Question

Prices of zero-coupon bonds reveal the following pattern of forward rates:

Year	Forward Rate
1	8	%
2	11
3	13

In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $55 with par value $1,000.

a. What is the price of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
b. What is the yield to maturity of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
c. Under the expectations hypothesis, what is the expected realized compound yield of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
d. If you forecast that the yield curve in 1 year will be flat at 8.0%, what is your forecast for the expected rate of return on the coupon bond for the 1-year holding period? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

a)
Price of coupon bond = ($55 / 1.08) + ($55 / (1.08 * 1.11)) + (($1000 + $55) / (1.08 * 1.11 * 1.13))
= $875.61

Price of coupon bond = $875.61

b)
FV = 1000
Nper = 3
PMT = 55
PV = 875.61

Yield to maturity can be calculated by using the following excel formula:
=RATE(nper,pmt,pv,fv)
=RATE(3,55,-875.61,1000)
= 10.55%

Yield to maturity = 10.55%

c)
Realized compound yield = ((($55 * 1.11 * 1.13) + ($55 * 1.13) + $1055) / $875.61)^(1/3) - 1
= 1.1065 - 1
= 10.65%

Realized compound yield = 10.65%

d)
Expected rate of return = (($55 / 1.08) + ($1055 / 1.08^2) + $55) / $875.61 - 1
= 1.1540 - 1
= 15.40%

Expected rate of return = 15.40%