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.