Question

You are given the task of calculating the cost of capital of N Corp. The company faces a tax rate of 40%. The company has 200,000 common shares and 50,000 preferred shares outstanding. Each preferred share has a par value of $50, and is currently priced at 90% of the par value. The preferred shares are paying dividends that total 5% of the par value. You estimate that the beta of the common stock is 1.5. The equity market risk premium is estimated to be 5%, and the risk-free rate is 5%. The company has just paid a dividend of $2 per share. You expect that the dividends will grow at a rate of 15% until Year 4. After Year 4, the dividends are expected to grow at a constant rate of 5% forever. You decide to employ the CAPM approach to calculate the cost of equity.

The company has two different debt issues that are outstanding. The first issue consists of 1,000 semi-annual coupon bonds. Each bond has a face value of $3,000. The annual coupon rate is 12%, and the bonds are currently trading at a YTM that equals 12%. The bonds will mature 10 years from now. The second issue consists of 1,000 zero coupon bonds. Each bond has a face value of $1,000, and will mature 15 years from now. The zero-coupon bonds are trading at 50% of their face value.  

Calculate the weighted average cost of capital

Answer 1

Calculation of WACC :

Cost of Debt 1 = YTM * (1 - Tax rate)

= 12% (1 - 0.40)

= 7.2%

Given that bonds are trading at YTM of 12 % which means that bonds are trading at par. When coupon rate is equal to yield rate bonds are trading at par.

Cost of Zero Coupon Bond

Using Financial Calculator

=RATE(nper,pmt,pv,fv)

where nper is Number of years i.e 15

pmt is Interest payment i.e 0 (It is zero coupon bond)

pv is Current Market Price

= - 500 (1000 * 50%)

Note : pv should be taken as negative.

fv is face value i.e 1000

=RATE(15,0,-500,1000)

therefore ,Before tax cost of Debt is 4.72941%

After tax cost of Debt = 4.72941% * (1 - Tax rate )

= 4.72941% * (1 - 0.40)

= 2.83765%

Calculation of Cost of Preferred Stock

Cost of Preferred Stock = Annual Dividend / Current Market Price

= (50 * 5%) / (50 * 90%)

= 2.5 / 45

=0.05555 or 5.56%

Calculation of Cost of Common Equity

Cost of Common Equity =Risk free rate + Beta * Market Risk Premium

= 5% + 1.5 * 5%

= 12.5%

Market Value of Debt 1 = Number of Bonds * Price per Bond

= 1000 * 3000

= 3,000,000

Given that bonds are trading at YTM of 12 % which means that bonds are trading at par. When coupon rate is equal to yield rate bonds are trading at par.

Market Value of Zero coupon Bond = Number of Bonds * Price per Bond

= 1000 * (1000 * 50%)

= 500,000

Market Value of Equity = Number of Equity shares * Price per share*

= 200,000 * 48.972175

= 9,794,435

*Price per share

Year	Dividend / Horizon Value	PVF @12.5%	Present Value of Dividend / Horizon Value
0	2	1
1	2.3 (2 * 1.19)	0.888888889	2.044444444
2	2.645 (2.3 * 1.19)	0.790123457	2.089876543
3	3.04175 (2.645 * 1.19)	0.702331962	2.136318244
4	3.4980125 (3.04175 * 1.19)	0.624295077	2.183791983
4(Horizon Value)	48.972175 (Working Note)	0.624295077	30.57308776
		P0	39.02751898

Working Note : Price per share = Expected Dividend / (Cost of Equity - Growth rate)

= [3.4980125 * (1 + 0.05)] / (0.125 - 0.05)

= 48.972175

Market Value of Preferred Stock = Number of Prefered Stock * Price per share

= 50,000 * (50 * 90%)

= 50000 * 45

= 2,250,000

Total Market Value = Market Value of Debt 1 + Market Value of Zero coupon Bond + Market Value of Equity + Market Value of Preferred Stock

= 3,000,000 + 500,000 + 9,794,435 + 2,250,000

= 15,544,435

WACC = (Cost of After tax Debt * Weight of Debt) +(Cost of Zero Coupon Bond * Weight of zero coupon Bond) + (Cost of Preferred Stock * Weight of Preferred Stock) + ( Cost of Equity * Weight of Equity)

= [7.2% * (3,000,000 / 15544435)] + [2.83765% + (500000 / 15544435) ] + [5.555555% * (2250000 / 15544435)] + [12.5% * (9794435 / 15544435)]

=1.3896% + 0.09126%+0.80415% + 7.8762%

= 10.16%

Note : Weights = Market Value / Total Market Value