Question

Making the assumption of no compounding interest, suppose you purchase a perpetuity bond from Vandalay Industries for $4,000 with an annual coupon rate of 3%. Specify all answers to the nearest dollar and assume a discount rate equal to that of the current interest rate.

1. What is the yearly return on your $4,000 investment?
yearly return: $______________

2. Changes in the economy push interest rates up from 3% to 5%. For how much can you sell your bond following this change in market interest rates?
price of bond: $______________

3. Suppose that interest rates instead change from 3% to 1%. For what price will you be able to sell your bond following this change in market interest rates?
price of bond: $______________

Answer 1

yearly return: $120

price of bond: $2,400

price of bond: $12,000

Step-by-step explanation:

To solve for the yearly return on the bond, simply multiply the value of the bond by the annual coupon rate. This yields

$4000 × 0.03 = $120

To calculate the price of a perpetuity bond following changes in the market interest rate, use the formula

price of bond = interest payment / yield

So if the yield on bonds is now 5% , the price of your existing bond from Vandalay Industries, which pays only 3% , falls to $2{,}400 since

$120 / 0.05 = $2400

However, if market interest rates fall to 1% , then the 3% yield on your current bond becomes very attractive to investors.

$120 / 0.01 = $12000

As such, investors would pay $12,000 for your bond when interest rates fall to 1% .

Although perpetuities may seem to be an unusual form of investment, note that the pattern of the bond price varying inversely with interest rates is common to other types of bonds.