Question

Net Present Value and Other Capital Budgeting Measures 4. Compute the Net Present Value (NPV), Internal Rate of Return (IRR), Profitability Index (PI), and Payback statistic for the project with the cash flows given below. Recommend whether the firm should accept or reject the project with the cash flows shown below if the appropriate cost of capital is 12 percent and the maximum allowable payback is 4 years. Time: Cash flow: 0 -2,100 1 350 2 700 3 800 4 750 5 525

Answer 1

NPV = PV of Cash Inflows - PV of Cash Outflows

Year	CF	PVF @12%	Disc CF
0	$ -2,100.00	1.0000	$ -2,100.00
1	$     350.00	0.8929	$      312.50
2	$     700.00	0.7972	$      558.04
3	$     800.00	0.7118	$      569.42
4	$     750.00	0.6355	$      476.64
5	$     525.00	0.5674	$      297.90
NPV			$      114.50

PI = PV of Cash Inflows / PV of Cash Outflows

Year	CF	PVF @12%	Disc CF
1	$     350.00	0.8929	$      312.50
2	$     700.00	0.7972	$      558.04
3	$     800.00	0.7118	$      569.42
4	$     750.00	0.6355	$      476.64
5	$     525.00	0.5674	$      297.90
PV of Cash Inflows			$ 2,214.50
PV of Cash Out flows			$   2,100.00
PI			1.05

IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows

Year	CF	PVF @14%	Disc CF	PVf @15%	Disc CF
0	$ -2,100.00	1.0000	-2100	1.0000	$ -2,100.00
1	$     350.00	0.8772	$      307.02	0.8696	$     304.35
2	$     700.00	0.7695	$      538.63	0.7561	$     529.30
3	$     800.00	0.6750	$      539.98	0.6575	$     526.01
4	$     750.00	0.5921	$      444.06	0.5718	$     428.81
5	$     525.00	0.5194	$      272.67	0.4972	$     261.02
NPV			$          2.35		$      -50.51

IRR = Rate at which least +ve NPV + [ NPV at that Rate / Cahnge in NPV due to 1% inc in DIsc Rate ] * 1%

= 14% + [ 2.35 / 52.86 ] * 1%

= 14% + 0.04%

= 14.04%

Pay back period is the period in which initial investment is recovered.

Year	Opening Bal	CF	Closing Bal
1	$ 2,100.00	$ 350.00	$ 1,750.00
2	$ 1,750.00	$ 700.00	$ 1,050.00
3	$ 1,050.00	$ 800.00	$     250.00
4	$    250.00	$ 750.00	$    -500.00
5	$ -500.00	$ 525.00	$ -1,025.00

PBP = Year in which least +ve CB + [ CB in that Year / CF in next Year ]

= 3 + [ 250 / 750 ]

= 3 +0.33

= 3.33 Years

Project Can be accepeted as

NPV > 0

IRR > Cost of Capital

PI > 1

Payback period is < desired PBP