Question

Apple Corporation had no debt on its balance sheet in 2008 , but paid $2 billion in taxes. Suppose Apple were to issue fufficient debt to reduce its taxes by $1.2 billion per year permanently. Assume Apple's marginal corporate tax rate is 30% and its borrowing cost is 7.4%. a. If Apple's investors do not pay personal taxes (because they hold their Apple stock in tax free retirement accounts), how much value would be created (what is the value of the tax shield)? b. How does your answer change if instead you assume that Apple's investors pay a 15% tax rate on income from equity and a 35% tax rate on interest income? a. If Apple's investors do not pay personal taxes (because they hold their Apple stock in tax free retirement accounts), how much value would be created (what is the value of the tax shield)? If Apple's investors do not pay personal taxes (because they hold their Apple stock in tax free retirement accounts), the value of the tax shield is $ billion. (Round to two decimal places.)

Answer 1

o calculate the value of the tax shield, we need to determine the present value of the tax savings from issuing debt.

a. Assuming Apple's marginal corporate tax rate is 30% and its borrowing cost is 7.4%, we can calculate the value of the tax shield as follows:

Tax savings per year = $1.2 billion

Tax rate = 30%

Present value factor of perpetual cash flow = 1 / (1 - tax rate) = 1 / (1 - 0.30) = 1 / 0.70 ≈ 1.4286

Value of tax shield = Tax savings per year * Present value factor of perpetual cash flow

= $1.2 billion * 1.4286

≈ $1.714 billion (rounded to two decimal places)

Therefore, if Apple's investors do not pay personal taxes, the value of the tax shield is approximately $1.714 billion.

b. If instead we assume Apple's investors pay a 15% tax rate on income from equity and a 35% tax rate on interest income, we need to adjust the calculations.

After-tax cost of debt = Pre-tax cost of debt * (1 - tax rate on interest income)

= 7.4% * (1 - 0.35)

≈ 7.4% * 0.65

≈ 4.81%

The present value factor of perpetual cash flow would now be 1 / (1 - tax rate on equity) = 1 / (1 - 0.15) = 1 / 0.85 ≈ 1.1765.

Value of tax shield = Tax savings per year * Present value factor of perpetual cash flow

= $1.2 billion * 1.1765

≈ $1.412 billion (rounded to two decimal places)

Therefore, if Apple's investors pay a 15% tax rate on income from equity and a 35% tax rate on interest income, the value of the tax shield would be approximately $1.412 billion.

Step-by-step explanation:

Answer 2

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.