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Part 1

Suppose Microsoft has no debt and a WACC of 

8.8 %8.8%. 

The average​ debt-to-value ratio for the software industry is 

8.4 %8.4%. 

What would be its cost of equity if it took on the average amount of debt for its industry at a cost of debt of 

6.2 %6.2%​?

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Part 1

The cost of equity is 

enter your response here​%. 

​ (Round to two decimal​ places.)

To solve this problem, we'll need to use the formula that adjusts the cost of equity using the Modigliani-Miller theorem with taxes, which accounts for the impact of taking on debt. The formula for the leveraged cost of equity \( r_E \) when a firm adds debt is:

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

Where:
- \( r_E \) = Leveraged cost of equity
- \( r_U \) = Unleveraged cost of equity (equal to the WACC for a company with no debt)
- \( r_D \) = Cost of debt
- \( D \) = Value of debt
- \( E \) = Value of equity
- \( \frac{D}{V} \) = Debt-to-value ratio (where \( V = D + E \))

Given:
- \( r_U = 8.8\% \) (since Microsoft has no debt, its WACC equals the unleveraged cost of equity)
- \( r_D = 6.2\% \) (cost of debt)
- \( \frac{D}{V} = 8.4\% \)

Now, let's solve for the leveraged cost of equity \( r_E \).

First, express \( \frac{D}{E} \) as:

\[
\frac{D}{E} = \frac{D}{V - D} = \frac{0.084}{1 - 0.084}
\]

Now we can compute the leveraged cost of equity.

The cost of equity, if Microsoft took on the average amount of debt for its industry, would be **9.04%**.

Do you want more details or have any questions?

Here are 5 related questions to further explore:
1. How does the Modigliani-Miller theorem apply in a real-world context?
2. What factors affect a company's weighted average cost of capital (WACC)?
3. How does taking on debt influence a firm's cost of equity?
4. What are the implications of having a low vs. high debt-to-value ratio?
5. How does the cost of debt compare to the cost of equity in different industries?

**Tip:** Increasing debt can lower WACC up to a point due to tax shields but also raises financial risk, increasing the cost of equity.

Suppose Microsoft has no debt and a WACC of 8.8%. The average debt-to-value ratio for the software industry is 8.4%. What would be its cost of equity if it took on the average amount of debt for its industry at a cost of debt of 6.2%? The cost of equity is __%. (Round to two decimal places.)

This problem explores how to calculate Microsoft's cost of equity if it takes on the average debt of its industry, using the WACC and Modigliani-Miller Theorem. The unleveraged WACC is 8.8%, the cost of debt is 6.2%, and the debt-to-value ratio is 8.4%. Learn how to apply financial formulas to solve this step-by-step.

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