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:
Where:
- is the new cost of equity (which we need to calculate).
- is the unlevered cost of equity (the original cost of equity when the firm was 100% equity-financed), which is 15%.
- is the cost of debt, which is 8%.
- is the debt-to-equity ratio (the firm will have 28% debt and 72% equity, so ).
Let's calculate the new cost of equity.
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:
- How does Modigliani-Miller Proposition II affect capital structure decisions?
- How does an increase in the proportion of debt affect the cost of equity?
- What happens to the WACC when a firm introduces debt?
- How does the risk of bankruptcy influence the decision to issue debt?
- 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
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