Suppose Microsoft has no debt and a WACC of 

8.9 %8.9%. 

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

7.5 %7.5%. 

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 

5.7 %5.7%​?

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Part 1

The cost of equity is 

enter your response here​%. 

​ (Round to two decimal​ places.)

To calculate Microsoft's cost of equity if it took on the average amount of debt for its industry, we can use the **WACC formula** and solve for the new cost of equity \(r_E\) when debt is introduced.

The formula for the Weighted Average Cost of Capital (WACC) is:

\[
\text{WACC} = \frac{D}{V} \cdot r_D \cdot (1 - T_c) + \frac{E}{V} \cdot r_E
\]

Where:
- \( \text{WACC} \) = Weighted Average Cost of Capital = 8.9% = 0.089
- \( \frac{D}{V} \) = Debt-to-value ratio = 7.5% = 0.075
- \( \frac{E}{V} \) = Equity-to-value ratio = \(1 - \frac{D}{V}\) = 1 - 0.075 = 0.925
- \( r_D \) = Cost of debt = 5.7% = 0.057
- \( r_E \) = Cost of equity (to be calculated)
- \( T_c \) = Corporate tax rate (which we will assume is 0 since it's not provided).

The WACC formula simplifies to:

\[
0.089 = 0.075 \cdot 0.057 + 0.925 \cdot r_E
\]

Now, we can solve for \(r_E\).

### Step-by-step calculation:
1. Calculate the debt component of the WACC:
\[
0.075 \cdot 0.057 = 0.004275
\]

2. Substitute this value into the WACC equation:
\[
0.089 = 0.004275 + 0.925 \cdot r_E
\]

3. Subtract 0.004275 from both sides:
\[
0.089 - 0.004275 = 0.925 \cdot r_E
\]
\[
0.084725 = 0.925 \cdot r_E
\]

4. Divide both sides by 0.925 to isolate \(r_E\):
\[
r_E = \frac{0.084725}{0.925} \approx 0.0916
\]

So, the cost of equity is approximately **9.16%**.

---

Would you like further details on any part of this process, or have any questions? Here are 5 related questions you can explore:

1. How does taking on debt affect a company's WACC?
2. What happens to the cost of equity as the debt-to-value ratio increases?
3. How is the corporate tax rate typically factored into WACC?
4. What is the Modigliani-Miller theorem in relation to capital structure?
5. How can companies optimize their capital structure to minimize WACC?

**Tip:** The cost of equity increases when debt is added because equity holders take on more risk, given that debt holders have priority in case of bankruptcy.

Suppose Microsoft has no debt and a WACC of 8.9%. The average debt-to-value ratio for the software industry is 7.5%. 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 5.7%? (Round to two decimal places.)

Explore how to calculate Microsoft's cost of equity if it assumes the average debt-to-value ratio for its industry at a cost of debt of 5.7%, with a WACC of 8.9%. Includes key finance concepts like the WACC formula, debt-to-equity ratios, and a step-by-step solution.

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