# Tax shield

A tax shield is the reduction in income taxes that results from taking an allowable deduction from taxable income. For example, because interest on debt is a tax-deductible expense, taking on debt creates a tax shield. Since a tax shield is a way to save cash flows, it increases the value of the business, and it is an important aspect of business valuation.

## Example

### Case A

• Consider one unit of investment that costs \$1,000 and returns \$1,100 at the end of year 1, i.e. a 10% return on investment before taxes.
• Now assume tax rate of 20%.
• If an investor pays \$1,000 of capital, at the end of the year, he will have (\$1,000 return of capital, \$100 income and –\$20 tax) \$1,080. He earned net income of \$80, or 8% return on capital.

The concept was originally added to the methodology proposed by Franco Modigliani and Merton Miller for the calculation of the weighted average cost of capital of a corporation.

### Case B

• Consider the investor now has an option to borrow \$4,000 at 8% interest rate.
• If the investor still pays \$1,000 of his initial equity capital, in addition to borrowing \$4,000 at the terms above, the investor can purchase 5 units of investment for \$5000 total.
• At the end of the year, he will have: (\$5,000 return of capital, \$500 revenue (due to the 10% return on each unit of investment), –\$4,000 repayment of debt, –\$320 interest payment, and \$(500-320)*20%= \$36 tax). Therefore, he is left with \$1,144. He earned net income of \$144, or 14.4% return on his \$1000 initial equity capital.

The reason that he was able to earn additional income is because the cost of debt (i.e. 8% interest rate) is less than the return earned on the investment (i.e. 10%). The 2% difference makes income of \$80 and another \$100 is made by the return on equity capital. Total income becomes \$180 which becomes taxable at 20%, leading to the net income of \$144.

### Value of the Tax Shield

In most business valuation scenarios, it is assumed that the business will continue forever. Under this assumption, the value of the tax shield is: (interest bearing debt) x (tax rate).

Using the above examples:

• Assume Case A brings after-tax income of \$80 per year, forever.
• Assume Case B brings after-tax income of \$144 per year, forever.
• Value of firm = after-tax income / (return of capital), therefore
• Value of firm in Case A: \$80/0.08 = \$1,000
• Value of firm in Case B: \$144/0.08 = \$1,800
• Increase in firm value due to borrowing: \$1,800 – \$1,000 = \$800
• Alternatively, debt x tax rate: \$4,000 x 20% = \$800;