Question

Bonds of Francesca Corporation with a par value of $1,000 sell for $940, mature in six years, and have a 7% annual coupon rate paid semiannually. Do not round intermediate calculations. Round your answers to two decimal places. Calculate:

a. current yield.
% annually

b. yield to maturity, to the nearest basis point.
% annually

c. horizon yield (or realized return) for an investor with a four-year holding period and a reinvestment rate of 5% over the period. At the end of four years, the 7% coupon bonds with two years remaining will sell to yield 7%.
% annually

Answer 1

A bond's present value is calculated using the present value formula on its expected cash flows, which includes interest payments and the principal. This calculation changes as interest rates change, inversely affecting bond prices.

Step-by-step explanation:

Understanding the value of a bond in the present requires applying the present value formula to the expected cash flows. For a simple two-year bond with a face value of $3,000 and an 8% annual coupon rate, the bond will pay $240 in interest each year (8% of $3,000). To find the present value at an 8% discount rate, we calculate the present value of each interest payment and the principal:

• Present Value of Year 1 Interest = $240 / (1 + 0.08)

• Present Value of Year 2 Interest plus Principal = ($240 + $3,000) / (1 + 0.08)^2

Adding these two figures gives us the present value of the bond at an 8% discount rate. If interest rates rise, causing the discount rate to increase to 11%, the calculation changes as follows:

• Present Value of Year 1 Interest at 11% = $240 / (1 + 0.11)

• Present Value of Year 2 Interest plus Principal at 11% = ($240 + $3,000) / (1 + 0.11)^2

The present value will be lower with a higher discount rate, reflecting the inverse relationship between interest rates and bond prices.