Question

Suppose that you have a one-year investment horizon. You are trying to choose among three bonds. They are all default risk free. Also they all have $100 face value and have 5 years to mature. The Örst is a zero-coupon bond. The second has an 8% annual coupon rate and pays the $8 coupon once per year. The third has a 10% annual coupon rate and pays the $10 coupon once per year. (a) If all three bonds are now priced to have 8% yield to maturity, what are their prices? (b) If you expect their yields to maturity to be 8% at the beginning of next year, what will their prices be then? What is your rate of return on each bond during the one-year holding period? (c) If, instead, you expect their yields to maturity to be 6% at the beginning of next year, what will their prices be then? What is your rate of return on each bond during the one-year holding period? (d) In the case presented in (c), if the yield to maturity of 6% is expected to continue through the end of the second year, what will be the prices of the bonds at the end of the second year? What is your annual geometric average rate of return on each bond during the two-year holding period?

Answer 1

Zero-coupon bond will be referred as B1.

8% annual coupon will be referred as B2.

10% annual coupon will be referred as B3.

time to maturity (n) = 5 years.

PV means present value, FV means Face value, C means annual coupon, r means required rate of return (in this case yield to maturity).

Bond cuurent price is calulated by discounting all the future cash flows to the present date.

Price of bond = Present value of annual coupons + present value of the maturity value(FV)

Formula for Current Bond Price: