Chapter 4 Valuing Bonds - Cengage

[Pages:4]Chapter 4

Valuing Bonds

Answers to Concept Review Questions

1. Why is it important for corporate managers to understand how bonds and stocks are priced? Managers need to know this because (1) firms regularly issue stocks and bonds to raise money for investment (2) understanding how securities are priced is helpful when conducting an acquisition or a divestiture, (3) the stock price is an objective signal of how managers are performing, and (4) finance theory teaches that the goal of the manager should be to maximize the firm's stock price.

2. Holding constant an asset's future benefit stream, what happens to the asset's price if its risk increases? Holding future cash flows constant, the asset's price falls if risk rises because those future cash flows will be discounted at a higher rate.

3. Holding constant an asset's risk, what happens to the asset's price if its future benefit stream increases? Holding risk constant, an increase in expected future cash flows will increase the asset's price today.

4. Keeping in mind Equation 4.1, discuss how one might determine the price per acre of farmland in a particular region. The price of the land would depend on the cash flow generated by growing and selling crops. The price would depend on the crop yield, i.e., how much of a given type of crop could be harvested in one acre, the selling price of the crop, and the costs of producing the crop.

5. How is a bond's coupon rate different from its coupon yield? The coupon rate equals the annual coupon payment divided by par value. The coupon yield equals the annual coupon payment divided by the bond's market price.

6. In general, when will a bond sell at a discount? A bond sells at a discount when the bond's coupon rate is lower than the market's required rate of return on the bond.)

7. Explain what is meant by the term interest rate risk. Interest rate risk refers to the possibility that a bond's price will change because the market's required return on that bond changes.

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8. Why do bond prices and bond yields move in opposite directions?

The cash flows of ordinary bonds are contractually fixed. Thus, an increase in bond yields means that these cash flows are being discounted at a higher rate, resulting in a lower present value of price. The opposite is true if bond yields fall.

9. What are the three main types of issuers of bonds in the U.S.?

The federal government, state and local governments, and corporations.

10. What is the difference between a pure discount bond and an ordinary bond that sells at a discount?

A pure discount bond makes no coupon payments, while an ordinary bond selling at a discount makes coupon payments that are below the market's required return.)

11. Explain who benefits from the option to call a bond? The option to convert a bond into shares?

The call option benefits the issuer because it allows them to repurchase bonds at a fixed price. Issuers are likely to exercise this option when interest rates have fallen. Issuers repurchase the bonds and then issue new ones at a lower interest rate. The option to convert bonds into common stock benefits bondholders. Once the stock price rises high enough, the value of the bonds starts to behave like the value of the stock. So convertible bonds offer investors some minimal level of return plus a lot of upside potential.)

12. Suppose you calculate a bond's yield-to-maturity using the ask price, then you repeat the calculation using the bond's bid price. Which yield-to-maturity will be higher?

Bond yields and prices are inversely related, so the lower the price, the higher the yield. The ask price is always higher than the bid price, so calculating the YTM using the bid produces a higher number than if you calculate the YTM using the ask).

13. You look up the price of a certain Treasury note and find that it is quoted as 98:10. What is the dollar price of this note if its par value is $1,000?

The price is 98 10/32 percent of par value or $983.125).

14. Explain why the yield spread on corporate bonds versus Treasury bonds must always be positive. Is the same true for the yield spread on municipal bonds?

Corporate bonds are riskier, so they must offer higher yields than Treasury bonds do. This means the yield spread is always positive. Municipal bonds are also riskier than Treasuries, but remember that interest on municipal bonds is exempt from federal income taxes. This means that the pre-tax return that investors will accept on municipal bonds is lower than the pre-tax return they would accept on equally risky corporate bonds. The municipal spread could be negative. As an example, suppose a 5-year Treasury bond offers a 4 percent yield-to-maturity. A corporate bond with a AAA rating might offer a 5 percent yield, for a spread of 100 basis points. Now consider a AAA rated municipal bond. If investors require a pre-tax return of 5 percent on AAA bonds, and if the personal income tax rate is 30 percent, then a municipal bond could offer a yield of 3.5 percent

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(5% x (1 ? 30%) and still be competitive with AAA corporate bonds. Notice that the yield spread on the municipal bond relative to the Treasury is negative 50 basis points.)

15. Explain why the height of the yield curve depends on inflation.

Investors are aware that inflation erodes the value of a fixed cash payment. As a result, when investors expect high inflation, they will require high returns on bonds. When inflation expectations are lower, investors will accept lower rates on bonds.)

16. Suppose the Treasury issues two five-year bonds. One is an ordinary bond that offers a fixed nominal coupon rate of four percent. The other bond is an inflation-indexed bond (or TIPS). When the TIPS bond is issued, will it have a coupon rate of four percent, more than four percent, or less than four percent?

TIPS provide protection against inflation. Because TIPS coupon payments rise with inflation, the coupon rate on TIPS is effectively fixed in real terms rather than in nominal terms. An ordinary bond offers a fixed nominal coupon rate, and this rate must be set high enough to convince investors that it also compensates them for inflation. Therefore, the coupon rate on an ordinary bond, which is expressed in nominal terms, must be higher than the coupon rate on a TIPS, which is expressed in real terms.

Answers to Self-Test Questions

ST4-1. A 5-year bond pays interest annually. The par value is $1,000 and the coupon rate equals 7 percent. If the market's required return on the bond is 8 percent, what is the bond's market price?

P

=

$70 1.081

+

$70 1.082

+

$70 1.083

+

$70 1.084

+

$1,070 1.085

=

$960.07

You could also obtain this answer by valuing the annuity of coupon payments and the lump sum principal amount separately as follows.

P0

=

1 - $70

1 (1 + 0.08)5

0.08

+

$1,000 (1 + 0.08)5

= $279.49 + $680.58 = $960.07

ST4-2. A bond that matures in 2 years makes semiannual interest payments. The par value is $1,000, the coupon rate equals 4 percent, and the bond's market price is $1,019.27. What is the bond's yield to maturity?

The YTM is the value of r that solves this equation.

$1,019.27

=

$20 (1 + r )1

+

$20 (1 + r )2

+

$20 (1 + r )3

+

$1,020 (1 + r )4

2

2

2

2

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Because the bond sells at a premium, the YTM must be less than the coupon rate. We can try to find the YTM by trial and error. Inserting r = 0.035 into the equation produces a price of $1,009.58. This price is too low, so we have chosen a YTM that is too high. Next try r = 0.03. At that interest rate, the market price is $1,019.27, so the YTM = 3%.

An alternative approach to this problem uses the Excel function, =IRR. This function requires that you input the price of the bond as a negative value, followed by the positive cash flows that the bond promises. (Note, this should be set up to look like an Excel screen shot).

A

1

-1,019.27

2

20

3

20

4

20

5

20

Now in an empty cell type the function, =IRR(A1:A5), and Excel will return the value 1.5%. This is the YTM stated on a semiannual basis (equivalent to r/2 in the equation above), so multiply it times 2 to get the annual YTM of 3%. Note, you need to be sure that the cell in which you type the IRR formula is formatted in a way that allows you to see several decimal places. Otherwise, Excel may round off the YTM and you will not know it.

ST4-3. Two bonds offer a five percent coupon rate, paid annually, and sell at par ($1,000). One bond matures in two years and the other matures in ten years. What are the YTMs on each bond? If the YTM changes to four percent, what happens to the price of each bond? What happens if the YTM changes to six percent?

Because the bonds currently sell at par, the coupon rate and the YTM must be equal at five percent. If the YTM drops to four percent, both bonds will sell at a premium, but the price of the ten-year bond will increase more than the price of the two-year bond.

P2- yr

=

1 - $50

1 (1 + 0.04)2

0.04

+

$1,000 (1 + 0.04)2

= $94.30 + $924.56 = $1,018.86

P10- yr

=

1 - $50

1 (1 + 0.04)10

0.04

+

$1,000 (1 + 0.04)10

= $405.55 + $675.56 = $1,081.11

Repeating the calculations above at r = 0.06 we find that the two-year bond's price falls to $981.67 and the ten-year bond's price falls to $926.40. This illustrates that long-term bond prices are more sensitive to changes in interest rates than are short-term bond prices.

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