Question

You have purchased a bond one year ago. When you purchased this bond, it has a face value of $2500 with an annual coupon rate of 5% and 10 years to maturity. Calculate the price of this bond today if the required annual rate of return of similar bonds is 8 per cent. [15 marks]

b. How does your answer to (a) change with semi-annual coupon payments and a semi-annual discount rate of 4 per cent? Comment on your answer. [25 marks]

c. Assuming that a Stock is expected to pay a dividend of $6 in five years’ time. Thereafter the dividend growth is expected to be a constant annual rate of 6 per cent forever. If the required rate of return on similar stocks is 12 per cent, determine the price of this stocks.

Answer 1

Part (a)

Price of the bond = - PV (Rate, Nper, PMT, FV) = - PV (8%, 10 - 1, 5% x 2500, 2500) = 2,031.48

Part (b)

Price of the bond = - PV (Rate, Nper, PMT, FV) = - PV (8%/2, 2 x (10 - 1), 5%/2 x 2500, 2500) = 2,025.28

Because the frequency of compounding is now every 6 months rather than 1 year in part (a), the present value of the future payments are lower and hence the price of the bond under this method is lower than that calculated in part (a).

Part (c)

Price at the end of year 4 = P4 = D5 / (ke - g) = 6 / (12% - 6%) = 100

Price today = P4 x (1 + r)^-n = 100 x (1 + 12%)^-4 = 63.55