Question

A 30-year maturity 10% coupon bond paying coupons semiannually is callable in 10 years at a call price of $1,200. The bond currently sells at a yield to maturity of 5%.

a) What is the selling price of the bond at present?

b) What is the yield to call?

c) Suppose that the investor decided to hold the bond only for 5 years. The reinvestment rate of coupon payments is 8.5%. The forecasted yield to maturity by the end of the investment horizon is 6%. i. What is the selling price of the bond at the end of the investment horizon if it will not be called? ii. What is the return on investment during the holding period?

d) Suppose that a 31-year maturity bond yields 5.05%. What is the forward rate for the thirtyfirst year?

Answer 1

a) Price can be calculated using PV function on a calculator

N = 30 x 2 = 60, PMT = 10% x 1000 / 2 = 50, FV = 1000, I/Y = 5%/2 = 2.5%

=> Compute PV = $1,772.72

b) Yield to call can be calculated using I/Y function on a calculator

N = 10 x 2 = 20, PV = -1,772.72, FV = 1200, PMT = 50

=> Compute I/Y = 1.41% (semi-annual)

Annualized YTC = 1.41% x 2 = 2.82%

c) Selling Price after 5 years can be calculated using PV function

N = 25 x 2 = 50, PMT = 50, FV = 1000, I/Y = 6%/2 = 3%

=> Compute PV = $1,514.60

Future Value of all coupons reinvested at 8.5% can be calculated using FV function

N = 5 x 2 = 10, PMT = 50, I/Y = 8.5%/2 = 4.25%, PV = 0

=> Compute FV = $607.31

Return on investment = (1514.60 + 607.31) / 1772.72 - 1 = 19.70%

d) Using expectation hypothesis,

(1 + S31)^31 = (1 + S30)^30 x (1 + 30f1)

=> (1 + 5.05%)^31 = (1 + 5%)^30 x (1 + 30f1)

=> 30f1 = 6.56% is the forward rate for 31st year.