# Q31

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Question: A company is considering an investment project that will result in a taxable income of \$200,000 in the first year. The corporate tax rate is 30%. Calculate the present value of the tax shield generated by the project if the discount rate is 8% and the project is expected to last for 5 years. Answer: To calculate the present value of the tax shield, you can use the formula: PV(TaxShield)=∑t=1nT×TC(1+r)t PV ( TaxShield )= t =1 n (1+ r ) t T × TC Where: PV(TaxShield) PV ( TaxShield ) is the present value of the tax shield. T T is the taxable income in a given year. TC TC is the corporate tax rate. r r is the discount rate. t t is the year. n n is the number of years. In this case, T = \$200,000 , TC=30% TC =30% , r=8% r =8% , and n=5 n =5 . Let's calculate: PV(TaxShield)=200,000×0.30(1+0.08)1+200,000×0.30(1+0.08)2+200,000×0.3 0(1+0.08)3+200,000×0.30(1+0.08)4+200,000×0.30(1+0.08)5 PV ( TaxShield )= ( 1+0.08) 1 200,000×0.30 + (1+0.08) 2 200,000×0.30 + (1+0.08) 3 200,000×0.30 + (1+0.08) 4 200,000×0.30 + (1+0.08) 5 200,000×0.30 Calculating this using a calculator or spreadsheet software, you'll find that the present value of the tax shield is approximately \$414,080.68.
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