Hi Mark!
We can solve this problem using the Weighted Average Cost of Capital (WACC) formula. The key is determining whether the company needs to issue new common stock or can finance its equity portion entirely through retained earnings.
Step 1: Identify the given information
The company needs to raise $85,000.
Its capital structure consists of:
Debt = 60%
Preferred stock = 10%
Common equity = 30%
The component costs are:
Cost of debt = 5%
Cost of preferred stock = 7%
Cost of new common equity = 13%
Cost of retained earnings = 11%
Marginal tax rate = 30%
Available retained earnings = $26,000
Step 2: Calculate the amount needed from each financing source
The company wants to maintain its existing capital structure.
Therefore, we multiply the $85,000 financing requirement by each capital structure percentage.
Debt financing:
$85,000 × 0.60 = $51,000
Preferred stock financing:
$85,000 × 0.10 = $8,500
Common equity financing:
$85,000 × 0.30 = $25,500
The company needs $25,500 in common equity financing.
However, it expects to generate $26,000 in retained earnings.
Since $26,000 > $25,500, the company has enough retained earnings to cover its entire common equity requirement.
Therefore, it does not need to issue new common stock.
This means we use the 11% cost of retained earnings rather than the 13% cost of new equity.
Step 3: Calculate the after-tax cost of debt
Interest on debt is generally tax-deductible, so we must adjust the cost of debt for taxes.
Formula:
After-tax cost of debt = Cost of debt × (1 - Tax rate)
Substitute:
After-tax cost of debt = 5% × (1 - 0.30)
After-tax cost of debt = 5% × 0.70
After-tax cost of debt = 3.5%
Step 4: Calculate the Weighted Average Cost of Capital (WACC)
The formula is:
WACC = (Weight of debt × After-tax cost of debt) + (Weight of preferred stock × Cost of preferred stock) + (Weight of common equity × Cost of retained earnings)
Substitute the values:
WACC = (0.60 × 0.035) + (0.10 × 0.07) + (0.30 × 0.11)
Calculate each component:
Debt contribution:
0.60 × 0.035 = 0.021
Preferred stock contribution:
0.10 × 0.07 = 0.007
Common equity contribution:
0.30 × 0.11 = 0.033
Add them together:
WACC = 0.021 + 0.007 + 0.033
WACC = 0.061
WACC = 6.10%
Step 5: Check the retained earnings breakpoint
The retained earnings breakpoint tells us how much total financing the company can raise before it must issue new common equity.
Formula:
Retained earnings breakpoint = Available retained earnings / Common equity weight
Substitute:
Breakpoint = $26,000 / 0.30
Breakpoint = $86,666.67
Since the company only needs $85,000, it remains below the breakpoint.
Therefore, the company can finance the entire purchase without issuing new common stock.
If the company needed to raise more than $86,666.67, its marginal cost of capital would increase because it would need to use new equity at 13%.
The WACC above that breakpoint would be:
WACC = (0.60 × 0.035) + (0.10 × 0.07) + (0.30 × 0.13)
WACC = 0.021 + 0.007 + 0.039
WACC = 0.067
WACC = 6.70%
Final Answer
The company's marginal cost of capital for raising $85,000 is 6.10%.
The company needs $25,500 in common equity, and it has $26,000 available in retained earnings. Therefore, it can use retained earnings at 11% instead of issuing new equity at 13%.
Its marginal cost of capital remains 6.10% because the required financing is below the retained earnings breakpoint of $86,666.67.
Key Takeaway: Always check whether retained earnings are sufficient before using the cost of new common equity in a marginal cost of capital calculation.
I hope this helps!
