Formulas

Note

For PBP,NPV,PI,IRR, Cash flows are considered after tax but before depreciation.

For ARR, Cash flows are considered after tax and after depreciation.

Particular	Amount
Cash Flow	XXX
(-) Depreciation	XXX
Cash Flow after Depreciation	XXX
(-) Tax	XXX
Cash Flow after Tax	XXX (for ARR)
(+) Depreciation	XXX
Cash Flow after Tax and Depreciation	XXX (for PBP , NPV , PI , IRR)

Payback Period

Uniform Cash Flows

Payback period is the time required to recover the Original investment in a project. It is calculated as follows:

[ \text{Payback Period} = \frac{\text{Original Investment}}{\text{Annual Cash Flow}} ]

Non-Uniform Cash Flows

When the cash flows are not uniform, the payback period is calculated as follows:

Years	Cash Inflows	Cumulative Cash Flow
1	A1	A1
2	A2	A1 + A2
3	A3	A1 + A2 + A3
4	A4	A1 + A2 + A3 + A4
5	A5	A1 + A2 + A3 + A4 + A5

[\text{Payback Period} = \text{Year before full recovery} + \left(\frac{\text{Unrecovered cost at the beginning of the year}}{\text{Cash flow during the year}}\right)]

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Net Present Value (NPV)

Year	Cash Inflow	P/v Factor	Present Value of Cash Inflow
1	A1	1/(1+r)	A1/(1+r)
2	A2	1/(1+r)2	A2/(1+r)2
3	A3	1/(1+r)3	A3/(1+r)3
4	A4	1/(1+r)4	A4/(1+r)4
5	A5	1/(1+r)5	A5/(1+r)5

NPV = Sum of Present Value of Cash Inflows - Original Investment

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Profitability Index (PI)

Similar to NPV, but it is expressed as a ratio of present value of cash inflows to the original investment.

PI = Sum of Present Value of Cash Inflows / Original Investment

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Internal Rate of Return (IRR)

Discount Factor = Original Investment / Sum of Present Value of Cash Inflows

\text{IRR} = A + \frac{cC-O}{C-D} \cdot (B - A)

Where:

A = Lower discount rate

B = Higher discount rate

C = Sum of Present Value of Cash Inflows at A

D = Sum of Present Value of Cash Inflows at B

O = Original Investment

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