Question

To adjust the bond-valuation framework for semiannual interest, let n be the number of semiannual periods (2 × number of years), r the semiannual interest rate (annual interest rate ÷ 2), C the semiannual coupon payment (annual coupon payment ÷ 2), and M the par value ($1,000). Find the value of a bond maturing in 4 years with a $1000 par value and a coupon interest rate of 10% (5% paid semiannually) if the required return on similar bonds is 12% (6% paid semiannually).Use excel, financial calculator Bo =

Answer 1

The bond valuation formula for semiannual payments is applied with the given values for a semiannual coupon rate and market rate to calculate the present value of the bond.

Step-by-step explanation:

To find the value of a bond maturing in 4 years with a par value of $1,000 and a coupon interest rate of 10% paid semiannually when the required return on similar bonds is 12% paid semiannually, we have to use the bond valuation formula accounting for semiannual payments. Given n = 8 (4 years x 2), r = 6% (12% ÷ 2), C = $50 (10% of $1,000 ÷ 2), and M = $1,000:. The bond's price (Bo) is calculated using the present value of annuity formula for the coupon payments and the present value formula for the par value. The bond's price is the sum of these two present values:. Bo = C x [(1 - (1 + r)^-n) / r] + M x (1 + r)^-n Substituting the given values: . Bo = $50 x [(1 - (1 + 0.06)^-8) / 0.06] + $1,000 x (1 + 0.06)^-8 After calculating the above formula, we arrive at the bond's value based on the current market conditions.