Answer and Explanation:
To calculate the value of the tax shield for Apple Corporation, we need to determine the present value of the tax savings generated by issuing debt.
a. If Apple's investors do not pay personal taxes, the tax shield value can be calculated as follows:
1. Calculate the annual tax savings: $1.2 billion (tax reduction per year).
2. Apply the marginal corporate tax rate of 30% to the annual tax savings: 0.30 * $1.2 billion = $0.36 billion.
3. Calculate the present value of the tax shield using the borrowing cost of 7.4% as the discount rate. We can use the perpetuity formula:
Tax Shield Value = Annual Tax Savings / Discount Rate
Tax Shield Value = $0.36 billion / 0.074 (7.4% expressed as a decimal) = $4.86 billion.
Therefore, if Apple's investors do not pay personal taxes, the value of the tax shield would be $4.86 billion.
b. If instead we assume that Apple's investors pay a 15% tax rate on income from equity and a 35% tax rate on interest income, the tax shield value calculation would be different.
1. Calculate the after-tax cost of debt: borrowing cost * (1 - tax rate on interest income).
After-tax cost of debt = 7.4% * (1 - 0.35) = 4.81%.
2. Calculate the annual tax savings using the new after-tax cost of debt:
Annual tax savings = $1.2 billion * (1 - tax rate on interest income)
Annual tax savings = $1.2 billion * (1 - 0.35) = $0.78 billion.
3. Apply the marginal corporate tax rate of 30% to the annual tax savings:
0.30 * $0.78 billion = $0.234 billion.
4. Calculate the present value of the tax shield using the new after-tax cost of debt as the discount rate:
Tax Shield Value = Annual Tax Savings / Discount Rate
Tax Shield Value = $0.234 billion / 0.0481 (4.81% expressed as a decimal) = $4.86 billion.
Therefore, even if Apple's investors pay personal taxes, the value of the tax shield would still be $4.86 billion. The tax rates of the investors do not affect the value of the tax shield.