Question

3) (17 Marks) As a recent MSVU grad, you have been hired by Barrington Inc. to evaluate its target capital structure. The firm is currently all equity financed and is considering issuing debt and using the proceeds to repurchase some of its common stock. Through an analysis of the firm, you determine that the firm is not growing, and all earnings are paid out as cash dividends. The tax rate is 40%, the current risk-free rate is 6% and the return on the TSX (the market) is 12%. Your boss asks you to determine the impact of changing the firms' capital structure on the firm's overall weighted average cost of capital. To analyze the impact, you decide to provide your boss with the following schedule. Complete the schedule (a-f). What is the optimal proportion of debt? Proportion of Debt O 1 0. 0.2 0.3 0.4 8 Before tax Cost of debt 8% % 8.50% I 10% Beta 0.8 0.9 1 1.1 1.25 Cost of Equity 10.80% a) 12% c) 1 13.50% WACC 10.80% b) 10.62% d) 10.50% 9%

Answer 1

Proportion of debt	Before tax cost of debt	Beta	Cost of equity	WACC
0	8.00%	0.8	10.80%	10.80%
0.1	8.00%	0.9	11.40%	10.74%
0.2	8.50%	1	12.00%	10.62%
0.3	9.00%	1.1	12.60%	10.44%
0.4	10.00%	1.25	13.50%	10.50%
0.5	11.50%	1.4	14.40%	10.65%
0.6	13.00%	1.7	16.20%	11.16%

W	X		Y		Z	W * Y	X * Z
Proportion of debt	Proportion of Equity (1 - proportion of debt	Before tax cost of debt	Post tax cost of debt (pre tax cost of debt * (1-tax rate)	Beta	Cost of equity (Rf+(Beta*(Rm - Rf))			WACC
0.1	0.9	8.00%	4.80%	0.9	11.40%	0.48%	10.26%	10.74%
0.3	0.7	9.00%	5.40%	1.1	12.60%	1.62%	8.82%	10.44%
0.5	0.5	11.50%	6.90%	1.4	14.40%	3.45%	7.20%	10.65%

W	X		Y		Z	W * Y	X * Z
Proportion of debt	Proportion of Equity (1 - proportion of debt	Before tax cost of debt	Post tax cost of debt (pre tax cost of debt * (1-tax rate)	Beta	Cost of equity (Rf+(Beta*(Rm - Rf))			WACC
0.1	=1-0.1	8.00%	=8%*(1-40%)	0.9	=6%+(0.9*(12%-6%))	=0.1*4.8%	=0.9*11.4%	=0.48%+10.26%
0.3	=1-0.3	9.00%	=9%*(1-40%)	1.1	=6%+(1.1*(12%-6%))	=0.3*5.4%	=0.7*12.6%	=1.62%+8.82%
0.5	=1-0.5	11.50%	=11.5%*(1-40%)	1.4	=6%+(1.4*(12%-6%))	=0.5*6.9%	=0.5*14.4%	=3.45%+7.2%

Answers:
a	11.40%	b	10.74%
c	12.60%	d	10.44%
e	14.40%	f	10.65%

WACC is minimized at debt proportion 0.3 i.e. 10.44% is the least WACC among all other options.