Formula of Capital Budgeting

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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