Question

Capital Structure, the cost of capital, and stock price WACC = Wd (ra) (1-T) Ws (rs) 0.40 T 0.06 0.10 Capital Structure (Debt/Assets = Wd) Beta D/E WACC Value rd rs 1.60 10% 8.0% 0.2500 8.3% 9.0% 30% 40% 10.0% 12.0% 1.0000

Answer 1

1st Column

For, D/E = 0.25/1,

D/(D+E) = 025/(0.25+1) (by componendo and dividendo)

=> Debt/Assets = 0.20 = 20%  

Similarly, for D/E = 1

D/(D+E) = Debt/Assts = 1/(1+1) = 0.5 =50%

If Debt/Assets = 10%,=> Assets/Debt = 10

=> (Debt + Equity) /Debt = 10 => 1+ E/D = 10 => D/E = 1/9 =  0.1111

Similarly , for Debt/Assets = 30%, D/E = 30/70 = 0.428571

for Debt/Assets = 40%, D/E = 40/60 = 0.6666

Unlevered Beta (all equity) = Levered Beta / {1+ (1-t) * D/E}

   = 1.6/ {1+ (1-0.4) *0.11111}

=1.6/1.06666

= 1.5

For wd =20%, Levered beta = Unlevered beta * {1+ (1-t) * D/E}

= 1.5* (1+0.6*0.25)

=1.73

For wd =30%, Levered beta = Unlevered beta * {1+ (1-t) * D/E}

= 1.5* (1+0.6*0.43)

=1.89

For wd =40%, Levered beta = Unlevered beta * {1+ (1-t) * D/E}

= 1.5* (1+0.6*0.67)

=2.1

For wd =20%, Levered beta = Unlevered beta * {1+ (1-t) * D/E}

= 1.5* (1+0.6*1)

=2.4

From CAPM equation , rs can be calculated

rs= risk free rate + beta * (market return - risk free rate)

For wd = 0 , rs = 6%+ 1.5* (10%-6%) =12.00%

For wd =10% , rs = 6%+ 1.6* (10%-6%) =12.40%

For wd = 20% , rs = 6%+ 1.725* (10%-6%) =12.90%

For wd = 30% , rs = 6%+ 1.89* (10%-6%) =13.54%   

For wd = 40% , rs = 6%+ 2.1* (10%-6%) =14.40%

For wd = 50% , rs = 6%+ 2.4* (10%-6%) =15.60%

WACC

WACC = wd*rd*(1-t) + ws*rs

= wd *rd *(1-t) + (1-wd) * rs

For wd= 0 ,WACC = 0+ 1*rs = 12% (only equity, no debt)

For wd= 10%, WACC = 0.1*8%*0.6+ 0.9*12.4% = 11.64%

For wd= 20%, WACC = 0.2*8.3%*0.6+ 0.8*12.9% = 11.316%  

For wd= 30%, WACC = 0.3*9%*0.6+ 0.7*13.54% = 11.10%

For wd= 40%, WACC = 0.4*10%*0.6+ 0.6*14.4% = 11.04%

For wd= 50%, WACC = 0.5*12%*0.6+ 0.5*15.6% = 11.40%

So, the complete table looks like

Capital Structure
Debt/Assets	Rd	D/E	Beta	rs	WACC
0	-	-	1.50	12.00%	12.00%
10.00%	8.00%	0.11	1.60	12.40%	11.64%
20.00%	8.30%	0.25	1.73	12.90%	11.32%
30.00%	9.00%	0.43	1.89	13.54%	11.10%
40.00%	10.00%	0.67	2.10	14.40%	11.04%
50.00%	12.00%	1.00	2.40	15.60%	11.40%