Question

A four-year bond with a 14% coupon can be bought for $1,200.

a. Is the yield to maturity greater or less than 14% ?
b. Calculate the yield assuming that coupons are paid annually.
c. Now recalculate the yield assuming semiannual payments. You will need a financial calculator or a spreadsheet to answer parts (b) and (c).

Answer 1

a. The yield to maturity for the bond is less than 14%. b. The yield assuming annual payments is 11.67%. c. To calculate the yield assuming semiannual payments, you need to use a financial calculator or spreadsheet.

Step-by-step explanation:

a. The yield to maturity for the bond is less than 14% because the bond was purchased at a premium price of $1,200, which is higher than its face value.

b. To calculate the yield assuming annual payments, we can use the formula:

Yield = (Coupon / Price) + ((Face Value - Price) / Price) * (1 / Years)

Using the given information, the yield would be:

Yield = (0.14 / 1200) + ((1000 - 1200) / 1200) * (1/4) = 0.11667 = 11.67%

c. When assuming semiannual payments, we need to calculate the yield to maturity using a financial calculator or a spreadsheet, as it involves multiple calculations. The yield can be determined by finding the internal rate of return (IRR) of the bond's cash flows, taking into account the semiannual coupon payments.