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.)

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:

\[
r_E = r_U + (r_U - r_D) \cdot \frac{D}{E}
\]

Where:
- \( r_E \) is the new cost of equity (which we need to calculate).
- \( r_U \) is the unlevered cost of equity (the original cost of equity when the firm was 100% equity-financed), which is 15%.
- \( r_D \) is the cost of debt, which is 8%.
- \( \frac{D}{E} \) is the debt-to-equity ratio (the firm will have 28% debt and 72% equity, so \( \frac{D}{E} = \frac{28}{72} \)).

Let's calculate the new cost of equity.

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

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.

Your firm is financed 100% with equity and has a cost of equity capital of 15%. You are considering your first debt issue, which would change your capital structure to 28% debt and 72% equity. If your cost of debt is 8%, what will be your new cost of equity? Assume no change in your firm's WACC due to the change in capital structures. The new cost of equity is ____%. (Round to two decimal places.)

Learn how to calculate the new cost of equity when a firm introduces debt into its capital structure using Modigliani-Miller Proposition II. This problem covers core finance concepts such as capital structure, cost of capital, and the debt-to-equity ratio. Suitable for undergraduate finance students.

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