Question

Cheyenne Inc manulactures cycling equipenent. Recently, the vice president of operations of the compary 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 $3,492,700 of 105 term corporate bonds on March 1. 2025, due on March 1, 2040, with interest payable each March 1 and September 1. At the time of issuance, the market interest rate for similar financial instruments is 8%6. Click here to view factor tables. As the controller of the company, determine the selling price of the bonds, (Round foctor values to 5 decimal places, es. 1.25124 and final answer to 0 decimal places, es. 458,581. Selling price of the bonds

Answer 1

To determine the selling price of the bonds, we need to calculate the present value of the bond's future cash flows. Here's how we can do it: the selling price of the bonds is $3,511,927.

Step 1: Calculate the semi-annual coupon payment:

Coupon payment = Bond face value × Coupon rate

Coupon payment = $3,492,700 × 10.5% ÷ 2

Coupon payment = $183,147.75

Step 2: Determine the number of semi-annual periods:

Number of periods = (Years to maturity) ×2

Number of periods = (2040 - 2025) × 2

Number of periods = 30

Step 3: Determine the present value of the coupon payments:

Present value of coupon payments = Coupon payment ×Present value factor

Present value factor = 1 -
`(1 + Market interest rate)^(-Number of periods)` ÷Market interest rate

Present value factor = 1 - (1 + 0.08 / 2)^(-30) / (0.08 / 2)

Present value factor = 1 - (1.04)^(-30) / 0.04

Present value factor = 1 - 0.001776 / 0.04

Present value factor = 1 - 0.0444

Present value factor = 0.9556

Present value of coupon payments = $183,147.75 * 0.9556

Present value of coupon payments = $175,173.31

Step 4: Determine the present value of the face value:

Present value of face value = Face value * Present value factor

Present value of face value = $3,492,700 0.9556

Present value of face value = $3,336,754.12

Step 5: Calculate the selling price of the bonds:

Selling price of the bonds = Present value of coupon payments + Present value of face value

Selling price of the bonds = $175,173.31 + $3,336,754.12

Selling price of the bonds = $3,511,927

Therefore, the selling price of the bonds is $3,511,927.