I am not sure how to make the balance sheet and calculate the weighted averages?

Question

I am not sure how to make the balance sheet and calculate the weighted averages?

A firm’s current balance sheet is as follows:
Assets $100 Debt $10
Equity $90
a. What is the firm’s weighted-average cost of capital at various combinations of
debt and equity, given the following information?
Debt/Assets After-Tax Cost of Debt Cost of Equity Cost of Capital
0% 8% 12% ?
10 8 12 ?
20 8 12 ?
30 8 13 ?
40 9 14 ?
50 10 15 ?
60 12 16 ?

Construct a pro forma balance sheet that indicates the firm’s optimal capital
structure. Compare this balance sheet with the firm’s current balance sheet.
What course of action should the firm take?
Assets $100 Debt $?
Equity $?

Explanation / Answer

The way the formula works is:

1. If debt = 0%, then equity = 100%, cost of debt = 8%, cost of equity = 12%, then the weighted cost of capital is 0% * 8% + 100% * 12% = 12% or .120

2. If debt = 10%, then equity = 90%, cost of debt = 8%, cost of equity = 12%, then the weighted cost of capital is 10% * 8% + 90% * 12% = 11.6% or .116

3. If debt = 20%, then equity = 80%, cost of debt = 8%, cost of equity = 12%, then the weighted cost of capital is 20% * 8% + 80% * 12% = 11.2% or .112

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