Question

Investors require a return of 5% on a 6% coupon, 15-year, semiannual bond. What would this bond be selling for today?

Group of answer choices
a) $1,309.53
b) $1,104.65
c) $1,153.72
d) $954.22
e) $1,061.91

Answer 1

The semiannual bond with a 6% coupon rate sells for $1,104.65 (Option b) when investors require a 5% return, calculated by discounting the future cash flows at the market interest rate.. The correct answer is option b.

Step-by-step explanation:

The question from a college student pertains to the valuation of a semiannual coupon bond and to determine its present value considering the required market return. In this scenario, the bond has a face value of $1,000, a coupon rate of 6%, a market interest rate (yield to maturity) of 5%, and 15 years until maturity. As the coupon payments are distributed semiannually, this translates into $30 every six months (6% of $1,000 divided by two) for 30 periods (15 years multiplied by two).

To calculate the present value of the bond, we must discount the future cash flows (semiannual interest payments) and the final face value at the market interest rate. Using the formula for the present value of an annuity and the present value of a lump sum, we sum these two present values to get the current bond price:

1. Present value of the annuity (PVA) = C * [(1 - (1 + r)^-n) / r], where C = semiannual coupon payment, r = market interest rate per period, and n = total number of periods.
2. Present value of the lump sum (PVL) = Face value / (1 + r)^n.

After plugging the values into the formulas and summing the PVA and PVL, we find that the bond would be selling for more than its face value (at a premium) because the coupon rate is higher than the market rate. Option (b) $1,104.65 is the correct choice and represents the bond's current price.