Suppose you were thinking about buying a coupon bond with a face value of $1000,

Question

Suppose you were thinking about buying a coupon bond with a face value of $1000, an annual coupon rate of 7.5%, and a maturity for 5 years:

a. If the market rate of interest is currently at 8%, what is the most you'd be willing to pay for the bond (defined as the point where you are indifferent between the bond and your next best investment alternative)?

b. How would you classify your bond? Par bond, premium bond, or discount bond?

c. If you sell your bond after the second year for $990, what is your rate of return on the investment?

Explanation / Answer

Ans:

Value of the bond is the present value of future payments expected to arise from the bond

Value of the bond = cash flow * 1/(1+r)^n

= $75 * 1/(1+0.08)^1 + $75 * 1/(1+0.08)^2+ $75 * 1/(1+0.08)^3 + $75 * 1/(1+0.08)^4 + $75 * 1/(1+0.08)^5

= $75 * 0.9259 + $75 * 0.8573 + $75 * 0.7938 + $75 * 0.7350 + $75 * 0.6806

= $69.44 + $64.38 + $59.53 + $55.12 + $51.04

= $300

so, maximum price that can be paid for the bond is $300.

b) Discount bond

Discount bond is a bond that is priced lower than its par value.

c) Rate of return on investment = ($990 - $300) / $300

= $690 / $300

= 2.3 or 230%

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