 par value. The firm’s additional paid-in capital account has a balance of $18,000,000. The previous year’s retained earnings account was $124,000,000. In the year just ended, Micromain generated net income of $16,000,000 and the firm has a dividend payout ratio of 40 percent. What will Micromain’s book value per share be when based on the final year-end balance sheet?
a. | $20.75 |
b. | $15.00 |
c. | $15.96 |
d. | $19.95 |
e. | $18.75 |
ANS: D
Construct a summary of the common stockholders’ equity accounts:
(In millions) | This Year | Last Year |
Common stock (10 million authorized, 8 | | |
million outstanding, $1.00 par value) | $ 8.0 | $ 8.0 |
Additional paid-in capital | 18.0 | 18.0 |
Retained earnings | 133.6 | 124.0 |
Total common stockholders’ equity | $159.6 | $150.0 |
Addition to RE = $16,000,000 – 0.40($16,000,000) = $9,600,000.
Calculate the book value per share:
Book value per share = $159.6/8 million shares = $19.95.
DIF: Medium OBJ: TYPE: Problem TOP: Book value per share
- Nahanni Treasures Corporation is planning a new common stock issue of five million shares to fund a new project. The increase in shares will bring to 25 million the number of shares outstanding. Nahanni’s long-term growth rate is 6 percent, and its current required rate of return is 12.6 percent. The firm just paid a $1.00 dividend and the stock sells for $16.06 in the market. On the announcement of the new equity issue, the firm’s stock price dropped. Nahanni estimates that the company’s growth rate will increase to 6.5 percent with the new project, but since the project is riskier than average, the firm’s cost of capital will increase to 13.5 percent. Using the DDM constant growth model, what is the change in the equilibrium stock price?
a. | -$1.77 |
b. | -$1.06 |
c. | -$0.85 |
d. | -$0.66 |
e. | -$0.08 |
ANS: C
Calculate new equilibrium price and determine change:
P_{0,old }=
P_{0,onew }=
Change in price = $16.06 – $15.21 = $0.85
DIF: Medium OBJ: TYPE: Problem TOP: New equity and equilibrium price
- Mesmer Analytic, a biotechnology firm, floated an initial public offering of 2,000,000 shares at a price of $5.00 per share. The firm’s owner/managers held 60 percent of the company’s $1.00 par value authorized and issued stock following the public offering. One month after the IPO, the firm’s board of directors declared a one-time dividend of $0.50 per share payable to all stockholders, meaning that the owner/managers would receive an immediate dividend, in part out of the pockets of the new public stockholders. What was the book value per share of the firm before and after the special dividend was paid?
a. | $2.60; $2.10 |
b. | $2.60; $2.60 |
c. | $2.60; $2.30 |
d. | $1.60; $1.10 |
e. | $1.60; $1.00 |
ANS: A
Calculate the total shares and amount of the special dividend:
Total shares = 2,000,000/(1 – 0.6) = 5,000,000.
Special dividend = 5,000,000 shares ´ $0.50 = $2,500,000.
Construct summary of common equity accounts:
Par value (5,000,000 shares ´ $1.00) | $ 5,000,000 |
Additional paid-in capital | |
(2,000,000 ´ ($5 – $1)) | 8,000,000 |
Retained earnings (new issue) | 0 |
Total stockholders’ equity | $13,000,000 |
Less special dividend | (2,500,000) |
Total stockholders’ equity | |
after special dividend | $10,500,000 |
Book value per share_{Before} = $13,000,000/5,000,000 shares = $2.60.
Book value per share_{After} = $10,500,000/5,000,000 shares = $2.10.
DIF: Medium OBJ: TYPE: Problem TOP: IPO and special dividend
- Assuming g will remain constant, the dividend yield is a good measure of the required return on a common stock under which of the following circumstances?
a. | g = 0 |
b. | g > 0 |
c. | g < 0 |
d. | Under no circumstances. |
e. | Answers a and b are both correct. |
ANS: A DIF: Easy OBJ: TYPE: Conceptual
TOP: Dividend yield and g
- If the expected rate of return on a stock exceeds the required rate,
a. | The stock is experiencing supernormal growth. |
b. | The stock should be sold. |
c. | The company is probably not trying to maximize price per share. |
d. | The stock is a good buy. |
e. | Dividends are not being declared. |
ANS: D DIF: Easy OBJ: TYPE: Conceptual TOP: Required return
- Which of the following statements is correct?
a. | The constant growth DDM model can be used to value a stock only if the stock’s dividends are expected to grow forever at a constant rate which is less than the required rate of return on the stock. |
b. | If the growth rate is negative, the constant growth DDM model cannot be used. |
c. | The constant growth DDM model may be written as r_{0} = D_{0}/P_{0} + g. |
d. | The constant growth DDM model may be written as P_{0} = D_{0}/(r + g). |
e. | The constant growth DDM model may be written as P_{0} = D_{0}/(r – g). |
ANS: A
Statement a is the condition necessary for the constant growth model. All the other statements are false.
DIF: Easy OBJ: TYPE: Conceptual TOP: Constant growth model
- Alpha’s preferred stock currently has a market price equal to $80 per share. If the dividend paid on this stock is $6 per share, what is the required rate of return investors are demanding from Alpha’s preferred stock?
a. | 7.5% |
b. | 13.3% |
c. | 6.0% |
d. | $6.00 |
e. | None of the above is a correct answer. |
ANS: A DIF: Easy OBJ: TYPE: Conceptual TOP: Stock valuation
- Manners Catering (MMC) has paid a constant $1.50 per share dividend to its common stockholders for the past 25 years. MMC expects to continue this policy for the next two years, and then begin to increase the dividend at a constant rate equal to 2 percent per year into perpetuity. Investors require a 12 percent rate of return to purchase MMC’s common stock. What is the market value of MMC’s common stock?
a. | $14.73 |
b. | $15.00 |
c. | $15.58 |
d. | $15.30 |
e. | $12.20 |
ANS: A DIF: Medium OBJ: TYPE: Conceptual
TOP: Nonconstant growth stock
- A share of perpetual preferred stock pays an annual dividend of $6 per share. If investors require a 12 percent rate of return, what should be the price of this preferred stock?
a. | $57.25 |
b. | $50.00 |
c. | $62.38 |
d. | $46.75 |
e. | $41.64 |
ANS: B
V_{ps} = D_{ps}/r_{ps} = $6/0.12 = $50.
DIF: Easy OBJ: TYPE: Problem TOP: Preferred stock value
- A share of preferred stock pays a quarterly dividend of $2.50. If the price of this preferred stock is currently $50, what is the simple annual rate of return?
a. | 12% |
b. | 18% |
c. | 20% |
d. | 23% |
e. | 28% |
ANS: C
Annual dividend = $2.50(4) = $10.
r_{ps} = D_{ps}/V_{ps} = $10/$50 = 0.20 = 20%.
DIF: Easy OBJ: TYPE: Problem TOP: Preferred stock yield
- A share of preferred stock pays a dividend of $0.50 each quarter. If you are willing to pay $20.00 for this preferred stock, what is your simple (not effective) annual rate of return?
ANS: A
Yearly dividend = $0.50(4) = $2.00.
r_{ps} = D_{ps}/V_{ps} = $2.00/$20.00 = 0.10 = 10%.
DIF: Easy OBJ: TYPE: Problem TOP: Preferred stock yield
- The last dividend on Spirex Corporation’s common stock was $4.00, and the expected growth rate is 10 percent. If you require a rate of return of 20 percent, what is the highest price you should be willing to pay for this stock?
a. | $44.00 |
b. | $38.50 |
c. | $40.00 |
d. | $45.69 |
e. | $50.00 |
ANS: A
P_{0} =
DIF: Easy OBJ: TYPE: Problem TOP: Stock price
- You are trying to determine the appropriate price to pay for a share of common stock. If you purchase this stock, you plan to hold it for 1 year. At the end of the year you expect to receive a dividend of $5.50 and to sell the stock for $154. The appropriate rate of return for this stock is 16 percent. What should be the current price of this stock?
a. | $137.50 |
b. | $150.22 |
c. | $162.18 |
d. | $98.25 |
e. | $175.83 |
ANS: A
Numerical solution:
P_{0} =
DIF: Easy OBJ: TYPE: Problem TOP: Stock price
- A share of common stock has a current price of $82.50 and is expected to grow at a constant rate of 10 percent. If you require a 14 percent rate of return, what is the current dividend on this stock?
a. | $3.00 |
b. | $3.81 |
c. | $4.29 |
d. | $4.75 |
e. | $6.13 |
ANS: A
P_{0} = $82.50 =
$4.40 = D_{0} (1.10)
D_{0 } = $3.00.
DIF: Easy OBJ: TYPE: Problem TOP: Constant growth stock
- The last dividend paid by Klein Company was $1.00. Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever. Klein’s required rate of return on equity (r_{s}) is 12 percent. What is the current price of Klein’s common stock?
a. | $21.00 |
b. | $33.33 |
c. | $42.25 |
d. | $50.16 |
e. | $58.75 |
ANS: D
Enter in CFLO register = 0, = 1.05, and = 61.74.
Then enter I = 12, and press NPV to get NPV = P_{0} = $50.16.
DIF: Easy OBJ: TYPE: Problem TOP: Nonconstant growth stock
- You are given the following data:
(1) | The risk-free rate is 5 percent. |
(2) | The required return on the market is 8 percent. |
(3) | The expected growth rate for the firm is 4 percent. |
(4) | The last dividend paid was $0.80 per share. |
(5) | Beta is 1.3. |
Now assume the following changes occur:
(1) | The inflation premium drops by 1 percent. |
(2) | An increased degree of risk aversion causes the required return on the market to go to 10 percent after adjusting for the changed inflation premium. |
(3) | The expected growth rate increases to 6 percent. |
(4) | Beta rises to 1.5. |
What will be the change in price per share, assuming the stock was in equilibrium before the changes?
a. | +$12.11 |
b. | -$4.87 |
c. | +$6.28 |
d. | -$16.97 |
e. | +$2.78 |
ANS: B
Numerical solution:
Before: | r_{s} = 5% + (8% – 5%)1.3 = 8.9%. |
| |
| |
After: | r_{s} = 4% + (10% – 4%)1.5 = 13%. |
| |
Hence, we have $12.11 – $16.98 = -$4.87.
DIF: Medium OBJ: TYPE: Problem TOP: Equilibrium stock price
- You are considering an investment in the common stock of Cowher Corp. The stock is expected to pay a dividend of $2 per share at the end of the year (i.e., D_{1} = $2.0 ). The stock has a beta equal to 1.2. The risk-free rate is 6 percent. The market risk premium is 5 percent. The stock’s dividend is expected to grow at some constant rage, g. The stock currently sells for $40 a share. Assuming the market is in equilibrium, what does the market believe the stock price will be at the end of three years? (In other words, what is P_{3}?)
a. | $40.00 |
b. | $42.35 |
c. | $45.67 |
d. | $46.31 |
e. | $49.00 |
ANS: E
Step 1 | Calculate r_{s}: |
| |
| r_{s} = r_{RF} + (RP_{M})b |
| = 6% + (5%)1.2 |
| = 12%. |
| |
Step 2 | Calculate g : |
| 7% = g |
Step 3 |
Calculate:
= $40(1.07)^{3} |
| = $49.00 |
DIF: Medium OBJ: TYPE: Problem TOP: Future stock price
- A firm expects to pay dividends at the end of each of the next four years of $2.00, $1.50, $2.50, and $3.50. If growth is then expected to level off at 8 percent, and if you require a 14 percent rate of return, how much should you be willing to pay for this stock?
a. | $67.81 |
b. | $22.49 |
c. | $58.15 |
d. | $31.00 |
e. | $43.97 |
ANS: E
Numerical solution:
P_{4} | = ($3.50)(1.08) / (0.06) = $63.00 |
| = $2.00 / (1.14) + $1.50 / (1.14)^{ 2} + $2.50 / (1.14)^{3} + $3.50 / (1.14)^{4}
+ $63.00 / (1.14)^{4} |
| = $1.754 + $1.154 + $1.687 + $39.373 = $43.97. |
Tabular solution:
| = $2.00 (PVIF_{14%,1}) + $1.50 (PVIF_{14%,2}) + $2.50 (PVIF_{14%,3}) + $66.50 (PVIF_{14%,4}) |
| = $2.00(0.8772) + $1.50(0.7695) + $2.50(0.6750) + $66.50(0.5921) |
| = $43.97. |
Financial calculator solution:
Inputs: = 0; 2.00; = 1.50; = 2.50; = 66.50; I = 14.
Output: NPV = $43.969 » $43.97.
= $43.97.
DIF: Medium OBJ: TYPE: Problem TOP: Nonconstant growth stock
- Eastern Auto Parts’ last dividend was D_{0} = $0.50, and the company expects to experience no growth for the next 2 years. However, Eastern will grow at an annual rate of 5 percent in the third and fourth years, and, beginning with the fifth year, it should attain a 10 percent growth rate which it should sustain thereafter. Eastern has a required rate of return of 12 percent. What should be the present price per share of Eastern common stock?
a. | $19.26 |
b. | $31.87 |
c. | $30.30 |
d. | $20.83 |
e. | $19.95 |
ANS: D
Tabular solution:
| = $0.50(PVIFA_{12%,2}) + $0.525(PVIF_{12%,3}) + $0.5513(PVIF_{12%,4}) + $30.32(PVIF_{12%,4}) |
| = $0.50(1.6901) + $0.53(0.7718) + $0.55(0.6355) + $30.30(0.6355) |
| = $0.845 + $0.377 + $0.35 + $19.256 = $20.83. |
Financial calculator solution:
Inputs: = 0; = 0.50; = 0.50; = 0.525; = 30.851; I = 12.
Output: NPV = $20.825 » $20.83. = $20.83.
DIF: Medium OBJ: TYPE: Problem TOP: Nonconstant growth stock
- The Satellite Building Company has fallen on hard times. Its management expects to pay no dividends for the next 2 years. However, the dividend for Year 3, D_{3}, will be $1.00 per share, and the dividend is expected to grow at a rate of 3 percent in Year 4, 6 percent in Year 5, and 10 percent in Year 6 and thereafter. If the required return for Satellite is 20 percent, what is the current equilibrium price of the stock?
a. | $0 |
b. | $5.26 |
c. | $6.34 |
d. | $12.00 |
e. | $13.09 |
ANS: C
Financial calculator solution
Inputs: = 0; = 0; N_{j} = 2; = 1.0; = 1.03; = 13.102.
Output: NPV = $6.34. = $6.34.
DIF: Medium OBJ: TYPE: Problem TOP: Nonconstant growth stock
- A share of stock has a dividend of D_{0} = $5. The dividend is expected to grow at a 20 percent annual rate for the next 10 years, then at a 15 percent rate for 10 more years, and then at a long-run normal growth rate of 10 percent forever. If investors require a 10 percent return on this stock, what is its current price?
a. | $100.00 |
b. | $82.35 |
c. | $195.50 |
d. | $212.62 |
e. | The data given in the problem are internally inconsistent, i.e., the situation described is impossible in that no equilibrium price can be produced. |
ANS: E
The data in the problem are unrealistic and inconsistent with the requirements of the growth model; r less than g implies a negative stock price. If r equals g, the denominator is zero, and the numerical result is undefined. r must be greater than g for a reasonable application of the model.
DIF: Medium OBJ: TYPE: Problem TOP: Supernormal growth stock
- You are considering the purchase of a common stock that just paid a dividend of $2.00. You expect this stock to have a growth rate of 30 percent for the next 3 years, then to have a long-run normal growth rate of 10 percent thereafter. If you require a 15 percent rate of return, how much should you be willing to pay for this stock?
a. | $71.26 |
b. | $97.50 |
c. | $82.46 |
d. | $79.15 |
e. | $62.68 |
ANS: A
Financial calculator solution
Inputs: = 0; = 2.60; = 3.38; = 101.054; I = 15.
Output: NPV = $71.26. = $71.26.
DIF: Medium OBJ: TYPE: Problem TOP: Supernormal growth stock
- DAA’s stock is selling for $15 per share. The firm’s income, assets, and stock price have been growing at an annual 15 percent rate and are expected to continue to grow at this rate for 3 more years. No dividends have been declared as yet, but the firm intends to declare a dividend of D_{3} = $2.00 at the end of the last year of its supernormal growth. After that, dividends are expected to grow at the firm’s normal growth rate of 6 percent. The firm’s required rate of return is 18 percent. The stock is
a. | Undervalued by $3.03. |
b. | Overvalued by $3.03. |
c. | Correctly valued. |
d. | Overvalued by $2.25. |
e. | Undervalued by $2.25. |
ANS: B
Financial calculator solution
Calculate current expected price of stock,
Inputs: = 0; = 0; N_{j} = 2; = 19.67; I = 18.
Output: NPV = $11.97. = $11.97.
Therefore, it is overvalued by $15.00 – $11.97 = $3.03.
DIF: Medium OBJ: TYPE: Problem TOP: Supernormal growth stock
- Berg Inc. has just paid a dividend of $2.00. Its stock is now selling for $48 per share. The firm is half as risky as the market. The expected return on the market is 14 percent, and the yield on U.S. Treasury bonds is 11 percent. If the market is in equilibrium, what rate of growth is expected?
ANS: D
Numerical solution:
Required rate of return: r_{s} = 11% + (14% – 11%) 0.5 = 12.5%.
Calculate growth rate using r_{s}:
$6 – $48g | = $2 + $2g (Multiply both sides by (0.125 – g) |
$50g | = $4 |
g | = 0.08 = 8%. |
Required return equals total yield (Dividend yield + Capital gains yield).
Dividend yield = $2.16/$48.00 = 4.5%; Capital gains yields = g = 8%.
DIF: Medium OBJ: TYPE: Problem TOP: Stock growth rate
- You have a chance to purchase a perpetual security that has a stated annual payment (cash flow) of $50. However, this is an unusual security in that the payment will increase at an annual rate of 5 percent per year; this increase is designed to help you keep up with inflation. The next payment to be received (your first payment, due in 1 year) will be $52.50. If your required rate of return is 15 percent, how much should you be willing to pay for this security?
a. | $350 |
b. | $482 |
c. | $525 |
d. | $556 |
e. | $610 |
ANS: C
This is the same as a constant growth stock (g = 5%) and can be evaluated using the Gordon constant growth model:
DIF: Medium OBJ: TYPE: Problem TOP: Value of a “growing perpetuity”
- Suppose you are willing to pay $30 today for a share of stock which you expect to sell at the end of one year for $32. If you require an annual rate of return of 12 percent, what must be the amount of the annual dividend which you expect to receive at the end of Year 1?
a. | $2.25 |
b. | $1.00 |
c. | $1.60 |
d. | $3.00 |
e. | $1.95 |
ANS: C
Total yield = 12%.
Capital gains yield = ($32 – $30)/$30 = 6.67%.
Dividend yield = 12.0% – 6.67% = 5.33%.
Expected dividend = P_{0}(Dividend yield) = $30(0.0533) = $1.60.
DIF: Medium OBJ: TYPE: Problem TOP: Dividend yield
- Carlson Products, a constant growth company, has a current market (and equilibrium) stock price of $20.00. Carlson’s next dividend, D_{1}, is forecasted to be $2.00, and Carlson is growing at an annual rate of 6 percent. Carlson has a beta coefficient of 1.2, and a required rate of return on the market is 15 percent. As Carlson’s financial manager, you have access to insider information concerning a switch in product lines which would not change the growth rate, but would cut Carlson’s beta which would not change the growth rate, but would cut Carlson’s beta coefficient in half. If you buy the stock at the current market price, what is your expected percentage capital gain?
a. | 23% |
b. | 33% |
c. | 43% |
d. | 53% |
e. | There would be a capital loss. |
ANS: C
Step 1 | Calculate r_{s}, the required rate of return
r_{s} = |
| |
| |
Step 2 | Calculate r_{RF}, the risk-free rate |
| 16% = r_{RF} + (15% – r_{RF})1.2 |
| 16% = r_{RF} – 1.2r_{RF} + 18% |
| 0.2r_{RF} = 2% |
| r_{RF} = 10% |
| |
Step 3 | Calculate the new stock price and capital gain |
| New r_{s} = 10% + (15% – 10%)0.6 = 13% . |
| |
| Therefore, the percentage capital gain is 43%
. |
DIF: Medium OBJ: TYPE: Problem TOP: Capital gains
- Given the following information, calculate the expected capital gains yield for Chicago Bears Inc.: beta = 0.6; r_{M} = 15%; r_{RF} = 8%; = $2.00; P_{0} = $25.00. Assume the stock is in equilibrium and exhibits constant growth.
a. | 3.8% |
b. | 0% |
c. | 8.0% |
d. | 4.2% |
e. | None of the above. |
ANS: D
Required rate of return, r_{s} = 8% + (15% – 8%)0.6 = 12.2%.
Calculate dividend yield and use to calculate capital gains yield:
Dividend yield =
Capital gains yield = Total yield – Dividend yield = 12.2% – 8% = 4.2%.
Alternative method: :
$3.05 – $25g | = $2 (Multiply both sides by (0.122 – g)) |
$25g | = $1.05 |
g | = 0.042 = 4.2% |
Since the stock is growing at a constant rate, g = Capital gains yield.
DIF: Medium OBJ: TYPE: Problem TOP: Capital gains yield
- Over the past few years, Swanson Company has retained, on the average, 70 percent of its earnings in the business. The future retention rate is expected to remain at 70 percent of earnings, and long-run earnings growth is expected to be 10 percent. If the risk-free rate, r_{RF}, is 8 percent, the expected return on the market, r_{M}, is 12 percent, Swanson’s beta is 2.0, and the most recent dividend, D_{0}, was $1.50, what is the most likely market price and P/E ratio (P_{0}/E_{1}) for Swanson’s stock today?
a. | $27.50; 5.0x |
b. | $33.00; 6.0x |
c. | $25.00; 5.0x |
d. | $22.50; 4.5x |
e. | $45.00; 4.5x |
ANS: A
Step 1 | Calculate the required rate of return |
| |
| r_{s} = 8% + 2.0(12% – 8%) = 16% |
| |
Step 2 | Calculate the current market price |
| |
Step 3 | Calculate the earnings and P/E ratio |
| = = $1.50(1.10) = $1.65 = 0.30E_{1}. |
| E_{1} = $1.65/0.30 = $5.50. |
| = 5.0X |
DIF: Medium OBJ: TYPE: Problem TOP: Stock price and P/E/ ratios
- Yesterday BrandMart Supplies paid its common stockholders a dividend equal to $3 per share. BrandMart expects to pay a $5 per share one year from today. After the $5 dividend is paid, the company expects its growth rate will remain constant at 4 percent per year forever. If BrandMart’s investors demand a 12 percent rate of return, what should be the current market price of the company’s stock?
a. | $62.50 |
b. | $65.00 |
c. | $62.27 |
d. | $37.50 |
e. | None of the above is correct. |
ANS: A DIF: Medium OBJ: TYPE: Problem TOP: Stock valuation
- Philadelphia Corporation’s stock recently paid a dividend of $2.00 per share (D_{0} = $2), and the stock is in equilibrium. The company has a constant growth rate of 5 percent and a beta equal to 1.5. The required rate of return on the market is 15 percent, and the risk-free rate is 7 percent. Philadelphia is considering a change in policy which will increase its beta coefficient to 1.75. If market conditions remain unchanged, what new constant growth rate will cause the common stock price of Philadelphia to remain unchanged?
a. | 8.85% |
b. | 18.53% |
c. | 6.77% |
d. | 5.88% |
e. | 13.52% |
ANS: C
Calculate the initial required return and equilibrium price
r_{s} = 0.07 + (0.08)1.5 = 0.19 = 19%.
P_{0} =
Calculate the new required return and equilibrium growth rate
New r_{s} = 0.07 + (0.08)1.75 = 0.21.
New r_{s} = 0.21 =
3.15 – 2.0 | = 2g + 15g (Multiply both sides by 15, combine like terms.) |
1.15 | = 17g |
g | = 0.06765 » 6.77% |
DIF: Tough OBJ: TYPE: Problem TOP: Constant growth stock
- Hard Hat Construction’s stock is currently selling at an equilibrium price of $30 per share. The firm has been experiencing a 6 percent annual growth rate. Last year’s earnings per share, E_{0}, were $4.00, and the dividend payout ratio is 40 percent. The risk-free rate is 8 percent, and the market risk premium is 5 percent. If systematic risk (beta) increases by 50 percent, and all other factors remain constant, by how much will the stock price change? (Hint: Use four decimal places in your calculations.)
a. | -$7.33 |
b. | +$7.14 |
c. | -$15.00 |
d. | -$15.22 |
e. | +$22.63 |
ANS: A
Calculate the required rate of return
D_{0} = E_{0}(Payout ratio) = $4.00(0.40) = $1.60.
Required rate of return:
Calculate beta
11.65% = 8% + (5%)β; β = 0.73.
Calculate the new beta
b_{New} = 0.73(1.5) = 1.095.
Calculate the new required rate of return
r_{s} = 8% + (5%)1.095 = 13.475% » 13.48%.
Calculate the new expected equilibrium stock price:
Change in stock price = $30 – $22.67 = $7.33 decrease.
DIF: Tough OBJ: TYPE: Problem TOP: Risk and stock price
- The Hart Mountain Company has recently discovered a new type of kitty litter which is extremely absorbent. It is expected that the firm will experience (beginning now) an unusually high growth rate (20 percent) during the period (3 years) it has exclusive rights to the property where the raw material used to make this kitty litter is found. However, beginning with the fourth year the firm’s competition will have access to the material, and from that time on the firm will achieve a normal growth rate of 8 percent annually. During the rapid growth period, the firm’s dividend payout ratio will be relatively low (20 percent) in order to conserve funds for reinvestment. However, the decrease in growth in the fourth year will be accompanied by an increase in dividend payout to 50 percent. Last year’s earnings were E_{0} = $2.00 per share, and the firm’s required return is 10 percent. What should be the current price of the common stock?
a. | $66.50 |
b. | $87.96 |
c. | $71.53 |
d. | $61.78 |
e. | $93.50 |
ANS: C
Financial calculator solution:
Inputs: = 0; = 0.48; = 0.576; = 93.991; I = 10.
Output: NPV = $71.53. = $71.53.
DIF: Tough OBJ: TYPE: Problem TOP: Supernormal growth stock
- NYC Company has decided to make a major investment. The investment will require a substantial early cash outflow, and inflows will be relatively late. As a result, it is expected that the impact on the firm’s earnings for the first 2 years will cause a negative growth of 5 percent annually. Further, it is anticipated that the firm will then experience 2 years of zero growth, after which it will begin a positive annual sustainable growth of 6 percent. If the firm’s required return is 10 percent and its last dividend, D_{0}, was $2 per share, what should be the current price per share?
a. | $32.66 |
b. | $47.83 |
c. | $53.64 |
d. | $38.47 |
e. | $42.49 |
ANS: D
Financial calculator solution:
Inputs: = 0; = 1.90; = 1.805; N_{j} = 2; = 49.63; I = 10.
Output: NPV = $38.47. = $38.47.
DIF: Tough OBJ: TYPE: Problem TOP: Nonconstant growth stock
- Club Auto Parts’ last dividend, D_{0}, was $0.50, and the company expects to experience no growth for the next 2 years. However, Club will grow at an annual rate of 5 percent in the third and fourth years, and, beginning with the fifth year, it should attain a 10 percent growth rate which it will sustain thereafter. Club has a required rate of return of 12 percent. What should be the price per share of Club stock at the beginning of the third year, P_{2}?
a. | $19.98 |
b. | $25.06 |
c. | $31.21 |
d. | $19.48 |
e. | $27.55 |
ANS: B
Financial calculator solution:
Calculate the PV of the stock’s expected cash flows as of time = 2; thus, = 0; = 0.525, which is D_{3}; = 30.851, which is actually .
Inputs: = 0; = = 0.525; = = 30.851; I = 12.
Output: NPV = $25.06. = = $25.06.
DIF: Tough OBJ: TYPE: Problem TOP: Nonconstant growth stock
- Modular Systems Inc. just paid dividend D_{0}, and it is expecting both earnings and dividends to grow by 0 percent in Year 2, by 5 percent in Year 3, and at a rate of 10 percent in Year 4 and thereafter. The required return on Modular is 15 percent, and it sells at its equilibrium price, P_{0} = $49.87. What is the expected value of the next dividend? (Hint: Set up and solve an equation with the unknown.)
a. | It cannot be estimated without more data. |
b. | $1.35 |
c. | $1.85 |
d. | $2.35 |
e. | $2.85 |
ANS: E
Solution:
P_{0} = $49.87;
$49.87=
$49.87 = 0.8696 + 0.7561 + 0.6904 + 15.1886
$49.87 = 17.5047
$2.85 =
DIF: Tough OBJ: TYPE: Problem TOP: Nonconstant growth stock
- Laserclok Corporation paid a dividend for 50 years until it experienced financial difficulty three years ago, at which time the dividend payment was suspended (that is, a dividend has not been paid during the past three years). The company is now much stronger financially, but Laserclok does not expect to pay a dividend for the next five years. Beginning six years from today, the company will pay a dividend equal to $2.10, which is 5 percent greater than the last dividend paid three years ago. After the dividend payments start again, Laserclok expects the dividend to continue to be paid and to grow at a constant rate of 5 percent. If the appropriate market rate for investments similar to Laserclok’s stock is 15 percent, at what price should the stock currently be selling in the financial markets?
a. | $21.00 |
b. | $10.44 |
c. | $14.00 |
d. | There is not enough information to answer the question. |
e. | None of the above. |
ANS: B DIF: Tough OBJ: TYPE: Problem
TOP: Nonconstant growth stock
Financial Calculator Section
The following question(s) may require the use of a financial calculator.
- Your company paid a dividend of $2.00 last year. The growth rate is expected to be 4 percent for 1 year, 5 percent the next year, then 6 percent for the following year, and then the growth rate is expected to be a constant 7 percent thereafter. The required rate of return on equity (k_{s}) is 10 percent. What is the current price of the common stock?
a. | $53.45 |
b. | $60.98 |
c. | $64.49 |
d. | $67.47 |
e. | $69.21 |
ANS: D
Enter in calculator = 0, = 2.08, = 2.1840, and = 84.8833.
Then enter I = 10, and press NPV to get NPV = P_{0} = $67.47.
DIF: Easy OBJ: TYPE: Financial Calculator TOP: Nonconstant growth stock
- Garcia Inc. has a current dividend of $3.00 per share (D_{0} = $3.00). Analysts expect that the dividend will grow at a rate of 25 percent a year for the next three years, and thereafter it will grow at a constant rate of 10 percent a year. The company’s cost of equity capital is estimated to be 15 percent. What is the current stock price of Garcia Inc.?
a. | $75.00 |
b. | $88.55 |
c. | $95.42 |
d. | $103.25 |
e. | $110.00 |
ANS: C
Step 1 | Find the dividend stream to D_{3}: |
| = $3.00 |
| = ($3.00)(1.25) = $3.7500 |
| = ($3.75)(1.25) = $4.6875 |
| = ($4.6875)(1.25) = $5.8594 |
| |
Step 2 | Find ; |
| |
| |
Step 3 | Find the NPV of the cash flows, the stock’s value: |
| = 0 |
| = 3.7500 |
| = 4.6875 |
| = 134.7654 |
| I = 15 |
| Solve for NPV = $95.42. |
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Nonconstant growth stock
- Worldwide Inc., a large conglomerate, has decided to acquire another firm. Analysts are forecasting a period (2 years) of extraordinary growth (20 percent), followed by another 2 years of unusual growth (10 percent), and finally a normal (sustainable) growth rate of 6 percent annually. If the last dividend was D_{0} = $1.00 per share and the required return is 8 percent, what should the market price be today?
a. | $93.70 |
b. | $72.76 |
c. | $99.66 |
d. | $98.57 |
e. | $68.87 |
ANS: B
Financial calculator solution:
Inputs: = 0; = 1.20; = 1.44; = 1.584; = 94.092; I = 8.
Output: NPV = $72.764 » $72.76. = $72.76.
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Supernormal growth stock
- Assume that the average firm in your company’s industry is expected to grow at a constant rate of 5 percent, and its dividend yield is 4 percent. You company is about as risky as the average firm in the industry, but it has just developed a line of innovative new products which leads you to expect that its earnings and dividends will grow at a rate of 40 percent. ( = D_{0} ((1 + g) = D_{0} (1.40)) this year and 25 percent the following year, after which growth should match the 5 percent industry average rate. The last dividend paid (D_{0}) was $2. What is the value per share of your firm’s stock?
a. | $42.60 |
b. | $82.84 |
c. | $91.88 |
d. | $101.15 |
e. | $110.37 |
ANS: B
r_{s} = Dividend yield + g = 0.04 + 0.05 = 0.09 » 9%.
Financial calculator solution:
Inputs: = 0; = 2.80; = 95.375; I = 9.
Output: NPV = $82.84; = $82.84.
DIF: Medium OBJ: TYPE: Financial Calculator TOP: Stock valuation
- Assume that you would like to purchase 100 shares of preferred stock that pays an annual dividend of $6 per share. However, you have limited resources now, so you cannot afford the purchase price. In fact, the best that you can do now is to invest your money in a bank account earning a simple interest rate of 6 percent, but where interest is compounded daily (assume a 365-day year). Because the preferred stock is riskier, it has a required annual rate of return of 12 percent (assume that this rate will remain constant over the next 5 years). For you to be able to purchase this stock at the end of 5 years, how much must you deposit in your bank account today, at t = 0?
a. | $2,985.00 |
b. | $4,291.23 |
c. | $3,138.52 |
d. | $3,704.18 |
e. | $4,831.25 |
ANS: D
Numerical solution:
P_{ps} =
Amount needed to buy 100 shares:
$50(100) | = $5,000 |
$5,000 | = PV(1 + 0.06/365)^{5(365)} |
$5,000 | = PV(1.3498) |
PV | = $3,704.18. |
Financial calculator solution:
Convert the simple interest rate to an EAR
Inputs: P/YR = 365; NOM% = 6. Output: EFF% = EAR = 6.183%.
Calculate PV of deposit required today
Inputs: N = 5; I = 6.183; FV = 5,000.
Output: PV = -$3,704.205 » -$3,704.21.
Note: The numerical solution is used as the correct answer because of its greater precision. If the financial calculator derived EAR is expressed to five decimal places it yields a PV = -3,704.18.
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Preferred stock value
- A financial analyst has been following Fast Start Inc., a new high-growth company. She estimates that the current risk-free rate is 6.25 percent, the market risk premium is 5 percent, and that Fast Start’s beta is 1.75. The current earnings per share (EPS_{0}) is $2.50. The company has a 40 percent payout ratio. The analyst estimates that the company’s dividend will grow at a rate of 25 percent this year, 20 percent next year, and 15 percent the following year. After three years the dividend is expected to grow at a constant rate of 7 percent a year. The company is expected to maintain its current payout ratio. The analyst believes that the stock is fairly priced. What is the current price of the stock?
a. | $16.51 |
b. | $17.33 |
c. | $18.53 |
d. | $19.25 |
e. | $19.89 |
ANS: C
a. | Use the SML equation to solve for r_{s}. |
| r_{s }= 0.0625 + (0.05)(1.75) = 0.15 = 15%. |
| |
b. | Calculate dividend per share, D_{0}: |
| (EPS_{0})(Payout ratio) = D_{0} |
| ($2.50)(0.4) = $1.00. |
| |
c. | Calculate the dividend and price stream (once the stock becomes a constant growth stock): |
| |
| D_{0} = $1.00; D_{1} = $1.00 ´ 1.25 = $1.25; D_{2} = $1.25 ´ 1.20 = $1.50; D_{3} = $1.50 ´ 1.15 = $1.725; D_{4} = $1.725 ´ 1.07 = $1.8458. |
d. | Use the cash flow register to calculate PV: |
| = = 0; = = 1.25; = = 1.50; = = 24.797; I = 15%. |
| Solve for NPV = $18.53. |
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Nonconstant growth stock
- Assume an all equity firm has been growing at a 15 percent annual rate and is expected to continue to do so for 3 more years. At that time, growth is expected to slow to a constant 4 percent rate. The firm maintains a 30 percent payout ratio, and this year’s retained earnings net of dividends were $1.4 million. The firm’s beta is 1.25, the risk-free rate is 8 percent, and the market risk premium is 4 percent. If the market is in equilibrium, what is the market value of the firm’s common equity (1 million shares outstanding)?
a. | $6.41 million |
b. | $12.96 million |
c. | $9.18 million |
d. | $10.56 million |
e. | $7.32 million |
ANS: C
Calculate required rate of return
r_{s} = 8% + 4%(1.25) = 13.0%.
Calculate net income, total dividends, and D_{0}
Net income | = $1.4 million / (1 – payout ratio) |
| = $1.4 million / 0.7 = $2.0 million |
Dividends | = $2.0 million ´ 0.3 = $0.6 million |
D_{0} | = $600,000 / 1,000,000 shares = $0.60 |
Financial calculator solution:
Inputs: = = 0; = = 0.69; = = 0.794; = = 11.469; I = 13.
Output: NPV = $9.18; = P_{0} = $9.18.
Total market value = P_{0} ´ shares outstanding = $9.18 ´ 1,000,000 = $9,180,000.
DIF: Tough OBJ: TYPE: Financial Calculator TOP: Firm valuation