Question

You are the CFO of a business and have the opportunity to evaluate two different investment opportunities. Information related to these investments follows: Investment Cost Salvage Value Useful Life Required Rate of Return Sales Variable Costs Fixed Costs (excluding depreciation) Tax Rate Investment 1 $ 900,000 $ 90,000 9 years 10% $ 500,000 $ 200,000 $ 100,000 35% Investment 2 $ 600,000 $ 60,000 12 years 10% $ 500,000 $ 240,000 $ 120,000 35% Your company has a required rate of return of 10% for all new investments and is subject to a tax rate of 35%. 1) Determine the annual after tax cash flow for each investment. In addition, determine the after-tax cash flow for the salvage value if you assume that the actual market value of Investment #1 at the end of nine years is $100,000 and the actual market value of Investment #2 at the end of twelve years is $40,000. 2) Prepare a schedule of expected cash flows for each investment. Note that all positive cash flows must be shown as positive numbers and all negative cash flows must be shown as negative numbers. 3) Calculate the Net Present Value for each investment using the NPV function in Excel. 4) Calculate the Internal Rate of Return for each investment using the IRR function in Excel. (Note your guess for the interest rate in the formula should be the required rate of return) 5) Recalculate the Net Present Value for INVESTMENT #1 ONLY but assume that the required/target rate of return is 6%, 12%, and 20%.

Answer 1

The above Question completely based on Capital Asset pricing Model with help of NPV , IRR etc .

NPV = cash flow /(1+r)T=== Cash flow - net of cash inflow and outflow , r - discount factor ( see below 10% discount factor , 6% , 12% , 20% ) , t - number of years = 9 year / 12 year ,

In below complete calculation of PVIFA ( 10% , 9 years ) + PVIFA ( 10%,12 year ) -step by step

Answer -1 /2 and 3

	Investment -1	Investment -2
Investment Cost($)	9,00,000	6,00,000
Salvage Value ($)	90,000	60,000
Useful Life( Yrs)	9	12
Required rate iof return	10%	10%
Sales ($)	5,00,000	5,00,000
Variable Cost($)	2,00,000	2,40,000
Fixed Cost( Excld Depreciaiton)	1,00,000	1,20,000
Tax Rate	35%	35%
Actual Investment Value	1,00,000	40,000

Complete Analysis of Investment -1
Depreciation
Investment Cost($)	9,00,000
Salvage Value ($)	90,000
Useful Life($)	8,10,000
Useful Life( Yrs)	9
Per Year Depreciation($)	90,000
Revised Income Statement
Sales ($)	5,00,000
Variable Cost($)	2,00,000
Fixed Cost( Excld Depreciaiton)	1,00,000
Depreciation	90,000
Net Margin( Cash Inflow)-$	1,10,000
Required rate iof return
( Discount Rate)	10%
	Cash Inflow ($)	Tax (35%)($)	Cash Inflow -Net of Tax($)-A	Depreciation($)-B	Net Cash Inflow ($)(A+B)	Discount Factor('1/1+r) r=Discount factor -10%
Year1	1,10,000	38,500	71,500	90,000	1,61,500	0.909091
Year2	1,10,000	38,500	71,500	90,000	1,61,500	0.826446
Year3	1,10,000	38,500	71,500	90,000	1,61,500	0.751315
Year4	1,10,000	38,500	71,500	90,000	1,61,500	0.683013
Year5	1,10,000	38,500	71,500	90,000	1,61,500	0.620921
Year6	1,10,000	38,500	71,500	90,000	1,61,500	0.564474
Year7	1,10,000	38,500	71,500	90,000	1,61,500	0.513158
Year8	1,10,000	38,500	71,500	90,000	1,61,500	0.466507
Year9	1,10,000	38,500	71,500	90,000	1,61,500	0.424098
Year9	1,00,000		1,00,000		1,00,000
					15,53,500	5.759024
Cash outflow at Initial Investment					-9,00,000

Present Value of Cash inflow
	Net Cash inflow ( Yearly) * PVIFA+Salvage value at 9th Year * PVIF at 9th Year- Initial Investment
Net Cash inflow ( yearly)	1,61,500
PVIFA(10%,9yr- calculate-Q1)	5.759
Salvage Value($)	1,00,000
PVIF(10% , 9th year(1/1.1^9)	0.424
Present Value of Cash inflow ($)	9,72,492
NPV - 1 Investment	Amnt($)
Present Value of Cash inflow	9,72,492
Less - Initial Investment	9,00,000
	72,492

Complete Analysis of Investment -2
Depreciation
Investment Cost($)	6,00,000
Salvage Value ($)	60,000
Useful Life($)	5,40,000
Useful Life( Yrs)	12
Per Year Depreciation($)	45000
Revised Income Statement
Sales ($)	5,00,000
Variable Cost($)	2,40,000
Fixed Cost( Excld Dep)	1,20,000
Depreciation	45,000
Net Margin( Cash Inflow)-$	95,000
Tax '35%	33,250
Net Margin( Cash Inflow) after tax -$	61,750
Depreciation($)	45000
Net Cash inflow ($)	1,06,750

Present Value of Cash inflow
Net Cash inflow ( Yearly) * PVIFA+Salvage value at 9th Year * PVIF at 9th Year- Initial Investment
Net Cash inflow ( yearly)	1,06,750
PVIFA(10% , 12 year -calculated -Q1	6.814
Salvage Value($)	40,000
PVIF(10% at 12th year'(1/1.1)^12	0.319
Present Value of Cash inflow ($)	7,40,107
NPV - 2 Investment	Amnt($)
Present Value of Cash inflow	7,40,107
Less - Initial Investment	6,00,000
	1,40,107

Answer 4 - IRR ( Internal Rate of Return)

IRR easy formula to use = SUM of ( cash inflow year wise ) - Initial Investment .

Calculation of IRR - Investment -1		Calculation of IRR - Investment -2
	Amount($)		Amount($)
Initial Investment	-9,00,000	Initial Investment	-6,00,000
Cash inflow ( Already Calculated -Q1		Cash inflow ( Already Calculated -Q1
Year1	1,61,500		1,06,750
Year2	1,61,500		1,06,750
Year3	1,61,500		1,06,750
Year4	1,61,500		1,06,750
Year5	1,61,500		1,06,750
Year6	1,61,500		1,06,750
Year7	1,61,500		1,06,750
Year8	1,61,500		1,06,750
Year9	1,61,500		1,06,750
Year10			1,06,750
Year11			1,06,750
Year12			1,06,750
IRR	10.83%		14.161%

Answer of 5 -

Computation of NPV - Investment -1
Deatils	PVIFA(6%,9Yr)-$	PVIFA(12%,9Yr)-$	PVIFA(20%,9Yr)-$
Discount Factor	6.8017	5.3282	4.031
After Tax Cash Inflow	1,61,500	1,61,500	1,61,500
PV of Cash inflow	10,98,473	8,60,512	6,51,001
Less - Initial Investment	9,00,000	9,00,000	9,00,000
NPV-$	1,98,473	-39,488	-2,48,999
( Not consider Salvage Value )

PVIFA ( 6% for 9 year is derived number - same way - 10% for 9 year calculated as above in Q1