Question

A new financial analyst at Company X does the following NPV analysis.

Year	After-tax Cash flows	PV @ 12%
0	-100000	-100,000.00
1	30000	26,978.42
2	30000	24,261.17
3	35000	25,453.86
4	35000	22,890.16
5	35000	20,584.68
6	35000	18,511.40

He reports an NPV of $38,679.69, an IRR of 10.93% and a payback period of 5.02 years.

Check these results and correct his analysis if necessary.

Answer 1

NPV = Present Value of Cash Inflows - Present Value of Cash Outflows

= $ 35,449.00

Working:

Year	After-tax Cash flows	Discounting Factor (12%)	PV @ 12%
0	-100000	1	-1,00,000.00
1	30000	0.892857143	26,785.71
2	30000	0.797193878	23,915.82
3	35000	0.711780248	24,912.31
4	35000	0.635518078	22,243.13
5	35000	0.567426856	19,859.94
6	35000	0.506631121	17,732.09
	Net Present Value		35,449.00

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Let the IRR be x.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

100,000= 30000/(1.0x) +30000/ (1.0x)^2 +35000/(1.0x)^3+ 35000/(1.0x)^4+35000/(1.0x)^5+ 35000/(1.0x)^6

Or x= 23.35%

Hence the IRR is 23.35%

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Payback Period = ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

= 3 + (5000/35000)

= 3.14 years

Hence the correct answer is 3.14 years

Workings:

Year	Investment	Cash Inflow	Net Cash Flow
0	-1,00,000.00	-	-1,00,000.00	(Investment + Cash Inflow)
1	-	30,000.00	-70,000.00	(Net Cash Flow + Cash Inflow)
2	-	30,000.00	-40,000.00	(Net Cash Flow + Cash Inflow)
3	-	35,000.00	-5,000.00	(Net Cash Flow + Cash Inflow)
4	-	35,000.00	30,000.00	(Net Cash Flow + Cash Inflow)
5	-	35,000.00	65,000.00	(Net Cash Flow + Cash Inflow)
6	-	35,000.00	1,00,000.00	(Net Cash Flow + Cash Inflow)