Consider a two-year, 5 percent bond selling at par. Answer the following questio
ID: 2726918 • Letter: C
Question
Consider a two-year, 5 percent bond selling at par. Answer the following questions.
a. What is the bond's yield to maturity? What assumptions does the yield make regarding the first coupon rate?
b. Assume that in a year the one-year market rate is 7 percent (this future rate is unknown today; it is assumed to be known to illustrate the reinvestment risk). What is the return the bondholder will earn if she purchased the two-year bond today, reinvest the first coupon payment at that rate, and held the bond to maturity?
c. Assume that in a year the one-year market rate is 3 percent . What is the return the bondholder will earn if she purchased the two-year bond today, reinvest the first coupon payment at that rate, and held the bond to maturity?
Explanation / Answer
Part A
Since the bond is issued at par, its yield to maturity would be equal to its coupon rate. Therefore, yield to maturity would be 5%.
Part B
We have:
FV= 1000
PV= 1000
Pmt = 1000 x 5% = 50
50 dollars would be invested for one year at 7%, so FV of 50 dollars would be:
FV= 50 x (1+0.07)^1
= 53.50
Total amount received t maturity = 1000+50+53.50
FV = 1103.50
We can use following formula to compute return:
R= (FV/ PV)^(1/n) -1
= (1103.50/ 1000)^(1/2) -1
= 5.05%
Part c)
We have:
FV= 1000
PV= 1000
Pmt = 1000 x 5% = 50
50 dollars would be invested for one year at 3%, so FV of 50 dollars would be:
FV= 50 x (1+0.03)^1
= 51.50
Total amount received t maturity = 1000+50+51.50
FV = 1101.50
We can use following formula to compute return:
R= (FV/ PV)^(1/n) -1
= (1101.50/ 1000)^(1/2) -1
= 4.95%