Question

. Suppose a corporate bond with the face value of $1,000. Its coupon interest rate is 10% annually and the interest is paid at each year's end. The initial maturity is 3 years. You bought 1 issue of this bond by paying $1,000 when it was initially issued. After 1 year you sold the bond when the market interest rate became 8%. A. Calculate the bond's fair price at which you could sell it to a buyer. B. How much is the capital gain or capital loss from your transaction? C. What is the rate of return on your investment from holding the bond for a year?

Answer 1

Answer: A) Bond Price=1,035.38

B) Capital gains of $35.38

C) Rate of Return = 13.54%

Step-by-step explanation:

A) The price of a bond can be calculated using the formula C/(1+r)^n + C/(1+r)^n-1 + ... + C/(1+r)^2 + C/(1+r)^n + F/(1+r)^n

Where:

C is the annual coupon payment (in this case, 10% of $1,000, which is $100),

r is the annual interest rate (8% or 0.08 after 1 year),

n is the number of years remaining until maturity (2 years), and

F is the face value of the bond ($1,000).

Substitute the values into the formula.

B) The capital gain or loss is the difference between the selling price and the initial purchase price. Just use

Capital Gain/Loss=Selling Price−Initial Purchase Price

C)The rate of return can be calculated using the formula

(Ending Value − Beginning Value + Income) / Beginning Value) * 100%

​(1035.38 − 1,000 + 100)/1000 * 100%