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Bond Valuation Problems

3. Interpreting Bond Yields Suppose you buy a 9 percent coupon, 15-year bond today when it’s first issued. If interest rates suddenly rise to 15 percent, what happens to the value of your bond? Why?

Answer: $649.16

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Bond Valuation Problems

5. Bond Yields N&N Co. has 11 percent coupon bonds on the

market with 8 years left to maturity. The bonds make annual

payments. If the bond currently sells for $1,110.70 what is its YTM?

Answer: 9%

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Bond Valuation Problems

6. Coupon rates Merton Enterprises has bonds on the market

making annual payments, with 14 years to maturity, and selling for

$950. At this price, the bonds yield 7.5 percent. What must the

coupon rate be on Merton’s bonds?

Answer: 6.911%

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Bond Valuation Problems

22. Interest Rate Risk Bond J is a 4 percent coupon bond. Bond

K is a 10 percent coupon bond. Both bonds have 10 years to

maturity, make semi-annual payments and have a YTM of 9

percent. If interest rates suddenly rise by 2 percent, what is the

percentage price change of these bonds? What if rates suddenly

fall by 2 percent instead? What does this problem tell you about

the interest rate risk of lower-coupon bonds?

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Bond Valuation Problems

23. Bond Yields BrainDrain Software has 12 percent coupon

bonds on the market with 9 years to maturity. The bonds make

semiannual payments and currently sell for 125.32 percent of par.

What is the current yield on BrainDrain bonds? The YTM? The

effective annual yield?

Answer: CY=9.58% YTM=8% EAR=8.16%

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Example. Decomposition of total return

when YTM at the end of a period is same as YTM at the beginning

of the period thentotal realized return=YTM at the beginning of the period = capital gains yield + interest income

for instance: coupon rate=9% annual coupon N=10 years P=$882.22P10=882.22= 90 PVIFAk,10 + 1000PVIFk,10

k=11%=YTM at the beginning of the period

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Example. Decomposition of total return

after 1 year if YTM is still 11%P9= 90 PVIFA11%,9 + 1000PVIF11%,9=$889.26

total realized return=0.798%+10.202% =11% =YTM at the beginning of the period

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Example. Decomposition of total return

if YTM rises to 13% at the end of the periodP9=$794.73

total realized return=-9.917%+10.202% =0.285% YTM at the beginning of the periodNote: To be able to calculate realized return for more than one period we need to make assumptions about reinvestment rates.

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Bond Valuation Problems

40. Holding Period Yield The YTM on a bond is the interest rate you earn on your investment if interest rates don’t change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY).Suppose you buy a 10 percent coupon bond making annual payments today for $1,064.18. The bond has 10 years to maturity. What rate of return do you expect on your investment?Two years from now, the YTM on your bond has declined by 3 percent, and you decide to sell. What price will your bond sell for? What is the HPY on your investment assuming that you reinvest coupons at HPY? Compare this yield to theYTM when you first bought the bond. Why are they different?

Answer: 1,064.18=100 PVIFA10,k + 1,000 PVIF10,k

YTM=9%b. New YTM=9%-3%=6%$1,248.39=100 PVIFA8,6% + 1,000 PVIF8,6%

1,064.18=100 PVIFA2,HPY + 1,248.39 PVIF2,HPY

HPY=17.361% note this assumes you could reinvest $100 coupon at 17.361%