help with finance

Question

Palencia Paints Corporation has a target capital structure of 25% debt and 75% common equity, with no preferred stock. Its before-tax cost of debt is 13% and its marginal tax rate is 40%. The current stock price is P0 = $30.50. The last dividend was D0 = $3.50, and it is expected to grow at a 6% constant rate. What is its cost of common equity and its WACC?

Answer 1

This problem asks us to calculate two things:

1. The cost of common equity
2. The Weighted Average Cost of Capital (WACC)

We'll use the Dividend Growth Model to calculate the cost of equity and then use that result to calculate WACC.

Step 1: Identify the Information Given

Debt weight = 25% = 0.25

Common equity weight = 75% = 0.75

Before-tax cost of debt = 13% = 0.13

Tax rate = 40% = 0.40

Current stock price (P0) = $30.50

Most recent dividend (D0) = $3.50

Dividend growth rate (g) = 6% = 0.06

Step 2: Calculate the Next Expected Dividend (D1)

The Dividend Growth Model uses the next expected dividend, not the dividend that was just paid.

Formula:

D1 = D0 × (1 + g)

Substitute:

D1 = $3.50 × (1.06)

D1 = $3.71

Step 3: Calculate the Cost of Common Equity

Use the Dividend Growth Model:

Cost of Equity = (D1 / P0) + g

Substitute:

Cost of Equity = ($3.71 / $30.50) + 0.06

Cost of Equity = 0.121639 + 0.06

Cost of Equity = 0.181639

Cost of Common Equity = 18.16%

This means shareholders require an expected return of approximately 18.16% for investing in Palencia Paints Corporation.

Step 4: Calculate the After-Tax Cost of Debt

Interest expense is generally tax-deductible, so we adjust the cost of debt for the company's tax rate.

Formula:

After-Tax Cost of Debt = Before-Tax Cost of Debt × (1 - Tax Rate)

Substitute:

After-Tax Cost of Debt = 0.13 × (1 - 0.40)

After-Tax Cost of Debt = 0.13 × 0.60

After-Tax Cost of Debt = 0.078

After-Tax Cost of Debt = 7.80%

Step 5: Calculate WACC

WACC represents the weighted average cost of the company's financing sources.

Since the company has no preferred stock, we only need debt and common equity.

Formula:

WACC = (Debt Weight × After-Tax Cost of Debt) + (Equity Weight × Cost of Equity)

Substitute:

WACC = (0.25 × 0.078) + (0.75 × 0.181639)

WACC = 0.0195 + 0.136229

WACC = 0.155729

WACC = 15.57%

Final Answers

Cost of Common Equity = 18.16%

Weighted Average Cost of Capital (WACC) = 15.57%

Easy Way to Remember

The cost of common equity tells us the return shareholders expect.

WACC tells us the company's overall average financing cost after accounting for its mix of debt and equity.

For this problem:

Equity is more expensive at 18.16%.

Debt is cheaper after taxes at 7.80%.

Since the company finances 75% of its capital through equity, its WACC is closer to the cost of equity.

Important Tip:

A common mistake is using D0 instead of D1 when calculating the cost of equity.

Always calculate the next expected dividend first:

D1 = D0 × (1 + g)

Then use:

Cost of Equity = (D1 / P0) + g

This gives the correct cost of equity and WACC.