Question

A mortgage bond issued by Automation Engineering is for sale for $7,900. The bond has a face value of $10,000 with a coupon rate of 5% per year, payable quarterly. What rate of return will be realized if the purchaser holds the bond to maturity 7 years from now?

The rate of return will be  % per year.

Answer 1

We must have

Price of bond = Present value of coupon + Present value of face value

7900 = (5%*10000/4)*(P/A, i%, 7*4) + 10000(P/F, i%, 7*4)

Here coupon payment per quarter is (5%*10000/4) = $125

Time is 7 years or 7*4 = 28 quarters

Then we have -7900 + 125(P/A, i%, 7*4) + 10000(P/F, i%, 7*4) = 0

For i = 2%, NPV = 503.904 and for i = 3%, NPV = -1183.719

Then, rate of return per quarter is 2% + (3% - 2%)*(503.904/(503.904+1183.719)) = 2.28%

Now rate of return per year = (1 + 2.28%)^4 - 1 = 9.4%

Hence, rate of return is 9.4% per year