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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 can use the formula for the **levered cost of equity** under the Modigliani-Miller framework, which accounts for the tax shield on debt:

\[
r_e = r_u + \left( \frac{D}{E} \right) \times (r_u - r_d) \times (1 - T)
\]

Where:

- \( r_e \) = cost of equity with leverage
- \( r_u \) = unlevered cost of equity (WACC when there's no debt)
- \( \frac{D}{E} \) = debt-to-equity ratio
- \( r_d \) = cost of debt
- \( T \) = tax rate (if not given, we assume 0%)

### Step 1: Find the unlevered cost of equity ( \( r_u \) )
Since the company currently has no debt, the unlevered cost of equity equals the WACC. Therefore:

\[
r_u = 8.8\%
\]

### Step 2: Calculate the debt-to-equity ratio ( \( \frac{D}{E} \) )
We are given the debt-to-value ratio \( \frac{D}{V} = 8.4\% \), and we know that:

\[
\frac{D}{V} = \frac{D}{D+E}
\]

So to get the debt-to-equity ratio \( \frac{D}{E} \), we can rearrange the equation:

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

Substituting the value for \( \frac{D}{V} \):

\[
\frac{D}{E} = \frac{0.084}{1 - 0.084} = \frac{0.084}{0.916} = 0.0917
\]

### Step 3: Apply the formula for levered cost of equity ( \( r_e \) )
Now we can substitute all the values into the formula:

\[
r_e = 8.8\% + (0.0917) \times (8.8\% - 6.2\%)
\]

Simplifying:

\[
r_e = 8.8\% + (0.0917) \times (2.6\%) = 8.8\% + 0.2384\%
\]

\[
r_e = 9.04\%
\]

Thus, the cost of equity if Microsoft takes on the average industry debt is **9.04%**.

Would you like any further details or clarification?

---

### Related Questions:
1. What effect does debt have on a company's WACC?
2. How does the Modigliani-Miller theorem impact the capital structure decision?
3. Can a company reduce its WACC by taking on more debt?
4. What is the relationship between debt and equity in determining cost of capital?
5. How does tax influence the benefit of taking on debt?

### Tip:
Incorporating debt into a company's capital structure can reduce the overall WACC up to a point, as debt is generally cheaper than equity due to the tax shield. However, too much debt increases financial risk, which can increase 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.)

Learn how to calculate Microsoft's cost of equity using the levered cost of equity formula, assuming the company takes on the average debt-to-value ratio in the software industry. This finance problem involves WACC, debt-to-equity ratio, and the Modigliani-Miller theorem. Suitable for corporate finance students.

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