Question

Year           Cash Flow

0 -114,000

1                    48,000

2                   71,000

3                  104,000

Rate = 12%

Calculate for

1.)        Payback Period

2.)        The Internal Rate of Return

3.)        The NPV at capital cost

4.)        The Modified Internal Rate of Return

Answer 1

{Part A:

Payback period is the period in which initial investment is recoevred.

Year	Opening Bal	CF	Closing Bal
1	$ 1,14,000.00	$    48,000.00	$      66,000.00
2	$    66,000.00	$    71,000.00	$      -5,000.00
3	$     -5,000.00	$ 1,04,000.00	$ -1,09,000.00

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

= 1 + [ 66000 / 71000 ]

= 1 + 0.93

= 1.93 Years

Part B:

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

Year	CF	PVF @36%	Disc CF	PVF @37%	Disc CF
0	$ -1,14,000.00	1.0000	$ -1,14,000.00	1.0000	$ -1,14,000.00
1	$      48,000.00	0.7353	$      35,294.12	0.7299	$      35,036.50
2	$      71,000.00	0.5407	$      38,386.68	0.5328	$      37,828.33
3	$ 1,04,000.00	0.3975	$      41,344.39	0.3889	$      40,445.63
NPV			$        1,025.19		$          -689.54

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

= 36% + [ 1025.19 / 1714.72 ] * 1%

= 36% + 0.60%

= 36.60%

Part C:

NPV = PV of cash Inflows - PV of cash Outflows

Year	CF	PVF @12%	Disc CF
0	$ -1,14,000.00	1.0000	$ -1,14,000.00
1	$      48,000.00	0.8929	$      42,857.14
2	$      71,000.00	0.7972	$      56,600.77
3	$ 1,04,000.00	0.7118	$      74,025.15
NPV			$      59,483.05

Part D:

Modified IRR is similar to IRR. here intermediary Cfs are assumed as reinvested at Cost of Capital.

Year	CF	FVF @12%	FV of CF
1	$    48,000.00	1.2544	$    60,211.20
2	$    71,000.00	1.1200	$    79,520.00
3	$ 1,04,000.00	1.0000	$ 1,04,000.00
FV of CFs			$2,43,731.20

Thus 114000 has become 243731.2 over 3 years.

FV = PV(!+r)^n

243731.2 = 114000(1+r)^3

(1+r)^3 = 243731.2 / 114000

= 2.14

1+r = 2.14^ ( 1/3)

= 1.2883

r = 1.2883 - 1

= 0.2883 i.e 28.83%