Math Problem Statement

Your firm is financed​ 100% with equity and has a cost of equity capital of

1515​%.

You are considering your first debt​ issue, which would change your capital structure to

2828​%

debt and

7272​%

equity. If your cost of debt is

88​%,

what will be your new cost of​ equity? Assume no change in your​ firm's WACC due to the change in capital structures.

Question content area bottom

Part 1

The new cost of equity is

enter your response here​%.

​(Round to two decimal​ places.)

Solution

To solve this, we can use the following relationship from the Modigliani-Miller Proposition II (without taxes), which tells us how the cost of equity changes as a company introduces debt into its capital structure:

rE=rU+(rUrD)DEr_E = r_U + (r_U - r_D) \cdot \frac{D}{E}

Where:

  • rEr_E is the new cost of equity (which we need to calculate).
  • rUr_U is the unlevered cost of equity (the original cost of equity when the firm was 100% equity-financed), which is 15%.
  • rDr_D is the cost of debt, which is 8%.
  • DE\frac{D}{E} is the debt-to-equity ratio (the firm will have 28% debt and 72% equity, so DE=2872\frac{D}{E} = \frac{28}{72}).

Let's calculate the new cost of equity.

rE=15%+(15%8%)2872r_E = 15\% + (15\% - 8\%) \cdot \frac{28}{72}

Now, I'll compute the final result.The new cost of equity is 17.72%.

Would you like further details or clarification on any part of this calculation?

Here are five related questions to expand on this:

  1. How does Modigliani-Miller Proposition II affect capital structure decisions?
  2. How does an increase in the proportion of debt affect the cost of equity?
  3. What happens to the WACC when a firm introduces debt?
  4. How does the risk of bankruptcy influence the decision to issue debt?
  5. What are the tax implications when using debt in a firm's capital structure?

Tip: When increasing debt in a firm's capital structure, the cost of equity tends to rise because shareholders bear more risk, compensating for the additional financial leverage.

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Math Problem Analysis

Mathematical Concepts

Corporate Finance
Cost of Capital
Capital Structure
Modigliani-Miller Proposition II

Formulas

New Cost of Equity: r_E = r_U + (r_U - r_D) * (D/E)
Debt-to-Equity Ratio: D/E = Debt / Equity

Theorems

Modigliani-Miller Proposition II

Suitable Grade Level

Undergraduate Finance