Question

A company is selling bonds with a face value of $1,000 to raise money for a plant expansion. The bonds pay a coupon rate of 4% per year on a semiannual basis and mature in 5 years. Net of all fees, the company receives $760 from the sale of each bond. What is the company's cost of capital on an annual basis

Answer 1

Answer:

10.26%

Explanation:

According to the scenario, computation of the given data are as follow:-

Net sales = $760

Face value of bonds = $1,000

Coupon rate = 4% = $1,000 × 4 ÷ 100

= 40

N = Number of Years = 5 annually = semiannually = 5 × 2

= 10 years

We assume, interest rate = 10% = 0.10

P = Coupon Rate ÷ 2 × (PVIFA,Interest Rate ÷ 2%,No. of Years) + Future Value(PVIF,Interest Rate ÷ 2%, No. of Years)

=$40 ÷ 2 × [1 - 1 ÷ (1 + Interest Rate)N] ÷ Interest Rate + Future Value[1 ÷ (1 + Interest Rate) × N]

=$40 ÷ 2 × [1-1 ÷ (1 + 0.10 ÷ 2)^10] ÷ 0.05 + $1,000 × [1 ÷ (1 + 0.10 ÷ 2)^10]

=$20 × [1 - 1 ÷ (1.05)^10] ÷ 0.05 + $1,000 × [1 ÷ (1.05)^10]

=$20 × [1 -1 ÷ 1.6288946] ÷ 0.05 + $1,000 × [1 ÷ 1.6288946]

= 420 × 7.72173 + $1,000 × 0.613913

= $154.4346 + $613.913

= $768.3476

= $768.35

But the given value is 760, so we assume interest rate = 11%

=$40 ÷ 2 × [1-1 ÷ (1 + Interest Rate)^N] ÷ Interest Rate + Future Value[1 ÷ (1 + Interest Rate)^N]

= $40 ÷ 2 × [1 - 1 ÷(1 + 0.11 ÷ 2)^10] ÷ 0.055 + $1,000 × [1 ÷ (1 + 0.11 ÷ 2)^10]

= $20 × [1 - 1 ÷ (1.055)^10] ÷ 0.055 + $1,000 × [1 ÷ (1.055)^10]

= $20 × [1 - 1 ÷ 1.70814446] ÷ 0.055 + $1000 × [1 ÷ 1.70814446]

= $20 × 7.5376255 + $1,000 × 0.5854306

= $150.75 + $585.43

= $736.18

At the Interest rate of 10% the price is more than $760 and at the Interest rate of 1% the price is less than $760. So the required rate lies in between 10% to 11%.

So required rate  

Yield To Maturity = Lower Interest Rate + (Difference Between Interest Rate) × Higher Price - Received Price ÷ Higher Price - Lower Price

= 1 0+( 11 - 10) × $768.35 - $760 ÷ $768.35 - $736.18

= 10 + 1 × $8.35 ÷ $32.17

= 10 + 0.26

= 10.26%