Company J must choose between two alternate business expenditures. Expenditure 1 would require a $30,000 cash outlay and Expenditure 2 requires a $28,500 cash outlay. Determine the marginal tax rate at which the after-tax cash flows from the two expenditures are equal assuming that Expenditure 1 is fully deductible and Expenditure 2 is nondeductible. Determine the marginal tax rate at which the after-tax cash flows from the two expenditures are equal assuming that Expenditure 1 is 50% deductible and Expenditure 2 is nondeductible. Determine the marginal tax rate at which the after-tax cash flows from the two expenditures are equal assuming that Expenditure 1 is fully deductible and Expenditure 2 is 50 percent deductible.

Above statement means that Expenditure 1 = 30000 shall be reduced by an amount of tax saving ( since fully deductible) but expenditure - 2 = 28500 is final. ( since no tax saved)

Let............ r = tax rate. To convert any expenditure to after tax by reducing tax saving, we will multiply that expenditure with (1 - r)

So .............. 30000(1- r) = 28500

( 1 - r ) = 28500/30000 = 0.95

1 - r = 0.95 => ............r = 0.05

So Marginal tax rate must be 5%

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case 2 :

30000 ( 1 - 50%(r) ) = 28500

( 1 - 50%(r) ) = 28500/30000 = 0.95

- 50%(r) = 0.95 - 1 = - 0.05

0.50 * r = 0.05 ( negative cancelled on either sides)

r = 0.05 / 0.5 = 0.10 ..............(or) 10%

Thus marginal tax rate must be 10%

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Case 3 :

30000 ( 1 - r ) = 28500 ( 1 - 50%( r ) )

Expanding .......... 30000 - 30000*r = 28500 - 28500*50%*r

30000 * r - 14250 * r = 30000 - 28500

15750 * r = 1500

r = 1500/15750 = 0.0952 .(or) 9.52%

So Marginal tax rate must be 9.52%

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Hope this helps!