Case A
Consider one unit of investment cost $1,000 and returns $1,100 at the end of year 1. 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.
[edit]Case B
Consider the investor has an option to borrow $4000 at 8% interest (same rate as return of capital in Case A). By borrowing $4,000 (+$1,000 capital), the investor can purchase 5 units of investment. At the end of the year he will have ($5,000 return of capital, -$4,000 repayment of debt, $500 revenue, -$320 interest payment and -$36 tax) considering $1000 initial capital he is left with $1,144. He earned net income $144, or 14.4%.
The reason that he was able to earn additional income is because the cost of capital (opportunity cost, 8%) is not deductible for tax purposes, but the cost of debt (interest, 8%) is.
[edit]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 $80 after tax income per year, forever.
- Assume Case B brings $144 after tax income per year, forever.
- 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 tax shield: $1,800 - $1,000 = $800
- Debt x tax rate: $4,000 x 20% = $800