Goksel Company sold an issue of bonds with 10-year maturity, a $1,000 par value, 15% coupon rate, and semi annual interest payments. Three years after the initial offering, the going interest rate had risen to 20%. At what price would the bonds sell?
In the world of finance, bonds are a popular investment vehicle that allows both individuals and corporations to raise capital. The price of a bond is influenced by various factors, with changes in prevailing interest rates being one of the most significant. This essay explores the pricing of bonds in response to fluctuations in interest rates, using the example of Goksel Company’s bonds with a 10-year maturity, $1,000 par value, and a 15% coupon rate, which make semi-annual interest payments. We will delve into how the bonds would sell three years after the initial offering when the interest rate has risen to 20%.
To comprehend how the price of Goksel Company’s bonds would be affected by the change in interest rates, we need to understand the basics of bond pricing. The price of a bond is determined by its present value, which is the sum of the present values of all future cash flows the bondholder expects to receive. These cash flows include both periodic interest payments and the bond’s face value at maturity.
In the case of Goksel Company’s bonds, we have the following key information:
Par Value (FV) = $1,000
Coupon Rate (CR) = 15%
Maturity (N) = 10 years
Semi-annual interest payments
Change in interest rate: from 15% to 20% after 3 years
To determine the price at which Goksel Company’s bonds would sell three years after the initial offering, when the interest rate has risen to 20%, we need to calculate the present value of the bond’s future cash flows.
First, we calculate the semi-annual coupon payment:
Coupon Payment (CP) = (Coupon Rate / 2) * Par Value CP = (15% / 2) * $1,000 = $75
Next, we calculate the number of semi-annual periods remaining until maturity, which is 7 years (3 years have already passed, and the bond has a 10-year maturity).
Using the formula for the present value of an annuity, we can calculate the present value of the bond’s future coupon payments:
PV of Coupon Payments = CP * [(1 – (1 + r)^(-2N)) / r] PV of Coupon Payments = $75 * [(1 – (1 + 0.20/2)^(-2*7)) / (0.20/2)]
PV of Coupon Payments ≈ $433.92
Finally, we calculate the present value of the bond’s face value at maturity:
PV of Face Value = FV / (1 + r)^N PV of Face Value = $1,000 / (1 + 0.20)^7 ≈ $411.08
The total present value of the bond’s future cash flows is the sum of the PV of coupon payments and the PV of face value:
Total Present Value = PV of Coupon Payments + PV of Face Value Total Present Value ≈ $433.92 + $411.08 ≈ $845.00
In conclusion, when interest rates rise from 15% to 20% three years after the initial offering, Goksel Company’s bonds with a 10-year maturity and a 15% coupon rate would sell for approximately $845.00. The increase in interest rates has led to a decrease in the bond’s price, as the present value of its future cash flows is lower at the higher interest rate. Bond pricing is a crucial concept for both investors and issuers, as it directly impacts the market value of bonds and their attractiveness as investments.
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