# Ying Imports has several bond issues outstanding, each making semiannual interest payments. The...

## Question:

Ying Imports has several bond issues outstanding, each making semiannual interest payments. The bonds are listed below.

Bond 1

Coupon Rate: 6.00%

Price Quote: 103.18

Maturity: 5 years

Face Value $45,000,000

Bond 2

Coupon Rate: 7.50%

Price Quote: 110.50

Maturity: 8 years

Face Value $40,000,000

Bond 3

Coupon Rate: 7.20%

Price Quote: 109.85

Maturity: 15.5 years

Face Value $50,000,000

Bond 4

Coupon Rate: 6.80%

Price Quote: 102.75

Maturity: 25 years

Face Value $65,000,000

If the corporate tax rate is 34%, what is the after-tax cost of the company's debt?

## Cost of debt:

The cost of debt is the indicator of the return that a company is supposed to pay to its creditors.Generally if the company has issued bond then the bond yield has been considered as the cost of debt.

Cost of debt is used to calculate the cost of capital (WACC) of the company if the it has debt as a component of total capital.

## Answer and Explanation:

We calculate the cost of debt (Kd) as the YTM

**Bond 1**

Coupon Rate: 6.00%

Price Quote: 103.18

Maturity: 5 years

Face Value $45,000,000

Considering YTM (semi-annual) = R then,

{eq}103.18 = $3*PVIFA (R\%, 10 ~payments) + $100/(1+R)^{10}......................................(1) {/eq}

Solving the equation (1) for R we have

R = 2.63%

So annual YTM = 2.63%*2 = 5.27%

Number of debt instrument = $45,000,000/$100 = 4500000

Value of debt = 4500000*103.18 = $ 464,310,000

**Bond 2**

Coupon Rate: 7.50%

Price Quote: 110.50

Maturity: 8 years

Face Value $40,000,000

Considering YTM (semi-annual) = R then,

{eq}103.18 = $3.75*PVIFA (R\%, 16 payments) + $100/(1+R)^{16} .............................(2) {/eq}

Solving the equation (2) for R we have

R = 3.49%

So annual YTM = 3.49% *2 =6.97%

Number of debt instrument = $40,000,000/$100 = 4000000

Value of debt = 4000000*110.50 = $ 442,000,000

**Bond 3**

Coupon Rate: 7.20%

Price Quote: 109.85

Maturity: 15.5 years

Face Value $50,000,000

Considering YTM (semi-annual) = R then,

{eq}109.85 = $3.6*PVIFA (R\%, 31 ~payments) + $100/(1+R)^{31} ..................(3) {/eq}

Solving the equation (3) for R we have

R = 3.10%

So annual YTM = 3.10%*2 = 6.20%

Number of debt instrument = $50,000,000/$100 = 5000000

Value of debt = 5000000*109.85 = $ 549,250,000

**Bond 4**

Coupon Rate: 6.80%

Price Quote: 102.75

Maturity: 25 years

Face Value $65,000,000

Considering YTM (semi-annual) = R then,

{eq}109.85 = $3.4*PVIFA (R\%, 50 ~payments) + $100/(1+R)^{50}...............................(4) {/eq}

Solving the equation (3) for R we have

R = 3.02%

So annual YTM = 3.02%*2 = 6.03%

Number of debt instrument = $65,000,000/$100 = 6500000

Value of debt = 6500000*102.75 = $ 667,875,000

**Calculation of cost of debt:**

Total quantum of debt {eq}= $ 464,310,000 +$ 442,000,000 +$ 549,250,000 + $ 667,875,000 = $ 2,123,435,000 {/eq}

Considering the weighted average cost of debt:

{eq}Kd =$ 464,310,000*5.27\%/$ 2,123,435,000 + $ 442,000,000*6.97\%/$ 2,123,435,000 + $ 549,250,000*6.20\%/$ 2,123,435,000 + $ 667,875,000*6.03\%/$ 2,123,435,000 {/eq}

{eq}= 6.103\% {/eq}

After tax cost of debt {eq}= 6.103\%*(1-34\%) = 4.03\% {/eq}

#### Learn more about this topic:

from Corporate Finance: Help & Review

Chapter 3 / Lesson 18