Investment decision and evaluation techniques (PP, DPP, ARR, NPV, PI, IRR)

Definition of Investment decision

• The investment decision is concerned with the selection of assets in which funds will be invested by a firm.

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Evaluation techniques

Non-discounting (Not consider time value of money)

• Payback period (PP)
• Accounting rate of return (ARR)

 

Discounted (consider time value of money)

• Discounted payback period(DPP)
• Net present value (NPV)
• Profitability Index (PI)
• Internal rate of return (IRR)

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1. Payback period

• How soon can we get back our initial investment?

 

Formula 

IF cash flows are even,

• Initial investment / annual cash inflow

Example

Investments costs $600,000 and annual cash inflows are 200,000, then payback period is 3 years

 

 

IF cash flows are uneven,

• Years before fully recovery + unrecovered cost at start of the year / cash flow during the year

Example

Investment costs $200,000 and cash inflows are $70,000, $60,000, $55,000, $50,000, $30,000.

 

 

Payback period table

Years	Cash flows	Cumulative cash flow
0	(200,000)	(200,000)
1	70,000	(130,000)
2	60,000	(70,000)
3	55,000	(15,000)
4	50,000	35,000
5	30,000	65,000

Payback Period: 3 years + 15,000 / 50,000 = 3.3 years

 

 

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2. Discounted payback period (DPP)

Example

Investment costs $800,000, cash inflows are $250,000, $400,000, $300,000, $450,000

 

Discounted payback period table

Years	Cash flows	DF @ 10%	PV	C.NPV
0	(800,000)	1	(800,000)	(800,000)
1	250,000	0.909	227,250	(572,750)
2	400,000	0.826	330,400	(242,350)
3	300,000	0.751	225,300	(17,050)
4	450,000	0.683	307,350	290,300

DF: discount factor

PV: present value

C.NPV: cumulative net preset value

DPP: 3 + 17,050 / 307,350 = 3.055 years.

 

 

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3. Accouning (average) rate of return (ARR)

• This evaluation takes into account the earnings from the investment over its whole life.

 

Formula

• ARR = average profit / average investment
• Profit = cash inflows - depreciation - tax
• Depreciation = initial investment - scrap value
• Average profit = profit / number of years
• Average investment = (initial investment + scrap value) / 2 + additional working capital

Example

Initial investment costs $200,000, no scrap value, no working capital given. Cash inflows are $54,000, $48,000, $30,000, $64,000, $80,000. Tax rate is 40% and depreciation is straight line basis

Cash inflows: 54,000 + 48,000 + 30,000 + 64,000 + 80,000 =276,000

Profit: 276,000 – 200,000 – 30,400 = 45,600

Average profit = 45,600 / 5 = 9,120

Average investment = 200,000 / 2 = 100,000

ARR = 9,120 / 100,000 = 9.12%

 

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4. Net present value (NPV)

• The NPV technique is a discounted cash flow method that considers time value of money in evaluating capital investments.
• Decision rule: ACCEPT IF NPV > 0, REJECT, IF NPV < 0, choose the highest one if all projects are all > 0.

 

Example

 

Information for A and B

	Project A	Project B
Initial investment	40,000	60,000
Estimated life	5 years	5 years
Scrap value	2,000	4,000

Cash inflows for A and B

Year	1	2	3	4	5
Project A	10,000	20,000	20,000	6,000	4,000
Project B	40,000	20,000	10,000	6,000	4,000

 

Discount factor (DF) @ 10%

Year	1	2	3	4	5
DF@10%	0.909	0.826	0.751	0.683	0.621

 

Project A

Year	Cash flows	DF @ 10%	PV
0	(40,000)	1	(40,000)
1	10,000	0.909	9,090
2	20,000	0.826	16,520
3	20,000	0.751	15,020
4	6,000	0.683	4,098
5	4,000	0.621	2,484
5 (Scrap)	2,000	0.621	1,242
		NPV	8,454

Project B

Year	Cash flows	DF @ 10%	PV
0	(60,000)	1	(60,000)
1	40,000	0.909	36,360
2	20,000	0.826	16,520
3	10,000	0.751	7,510
4	6,000	0.683	4,098
5	4,000	0.621	2,484
5 (Scrap)	4,000	0.621	2,484
		NPV	9,456

 

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5. Internal rate of return (IRR)

• IRR represents the discount rate that makes NPV is zero (0). It is a discounted cash flow technique which takes into account the time value of money.
• IRR Decision Rule: ACCEPT if IRR > K, REJECT if IRR < K
• K = cost of capital
• NPV = 0 = PV of the expected cash inflows = initial cash outflow

 

Formula
IRR = L + [NL / NL - NH * (H - L)]

where,
L: lower rate
H: higher rate
NL: NPV at lower rate
NH: NPV at higher rate

 

 

Example

Calculate the internal rate of return of an investment of $134,000 which yields the following cash inflows.

Year	Cash flows
1	30,000
2	40,000
3	60,000
4	30,000
5	20,000

 

Year	Cash flows	DF @ 10%	PV	DF @ 12%	PV
0	(134,000)	1	(134,000)	1	(134,000)
1	30,000	0.909	27,270	0.893	26,790
2	40,000	0.826	33,040	0.797	31,880
3	60,000	0.751	45,060	0.712	42,720
4	30,000	0.683	20,490	0.636	19,080
5	20,000	0.621	12,420	0.567	11,340
		NPV	4,280	NPV	-2,190

 

IRR

= 10 + [4,280 / (4,280 +2,190) * (12-10)]

= 10 + [4,280 / 6,470 * 2]

= 10 + 1.3

= 11.3%

 

 

 

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6. Profitability Index (PI)

• The PI measures the ratio between the PV of future cash inflows and the PV of cash outflows.
• Acceptance Rule: IF PI > 1 Accept the project, IF PI < 1 Reject the project.
• The index is a useful tool for ranking investment projects and showing the value created per unit of investment.

Formula

• PI = PV of cash inflows / PV of cash outflows

 

Example

Suppose we have three projects involving discounted cash outflow of $530,000, $70,000 and $10,050,000. And suppose further that the sum of discounted cash inflows for these projects are $650,000, $85,000, and $10,060,00 respectiely. Calculate PI for the three projects 

 

Project A: 650,000 / 530,000 = 1.23

Project B: 85,000 / 70,000 = 1.21

Project C: 10,060,000 / 10,050,000 = 1.001