Project Management

Cash Flow

Cash flow is the net movement of cash into and out of a project over a period of time. It is the basic unit of project appraisal, because a project is judged by the actual cash it generates, not by accounting profit.

$\text{Net Cash Flow (NCF)} = \text{Cash Inflows} - \text{Cash Outflows}$

• Inflows: revenue from electricity sales, salvage value of assets, recovery of working capital, grants.
• Outflows: initial investment (plant, transmission lines, substations), operating and maintenance costs, taxes, interest and loan repayments.

Cash flows are arranged as a cash flow stream by year: a large negative flow at the start (Year 0), then positive flows during the operating life. Two conventions are used:

Depreciation is excluded because it is a book entry, not a cash transaction. Cash flow is the raw input for every appraisal technique — payback, NPV, IRR and benefit–cost ratio all work on cash flows, not on accounting profit.

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Time Value of Money (TVM)

Time value of money is the principle that Rs 1 received today is worth more than Rs 1 received in the future, because today's money can be invested to earn a return, and because of inflation and risk.

Reasons: (i) earning capacity / opportunity cost, (ii) inflation erodes purchasing power, (iii) uncertainty of future receipts, (iv) preference for present consumption.

Compounding (moving forward in time):

$FV = PV(1+i)^n$

Discounting (bringing future cash to present value):

$PV = \frac{FV}{(1+i)^n} = FV \times DF$

where $i$ = discount rate (cost of capital), $n$ = number of years, and $DF = 1/(1+i)^n$ is the discount factor.

For a series of equal annual cash flows (annuity):

$PV = A \times \frac{(1+i)^n - 1}{i(1+i)^n}$

Example: At $i = 10\%$, Rs 1,00,000 received after 3 years is worth today $PV = 1{,}00{,}000 / (1.10)^3 = \text{Rs } 75{,}131$.

Significance: TVM is the foundation of discounted appraisal. It allows cash flows occurring in different years to be brought to a common base (present value) so that projects of different size, life and timing can be compared. It also gives the decision rules: accept a project if NPV > 0 or IRR > cost of capital.

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Simple Payback Period (PBP)

Definition: The time required for the cumulative net cash inflows to recover the initial investment exactly. It measures liquidity and risk, not profitability.

Formula (equal annual cash flows):

$\text{PBP} = \frac{\text{Initial Investment}}{\text{Annual Net Cash Inflow}} \text{ years}$

Formula (unequal cash flows): cumulate the inflows year by year until the investment is recovered, then interpolate:

$\text{PBP} = A + \frac{B}{C}$

where $A$ = last full year before recovery, $B$ = unrecovered amount at start of that year, $C$ = cash inflow of the recovery year.

Example: Investment Rs 10,00,000; inflows Rs 3,00,000, Rs 4,00,000, Rs 4,00,000, Rs 2,00,000.

Recovery falls in Year 3. Unrecovered at start of Year 3 = Rs 3,00,000.

$\text{PBP} = 2 + \frac{3{,}00{,}000}{4{,}00{,}000} = 2.75 \text{ years} = 2 \text{ years } 9 \text{ months}$

Decision rule: Accept if PBP ≤ the firm's predetermined cut-off period; among alternatives, the shorter PBP is preferred.

Merits: Simple, easy to compute and explain; measures liquidity and how long capital stays at risk; useful where technology or demand is uncertain.

Demerits: Ignores time value of money; ignores all cash flows after the payback date, so it may reject a project with a large later return; the cut-off period is arbitrary.

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Discounted Payback Period (DPBP)

Definition: The time required to recover the initial investment from the present value of net cash inflows, i.e. the simple payback period adjusted for the time value of money. It is a stricter, more realistic measure than PBP.

Procedure:

1. Compute the discount factor for each year at the given discount rate $i$.
2. Multiply each year's cash inflow by its discount factor to get the discounted cash flow (DCF).
3. Cumulate the DCFs until the initial investment is recovered; interpolate for the fraction of the year.

Example: Investment Rs 10,00,000; discount rate 10%; same inflows as above.

Unrecovered at start of Year 4 = Rs 10,00,000 − Rs 9,03,832 = Rs 96,168.

$\text{DPBP} = 3 + \frac{96{,}168}{1{,}36{,}602} = 3.70 \text{ years} = 3 \text{ years } 8.4 \text{ months}$

Decision rule: Accept if DPBP ≤ the cut-off period; prefer the shorter DPBP.

Merits: Recognises the time value of money; still gives a simple "years to recover" figure; useful for ranking projects under capital rationing and for judging risk exposure.

Demerits: Still ignores cash flows beyond the payback date; requires an assumed discount rate; the cut-off remains subjective. It is always longer than the simple PBP, so a project may pass PBP but fail DPBP.

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Summary comparison

For a project such as a hydropower or transmission scheme in NEA, cash flows are first projected over the construction and operating periods, then discounted at the cost of capital; PBP and DPBP give a quick indication of how long the utility's funds remain at risk, while NPV and IRR give the final accept/reject decision.