A bond is currently selling for $910 and has a remaining life of three years. It makes an annual coupon payment of $60 and has a par of $1,000. If the yield to maturity is 9%, what is the net present value of the bond?
A) $24.06
B) $14.06
C) $9.83
D) $18.57

Question

A bond is currently selling for $910 and has a remaining life of three years.  It makes an annual coupon payment of $60 and has a par of $1,000.  If the yield to maturity is 9%, what is the net present value of the bond?
A) $24.06
B) $14.06
C) $9.83
D) $18.57

Quizplus · Accepted Answer

The net present value (NPV) of a bond can be calculated by discounting its future cash flows (coupon payments and the par value at maturity) back to the present value using the yield to maturity as the discount rate, and then subtracting the current price of the bond. Here, the future cash flows are $60 annual coupon payments for three years and a $1,000 par value at maturity. Using a 9% yield to maturity for discounting, the calculation is as follows:$$ NPV = \frac{60}{(1+0.09)^1} + \frac{60}{(1+0.09)^2} + \frac{60}{(1+0.09)^3} + \frac{1000}{(1+0.09)^3} - 910 $$$$ NPV = \frac{60}{1.09} + \frac{60}{1.1881} + \frac{60}{1.295029} + \frac{1000}{1.295029} - 910 $$$$ NPV = 55.05 + 50.50 + 46.32 + 772.17 - 910 $$$$ NPV = 924.04 - 910 = 14.04 $$The closest answer provided is $14.06, which is option B. The slight difference is likely due to rounding during the calculation process.

A Bond Is Currently Selling for $910 and Has a Remaining