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Net Present Value (NPV)

Net Present Value Assignment / Homework Help
NPV may be defined as the excess of present value of the project cash inflows over that of outflows. In case of this method, cash inflows and outflows associated with the project are first worked out. The present values of these cash inflows and outflows are then calculated at the rate of return acceptable to the management, generally the cost of capital.


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Some points to note about NPV:
  • Cash outflows represent the investment and commitments of cash in the project at various points of time.
  • The working capital is taken as the cash outflow in the year the project starts commercial production and generally would be released at the end of the project life and taken as cash inflow.
  • Profit after tax but before depreciation represents cash inflows.
  • If there is any salvage value associated with the asset utilized for the project, it would be taken as cash inflow at the last year.
  • Though opportunity costs do not represent real cash flows, it has to be treated as cash outflow for the purpose of capital decision appraisal because they represent the opportunity foregone.
  • If there is an expected inflation, the future cash flows have to be adjusted for inflation and for discounting purpose the discount rate has to be multiplied by the general inflation rate for calculation of NPV.
  • The NPV is the difference between total present value of future cash inflows and the total present value of future cash outflows.
The equation for NPV when there is conventional initial investment: (i.e., when cash outflows are required initially only)
Net Present Value Assignment / Homework Help
Where:

CF = Cash inflows
COF = Cash outflow (initial)
K = cost of capital
n = number of years or time

The equation for NPV when there is non-conventional cash flows (i.e., when there are a series of cash outflows and inflows)
Net Present Value Assignment / Homework Help
NPV as Accept/Reject Criterion:

In case the NPV is positive, the project should be accepted, otherwise rejected.
If NPV > Zero, Accept the project
If NPV < Zero, Reject the project.

Example: Say, a company is considering two alternatives; whether to procure Machine A or Machine B. The cost of both the machines is $56,125 with expected 5 years of life and $3,000 salvage value for Machine A only. The cash inflows after taxation are given below:

Machine A: Machine B:
Year 1 $3,375 $11,375
Year 2 $5,375 $9,375
Year 3 $7,375 $7,375
Year 4 $9,375 $5,375
Year 5 $11,375 $3,375

Depreciation per year is $10,625 for Machine A and $11,225 for Machine B. Assume the discount factor is 10%.

Step 1: To calculate Cash flows after tax (i.e., add back depreciation to get real cash flows).
Step 2: Locate the PV factors for 10% for years 1 to 5 in the Present value table.
Step 3: Multiply the cash flows after tax with PV factors and add up all the PVs to get the total Present value of future cash inflows.
Step 4: Calculate NPV by subtracting PV of cash inflows by PV of cash outflows.
Step 5: Decision making based on NPV.

Years PV factor @ 10% CFAT Machine A PV Machine A CFAT Machine B PV Machine B
1 0.9091 14,000.00 12,727.40 22,600.00 20,545.66
2 0.8264 16,000.00 13,222.40 20,600.00 17,023.84
3 0.7513 18,000.00 13,523.40 18,600.00 13,974.18
4 0.6830 20,000.00 13,660.00 16,600.00 11,337.80
5 0.6209 25,000.00 (incl. salvage) 15,522.50 14,600.00 9,065.14
Total PV 68,655.70 71,946.62

NPV of Machine A = $68,655.70 - $56,125 -> $12,530.70
NPV of Machine B = $71,946.62 - $56,125 -> $15,821.62

Accept/Reject Decision: In this example, both of the NPVs are positive. Among choosing alternative projects, the project which has the highest NPV should be chosen. In this case, Machine B has the highest NPV and hence it will be chosen. This is a perfect example which gives importance to time value of money. If these calculations were not done, one would simply total all the cash flows which would be the same for both the machines if adjustment for depreciation is not made. And further, Machine A gives a salvage value of $3000 and would be straight away preferred and a wrong decision would have been made. Thus the calculation of time value of money is significant.