Question

# Your firm is considering a project that would require purchasing  \$7.9 million worth of new equipment. Determine...

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.

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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