Question

You are given the task of calculating the cost of capital of Kingston Toys. The company faces a tax rate of 40%. The company has 100,000 common shares. 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%. 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 $1000. The annual coupon rate is 10%, 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 1000 zero coupon bonds. Each bond has a face value of $1000, and will mature 15 years from now and is trading at 50% of its face value. Using the information provided above, calculate the weighted average cost of capital of Kingston Toys.

No tables or spreadsheets please - need to see calculations clearly written out (by hand is preferred for clarity). Thanks

Answer 1

First of all lets calculate cost of equity

Cost of equity as per CAPM = Risk free rate of return + beta(Market Risk premium)

=5%+1.5(5%)

=5% + 7.5%

=12.5%

Now let us find price of equity shares

Year	Dividend	PVIF @12.5%	PV
1	2 +(2 x 15%)	2.30000	0.8889	2.04
2	2.3 + (2.3 x15%)	2.64500	0.7901	2.09
3	2.645 + (2.645 x 15%)	3.04175	0.7023	2.14
4	3.0418 + (3.0418 x 15%)	3.49801	0.6243	2.18
Horizon value/P4		48.97200	0.6243	30.57
Price of stock	39.03

Thus price of stock = $39.03

Horizon value = Dividend for year 5/Ke -g

g = growtrh rate = 5%

Ke= required rate = 12.5%

Dividend for year 5 = Dividend for year 4(1+g)

=3.49801(1+5%)

=3.49801(1.05)

=3.6729

Horizon value = 3.6729/12.5%-5%

=3.6729/7.5%

=48.972 $

Thus total market value of equity = No. of shares x Price per share

= 100,000 x 39.03

=39,02,740.97$

Bond 1)

Cost of Bond 1 = YTM(1-tax rate)

=12%(1-40%)

=12%(0.6)

=7.2%

Now lets calculate price of bond 1

Price of bond 1 = Interest x PVIFA(YTM%,n) + Redemption value x PVIF(YTM%,n)

Interest = 1000 x 10% x 1/2 = 50$

YTM = 12%/2 = 6%

n = no of interest payments = 10 x 2 = 20

= 50 x PVIFA(6%,20) + 1000 x PVIF(6%,20)

PVIFA(YTM%,n) = [1-(1/(1+r)^n / r ]

PVIFA(6%,20) = [ 1-(1/(1+6%)^20 / 6%)

=[1-(1/(1+0.06)^20 / 0.06]

=[1-(1/1.06)^20 /0.06]

= [1-0.3118 / 0.06]

= [ 0.6882 /0.06]

= 11.4699

PVIF(6%,20) = 1/(1+r)^n

=(1/(1+0.06)^20

=0.3118

Thus Value of bond 1 = 50 x 11.4699 + 1000 x 0.3118

= 573.49 + 311.80

=885.30 $

Thus total market value of bond 1 = No of bonds x Price per Bond

= 1000 x 885.3078

= 885300.78$

Bond 2)

First of all we need to find YTM of bond 2

YTM = Interest +(Face value -current market price/n) / (Face value + current market price/2)

Interest = 0

Face value = 1000

Current market price = 1000 x 50% =500$

n = No of year till maturity = 15

YTM = 0 +(1000-500)/15 / (1000+500)/2

=500/15 / 1500/2

=33.3333 / 750

=0.04444

Thus YTM = 4.44%

After tax YTM = 4.44%(1-tax rate)

=4.44%(1-0.4)

=4.44%(0.6)

=2.66%

Thus total market value of bond 2 = No of bonds x Price per Bond

=1000 x 500 = 500000$

Statement showing WACC

Particulars	Amount	Weight	Cost of capital	WACC
	a	b	c =axb
Equity	39,02,740.97	74%	12.5%	9.23%
Bond 1	8,85,300.78	17%	7.2%	1.21%
Bond 2	5,00,000.00	9%	2.660%	0.25%
	5288041.75			10.68%

Thus WACC = 10.68%