Question

Kevin Oh is planning to sell a bond that he owns. This bond has four years to maturity and pays a coupon of 10 percent on a semiannual basis. Similar bonds in the current market have a yield to maturity of 12 percent. What will be the price that he will get for his bond? (Do not round intermediate computations. Round your final answer to the nearest dollar.)

A) $1,044
B) $938
C) $970
D) $1,102

Answer 1

The price of Kevin's bond is calculated using the present value of its future coupon payments and its face value, discounted at the current market yield of 12 percent. The semiannual coupon of 10 percent results in $50 every six months over the next four years. The bond's estimated price is approximately $940, rounded to the nearest dollar, making option B ($938) the closest choice.

Step-by-step explanation:

To calculate the price that Kevin Oh will get for his bond, we need to find the present value of the bond's future cash flows discounted at the current market interest rate. Considering that the bond pays a semiannual coupon of 10 percent, it means that the coupon payment will be ($1,000 * 0.10) / 2 = $50 every six months. Since similar bonds in the current market have a yield to maturity of 12 percent semiannually, this rate will be used for discounting the bond's cash flows.

The bond's price is calculated by summing the present value of all future coupon payments and the present value of the bond's face value. The formula for the present value of an annuity (for the coupon payments) and a lump sum (for the face value) will be used. There are eight coupon payments remaining (4 years * 2 payments per year), each worth $50. The market yield of 12 percent needs to be halved to account for the semiannual payments, resulting in a 6 percent semiannual market yield.

The present value of the bond’s cash flows would be equal to:

1. The present value of the coupon payments: $50 * ((1 - (1 + 0.06)^-8) / 0.06)
2. The present value of the face value: $1,000 / (1 + 0.06)^8

Using the aforementioned formula, the present value of the coupon payments is $50 * (6.20979) = $310.49, and the present value of the face value is $1,000 / (1.5871) = $629.92.

Therefore, the estimated price of Kevin’s bond will be the sum of these two present values, which is $310.49 + $629.92 = $940.41, which would be rounded to the nearest dollar, giving a price of around $940. Hence, the closest answer to this calculation from the given options is $938 (Option B).