Question

Rieger International is evaluating the feasibility of investing ​$121,000 in a piece of equipment that has a 5​-year life. The firm has estimated the cash inflows associated with the proposal as shown in the following​ table: The firm has a 9​% cost of capital

Year ​(t​)	Cash inflows​ (CF)
1	​$30,000
2	​$40,000
3	​$40,000
4	​$40,000
5	​$25,000

a.  Calculate the payback period for the proposed investment.

b.  Calculate the net present value​ (NPV) for the proposed investment.

c.  Calculate the internal rate of return ​(IRR)​, rounded to the nearest whole​ percent, for the proposed investment.

d.  Evaluate the acceptability of the proposed investment using NPV and IRR. What recommendation would you make relative to implementation of the​ project?

Answer 1

Part A:

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

Year	Opening Bal	CF	Closing Bal
1	$ 1,21,000.00	$ 30,000.00	$ 91,000.00
2	$    91,000.00	$ 40,000.00	$ 51,000.00
3	$    51,000.00	$ 40,000.00	$ 11,000.00
4	$    11,000.00	$ 40,000.00	$ -29,000.00
5	$ -29,000.00	$ 25,000.00	$ -54,000.00

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

= 3 + [ 11000 / 40000 ]

= 3 + 0.275

= 3.275 Years

Part B:

NPV = PV of Cash Inflows - PV of Cash Outflows

Year	CF	PVF @9%	Disc CF
0	$ -1,21,000.00	1.0000	$ -1,21,000.00
1	$      30,000.00	0.9174	$      27,522.94
2	$      40,000.00	0.8417	$      33,667.20
3	$      40,000.00	0.7722	$      30,887.34
4	$      40,000.00	0.7084	$      28,337.01
5	$      25,000.00	0.6499	$      16,248.28
NPV			$     15,662.77

Part C:

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

Year	CF	PVF @13%	Disc CF	PVF @14%	Disc CF
0	$ -1,21,000.00	1.0000	$ -1,21,000.00	1.0000	$ -1,21,000.00
1	$      30,000.00	0.8850	$      26,548.67	0.8772	$      26,315.79
2	$      40,000.00	0.7831	$      31,325.87	0.7695	$      30,778.70
3	$      40,000.00	0.6931	$      27,722.01	0.6750	$      26,998.86
4	$      40,000.00	0.6133	$      24,532.75	0.5921	$      23,683.21
5	$      25,000.00	0.5428	$      13,569.00	0.5194	$      12,984.22
NPV			$        2,698.29		$          -239.22

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

= 13% + [ 2698.29 / 2937.51 ] * 1%

= 13% + 0.92%

= 13.92%

Part D:

Project can be accepted as NPV > 0 & IRR > COst of Capital