Question

5. Suppose that you bought a 14% Drexler bond with time to maturity of 9 years for $1,379.75 (semiannual coupons, interest rate=8%). After another ½ year, you sold the bond.

a. Assuming that the required rate of return remained at 8%, what would the selling price be? What is the rate of return from this investment?

b. Assuming that the required rate of return decreased to 7.5%, what would the selling price be? What is the rate of return from this investment?

6. Consider a five-year bond paying 10 percent coupon annually. The bond is priced at $1,200.

a. Find the yield to maturity.

b. Find the realized yield, assuming that coupons are reinvested at the yield to maturity.

c. Find the realized yield, assuming that coupons are reinvested at the following rates: r0=9%, r1=9.5%, r2=10%, r3=10.5%, r4=11%, r5=11.5%.

d. Refer to part (c). Explain why the yield is different than the yield to maturity.  

7. An 8 1/2 30-year US corporate bond is callable in 12 years. It is currently sold at a price of $960. The call premium is 10 percent. The prevailing market interest rate at the call date is 8 percent.

a. What is the yield to call to an investor who does not reinvest the call price at the prevailing interest rate at the call date?

b. What is the yield to call to an investor who reinvests the call price at the prevailing interest rate at the call date?

8. Consider a 90-day Treasury bill whose price is 94.5%.

a. Find the yield on a discount basis.

b. Find the yield on a coupon equivalent basis. c. Find the effective yield.

Answer 1

From the given information,

Bond price, PV = ?

Coupon, PMT = 0.14*1000/2 = 70

Term, N = 9*2 - 1 = 17

Face value, FV = 1000

YTM, R = 0.08/2 = 0.04
Using excel function, PV = PV(R,N,PMT,FV)

PV(0.04,17,-70,-1000) = 1364.97

Bond selling price = $1364.97

Return = (Selling price - Buying price + Interest)/Buying price = (1364.97-1379.75+70)/1364.97 = 0.0405 = 4.05%

b.

From the given information,

Bond price, PV = ?

Coupon, PMT = 0.14*1000/2 = 70

Term, N = 9*2 - 1 = 17

Face value, FV = 1000

YTM, R = 0.075/2 = 0.0375
Using excel function, PV = PV(R,N,PMT,FV)

PV(0.0375,17,-70,-1000) = 1403.16

Bond selling price = $1403.16

Return = (Selling price - Buying price + Interest)/Buying price = (1403.16-1379.75+70)/1364.97 = 0.0684 = 6.84%