By NEAS - 11/6/2022 2:13:22 PM
Corpfin Mod 18: Weighted average cost of capital and debt refinancing: practice exam problem
The corporate tax rate is 33%. Initially, at a 24% debt to value ratio, the cost of debt capital is 4.82% per annum and the weighted average cost of capital is 8.55% per annum. After refinancing to a 49% debt to value ratio, the cost of debt capital is 7.35% per annum.
Question 18.1: Initial equity to value ratio
At a 24% debt to value ratio, what is the equity to value ratio?
Answer 18.1: The equity to value ratio = 1 – the debt to value ratio = 1 – 24% = 76%.
Question 18.2: Initial cost of equity capital
What is the cost of equity capital at a 24% debt to value ratio?
At a 24% debt-to-value ratio, the firm’s cost of debt capital rD is 4.82% per annum, the corporate tax rate is 33%, the equity to value ratio = 1 – 24% = 76%, and the weighted average cost of capital is 8.55% per annum, so 24% × 4.82% × (1 – 33%) + 76% × rE = 8.55% ➾
rE = [ 8.55% – 24% × 4.82% × (1 – 33%) ] / 76% = 10.23%
Question 18.3: Opportunity cost of capital with all equity financing
What is the opportunity cost of capital with all equity financing?
Answer 18.3: The opportunity cost of capital with all equity financing is the weighted average cost of capital with no debt tax shield:
opportunity cost of capital with all equity financing = 24% × 4.82% + 76% × 10.23% = 8.93%
Question 18.4: Refinanced cost of equity capital
What is the cost of equity capital at a 49% debt to value ratio?
Answer 18.4: After refinancing to a 49% debt to value ratio, the cost of debt capital is 7.35% per annum, the equity to value ratio is 1 – 49% = 51%, and the return on equity capital is rE. The opportunity cost of capital with all equity financing is the WACC with no debt tax shield is 49% × 7.35% + 51% × rE = 8.93%, so the return on equity capital is
rE = (8.93% – (49% × 7.35%) ) / (51%) = 10.45%
Question 18.5: Weighted average cost of capital
What is the after-tax weighted average cost of capital at a 49% debt to value ratio?
Answer 18.5: The after-tax weighted average cost of capital at a 49% debt to value ratio is
49% × 7.35% × (1 – 33%) + 51% × 10.45% = 7.74%
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