Question

You bought a 10-year zero-coupon bond with a face value of $1,000 and a yield to maturity of 2.7% (EAR). You keep the bond for 5 years before selling it.

a:What was the price of the bond when you bought it?

b:What is your personal 5-year rate of return if the yield to maturity is still 2.7% when you sell the bond? (i.e. what is your rate of return given what you sold it for at the end of year 5 and what you paid at year-0.)

c:What is your personal 5-year rate of return if the yield to maturity is 4% when you sell the bond? (i.e. what is your rate of return given what you sold it for at the end of year 5 and what you paid at year-0.)

d:What is your personal 5-year rate of return if the yield to maturity is 1% when you sell the bond?

Answer 1

Part a)

The price of the bond = Face value/ ((YTM/100)+1)^maturity period

Thus, the price of the bond = 1000/(0.027+1)^10 = 1000/1.305 = 766.283$

Part b)

Using the same formula given above, we can determine the price given 5 years left for the bond to mature:

Price of the bond at the end of year 5 = 1000/(1.027)^5 = 1000/1.1425 = 875.273$

Thus the profit = 875.273-766.283 = 108.99$

Thus our rate of return = 108.99/766.283 = 0.1422 or 14.22%

Part c)

Using the same formula given above, we can determine the price given 5 years left for the bond to mature when YTM is 4%:

Price of the bond at the end of year 5 = 1000/(1.04)^5 = 1000/1.2166 = 821.963$

Thus the profit = 821.963 - 766.283 = 55.68$

Thus our rate of return = 55.68/766.283 = 0.07266 or 7.27%

Part d)

Using the same formula given above, we can determine the price given 5 years left for the bond to mature when YTM is 1%:

Price of the bond at the end of year 5 = 1000/(1.01)^5 = 1000/1.051 = 951.475$

Thus the profit = 951.475 - 766.283 = 185.192$

Thus our rate of return = 185.192/766.283 = 0.2417 or 24.17%