Question

8. During recessionary periods, bonds that were issued many years ago have a higher coupon rate than currently issued bonds. Therefore, they may sell at a premium, a price higher than their face value, because of currently low coupon rates. A $50,000 bond that was issued 15 years ago is for sale for $58,000. What rate of return per year will a purchaser make if the bond coupon rate is 20% per year payable semi-annually, and the bond is due 5 years from now?

Answer 1

8.

Let, semi annual rate of return = R

Time = 10 semiannual periods

semiannual coupon payment = (20%/2)*50000 = $5000

So,

58000 = 5000*(1-1/(1+R)^10)/R + 50000/(1+R)^10

At R = 7%

PW of cash inflows = $60535.37

At R = 8%

PW of cash inflows = $56710.08

As per the interpolation,

R = 7% + ((60535.37 - 58000)/(60535.37 - 56710.08))*(8% - 7%)

R = 7.65%

So,

Annual rate of return ( compounding semiannually) = 2*7.65%

Annual rate of return ( compounding semiannually) = 15.3%

Effective annual rate of return = (1+7.65%)^2 - 1

Effective annual rate of return = 15.89%