Questions: Skysong Inc. manufactures cycling equipment. Recently, the company's vice-president of operations has requested construction of a new plant to meet the increasing demand for the company's bikes. After a careful evaluation of the request, the board of directors has decided to raise funds for the new plant by issuing 2,250,000 of 9% term corporate bonds on March 1, 2023, due on March 1, 2037, with interest payable each March 1 and September 1. At the time of issuance, the market interest rate for similar financial instruments is 8%. As Skysong's controller, determine the selling price of the bonds. (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 5,275.)

Skysong Inc. manufactures cycling equipment. Recently, the company's vice-president of operations has requested construction of a new plant to meet the increasing demand for the company's bikes. After a careful evaluation of the request, the board of directors has decided to raise funds for the new plant by issuing 2,250,000 of 9% term corporate bonds on March 1, 2023, due on March 1, 2037, with interest payable each March 1 and September 1. At the time of issuance, the market interest rate for similar financial instruments is 8%.
As Skysong's controller, determine the selling price of the bonds. (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 5,275.)

Transcript text: Skysong Inc. manufactures cycling equipment. Recently, the company's vice-president of operations has requested construction of a new plant to meet the increasing demand for the company's bikes. After a careful evaluation of the request, the board of directors has decided to raise funds for the new plant by issuing $\$ 2,250,000$ of $9 \%$ term corporate bonds on March 1, 2023, due on March 1, 2037. with interest payable each March 1 and September 1. At the time of issuance, the market interest rate for similar financial instruments is $8 \%$. As Skysong's controller, determine the selling price of the bonds. (Round present value factor calculations to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 5,275.)

Solution

Solution Steps

To determine the selling price of the bonds, we need to calculate the present value of the bond's future cash flows, which include the semi-annual interest payments and the principal repayment at maturity. The present value calculations will use the market interest rate of 8% (or 4% per semi-annual period).

Calculate the present value of the semi-annual interest payments.
Calculate the present value of the principal repayment at maturity.
Sum the present values from steps 1 and 2 to get the selling price of the bonds.

Step 1: Calculate Semi-Annual Coupon Payment

The semi-annual coupon payment is calculated as follows: \[ \text{Semi-annual coupon} = \frac{9\%}{2} \times 2,250,000 = 101,250 \]

Step 2: Determine the Present Value of the Coupons

The present value of the semi-annual interest payments (an annuity) is calculated using the present value annuity factor: \[ \text{PV of Coupons} = 101,250 \times \sum_{t=1}^{28} \frac{1}{(1 + 0.04)^t} \approx 101,250 \times 16.6631 \approx 1,687,135.15 \]

Step 3: Calculate the Present Value of the Principal

The present value of the principal repayment at maturity is calculated as follows: \[ \text{PV of Principal} = \frac{2,250,000}{(1 + 0.04)^{28}} \approx 750,324.31 \]

Step 4: Calculate the Selling Price of the Bonds

The selling price of the bonds is the sum of the present values calculated in Steps 2 and 3: \[ \text{Selling Price} = \text{PV of Coupons} + \text{PV of Principal} \approx 1,687,135.15 + 750,324.31 \approx 2,437,459.46 \]