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:
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 |
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
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
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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