# Tax shield

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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;