Question

Your firm is considering a project that would require purchasing $7.9 million worth of new equipment. Determine the present value of the depreciation tax shield associated with this equipment if the firm's tax rate is 20% using the MACRS depreciation with a five-year recovery period and starting immediately. Note that because the depreciation tax shield is essentially a riskless cash flow (assuming the firm's tax rate remains constant), the appropriate cost of capital to evaluate the tax benefit from depreciation is the risk-free rate; assume this rate is 9% for all maturities. Give you answer in millions rounded to 3 decimal places.

Answer #1

Tax shield of Deprecitiation for

Year 1=[Cost*Depreciation rate]*tax rate

=[$7900,000*20%]*20%=$316,000

Year 2=[$7900,000*32%]*20%=$505,600

Year 3=[$7900,000*19.20%]*20%=$303,360

Year 4=[$7900,000*11.52%]*20%=$182,016

Year 5=[$7900,000*11.52%]*20%=$182,016

Year6=[$7900,000*5.76%]*20%=$91,008

Now,Present valuenof tax shield is calculated as follow;

Present value=Tax shield/(1+risk free rate)^no.of years

=$316,000/(1+0.09)^1+$505,600/(1+0.09)^2+$303,360/(1+0.09)^3+$182,016/(1+0.09)^4+$182,016/(1+0.09)^5+$91,008/(1+0.09)^6

=$1,251,218.97

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