Question

ABC Inc. issued 15-year bonds six years ago. The bonds have a face value of $1,000 and a coupon rate of 5.5%, with interest paid semiannually. What is the intrinsic value of bonds if investors require a return of 7%? (Hint: what is the remaining maturity of the bonds now?)

A. $1,000.00
B. $862.06
C. $927.53
D. $1,263.79
E. $901.08

Answer 1

The intrinsic value of the bonds is $852.71.

Step-by-step explanation:

The intrinsic value of bonds can be calculated using the present value formula. In this case, the remaining maturity of the bonds is 15 years - 6 years = 9 years. The semiannual coupon payment is $1,000 * 5.5% / 2 = $27.50, and the required return is 7% / 2 = 3.5% per semiannual period.

The present value of the future cash flows can be calculated as follows:

1. $27.50 / (1 + 0.035) = $26.50 (first semiannual payment)
2. $27.50 / (1 + 0.035)^2 = $25.49 (second semiannual payment)
3. ...
4. $27.50 / (1 + 0.035)^17 = $16.11 (16th semiannual payment)
5. $1,027.50 / (1 + 0.035)^17 = $756.24 (principal + last semiannual payment)

Adding up all the present values of the cash flows, the intrinsic value of the bonds is $26.50 + $25.49 + ... + $16.11 + $756.24 = $852.71. Therefore, the correct answer is option C. $927.53.