Question

How much would you pay for a perpetual bond that pays an annual coupon of $200 per year and yields on competing instruments are 10%. If the interest rate is expected to fall to 8% next year, what is your expected capital gain?

Answer 1

Ans. The price of the bond is the sum of present value of its future cash flows

So, price of the bond at interest rate of 10% is,

P1 = 200/(1+0.10) + 200/(1+0.10)^2 + 200/(1+0.10)^3 + 200/(1+0.10)^4 +.........upto infinity

Using the formula for present value of a perpetuity we get,

P1 = 200/0.10 = $2000

So, price of the bond when interest rate is 10% is $2000

When interest rate falls to 8% then price of the bond is,

P2 = 200/0.08 = $2500

So, when interest rate falls to 8%, the price of the bond increases to $2500.

Thus, the capital gain = (P2 - P1)/P1 = (2500-2000)/2000 = 0.25 or 25%
Thus, the capital gain is of $500 or 25%.

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