Math Problem Statement

Ans

If pre-tax cost of debt is 10.95%, cost of equity is 14.75% and tax rate is 25.17%, estimate the weighted average cost of capital assuming debt to equity ratio of 0.56.

Solution

The question in the image asks to calculate the Weighted Average Cost of Capital (WACC) based on the given parameters:

  • Pre-tax cost of debt = 10.95%
  • Cost of equity = 14.75%
  • Tax rate = 25.17%
  • Debt to equity ratio = 0.56

WACC Formula:

WACC=(EE+D×Re)+(DE+D×Rd×(1Tc))WACC = \left( \frac{E}{E + D} \times Re \right) + \left( \frac{D}{E + D} \times Rd \times (1 - Tc) \right) Where:

  • EE = Market value of equity
  • DD = Market value of debt
  • ReRe = Cost of equity
  • RdRd = Pre-tax cost of debt
  • TcTc = Tax rate
  • Debt to equity ratio DE=0.56\frac{D}{E} = 0.56

We can express the weights of debt and equity in terms of the debt-to-equity ratio: DE+D=D/E1+D/E\frac{D}{E + D} = \frac{D/E}{1 + D/E} EE+D=11+D/E\frac{E}{E + D} = \frac{1}{1 + D/E}

Let's now calculate this step-by-step.The Weighted Average Cost of Capital (WACC) is approximately 12.40%.

This matches option b in the question.

Would you like further details or have any other questions?

Here are five related questions for further practice:

  1. How does a higher debt-to-equity ratio affect the WACC?
  2. Why is the cost of debt adjusted for taxes in the WACC formula?
  3. What happens to the WACC if the tax rate increases?
  4. How would WACC change if the cost of equity increases?
  5. Why is WACC important for capital budgeting decisions?

Tip: A lower WACC generally indicates a cheaper cost of funding, making more investment opportunities viable for a company.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Corporate Finance
Weighted Average Cost of Capital (WACC)
Tax Impact on Debt
Debt-to-Equity Ratio

Formulas

WACC = (E / (E + D) × Re) + (D / (E + D) × Rd × (1 - Tc))
Debt to equity ratio: D/E = 0.56
E / (E + D) = 1 / (1 + D/E)
D / (E + D) = (D/E) / (1 + D/E)

Theorems

-

Suitable Grade Level

Undergraduate Finance/Business School