Several years ago the Jakob Company sold a $1,000 par value, noncallable bond that now has 20 years to maturity and a 7.00% annual coupon that is paid semiannually. The bond currently sells for $875 and the company’s tax rate is 25%. What is the component cost of debt for use in the WACC calculation? Do not round your intermediate calculations.

Based on the information given the component cost of debt for use in the WACC calculation is 6.7%.

First step is to calculate the semi-annual yield to maturity using financial calculator

Rate=(Nper,-pmt,pv.fv)

Where:

Nper=20 years×2=40

Pmt=-$1,000×7%/2=-35

Pv=$825

Fv=$1,000

Hence:

Rate=4.44%

Second step is to calculate the after tax annual yield or cost of debt using this formula

After tax cost of debt=(Cost of debt×2)×(1-Tax rate)

Let plug in the formula

After tax cost of debt=(4.44%×2)×(1-25%)

After tax cost of debt=8.88%×75%

After tax cost of debt=6.66%

After tax cost of debt=6.7%(Approximately)

Inconclusion the component cost of debt for use in the WACC calculation is 6.7%.

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The Component cost of debt for use in the WACC calculation will be 6.22%

Explanation:

Component cost of debt for use in the WACC calculation

=> The cost of debt for use in the WACC calculation is the after-tax Yield to maturity of the Bond

=> The Yield to maturity (YTM) of the Bond is the discount rate at which the Bond’s price equals to the present value of the coupon payments plus the present value of the Face Value/Par Value. YTM is also the estimated annual rate of return expected by the bondholders for the bond assuming that the they hold the Bonds until it’s maturity period/date.

=> YTM can be calculated using financial calculator

Set the below figures into the financial calculator to find out the Yield to Maturity of the Bond.

Variable: Par Value/Face Value of the Bond [$1,000]

Financial Calculator Key: FV

Figure : 1000

Variable: Coupon Amount [$1,000 x 7.00% x ½]

Financial Calculator Key: PMT

Figure : 35

Variable: Market Interest Rate or Yield to maturity on the Bond

Financial Calculator Key: 1/Y

Figure : ?

Variable: Maturity Period/Time to Maturity [20 Years x 2]

Financial Calculator Key: N

Figure : 40

Variable: Bond Price/Current market price of the Bond [-$875]

Financial Calculator Key: PV

Figure : -875

After entering the above keys in the financial calculator, we get the semi-annual yield to maturity on the bond (1/Y)

The semi-annual Yield to maturity (1/Y) = 4.145%.

∴The annual Yield to Maturity of the Bond = 4.145% x 2 = 8.29%

The after-tax cost of debt

The firm’s after-tax cost of debt on the Bond is the after-tax Yield to maturity (YTM)

After-tax cost of debt = Annual Yield to maturity on bond x (1 – Tax Rate)

After-tax cost of debt = 8.29% x (1 – 0.25)

After-tax cost of debt = 8.29% x 0.75

After-tax cost of debt = 6.22%

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