Question

Please answer question a using present worth and Internal rate of return methods and show your calculations

Exercise #25: An investment proposal is expected to have the following characteristics: Year 1 Year 2 Year 3 Gross income provide, S 17,000 22,000 19,000 Investment needed, 16,000 14,000 0 Operation expense, s 6,000 8,000 11,000 Depreciation charges, $ 10,000 10,000 10,000 Investments occur during the year and allow the indicated earnings, but both the income and investments are considered to have been made at the end of each year for the analysis purposes. In any year in which deductions exceed income, the tax benefits can be considered as additional income because the organization can apply the deductions against income earned from others operations. a) Determine the rate of return before taxes. b) If the effective income tax rate is 42 percent, what is the approximate after-tax rate of return? c) What is the actual after-tax rate of return?

Answer 1

Part (a)

year	gross income	investment needed	operation expense	cashflow before tax
1	17,000	16000	6000	-5,000
2	22,000	14000	8000	0
3	19,000	0	11000	8,000

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$before\ tax\ present\ worth,PW_{bt}=-5000(\frac{P}{F},i\%,1)+8000(\frac{P}{F},i\%,3)\\$

$at\ i=25\%\\ PW=-4000+4096=96\\ at\ i=30\%\\ PW=-3846.15+3641.329=-204.821\\ i_{1}=0.25,P_{1}=96,i_{2}=0.3,P_{2}=-204.821\\ using\ linear\ interpolation\\ i=i_{1}+\frac{P-P_{1}}{P_{2}-P_{1}}*(i_{2}-i_{1})\\ i=0.25+\frac{-96}{-204.821-96}(0.3-0.25)\\ i=0.25+0.15956=0.265956\\$

before tax rate of return is 26.595%

Part (b)

year	gross income	investment needed	operation expense	cashflow before tax	depreciation	taxable income	taxes	after-tax cashflow
1	17,000	16000	6000	-5,000	10000	1,000	420	-5,420
2	22,000	14000	8000	0	10000	4,000	1680	-1,680
3	19,000	0	11000	8,000	10000	-2,000	-840	8,840

$after-tax\ present\ worth,PW_{at}=-5420(\frac{P}{F},i\%,1)-1680(\frac{P}{F},i\%,2)+8840(\frac{P}{F},i\%,3)\\ at\ i=13\%\\ PW=-4796.46-1315.686+6126.563=14.417\\ at\ i=14\%\\ PW=-4754.385-1292.705+5966.748=-80.3417\\ using\ linear\ interpolation\\ i=i_{1}+\frac{P-P_{1}}{P_{2}-P_{1}}(i_{2}-i_{1})\\ i=0.13+\frac{-14.417}{-80.3417-14.417}*(0.14-0.13)\\ i=0.131521$

approximate after tax rate of return is 13.152%

Part (c)

actual after tax rate of return is 15.425%