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Net Present Value (NPV)

Net present value (NPV) is a standard method for financial evaluation of long-term projects. Used for capital budgeting, and widely throughout economics, it measures the excess or shortfall of cash flows, in present value (PV) terms, once financing charges are met. By definition,
NPV = Present value of cash inflows - Present value of cash outflows (or minus initial investment in most of the cases). For its expression, see the formula section below.

Alternative Capital Budgeting Methods

  • payback period which measures the time required for the cash inflows to equal the original outlay. It measures risk, not return.
  • cost-benefit analysis which tries to include issues other than cash.
  • real option method which attempts to value managerial flexibility that is assumed away in NPV.
  • Internal Rate of Return (IRR): which calculates the rate of return of a project without making assumptions about the reinvestment of the cash flows (hence internal)
  • Modified Internal Rate of Return - similar to Internal Rate of Return, but it makes explicit assumptions about the reinvestment of the cash flows. Sometimes called Growth Rate of Return

Formula

Each cash inflow/outflow is discounted back to its PV. Then they are summed. Therefore

Where

  t - the time of the cash flow
 
  n - the total time of the project
 
  r - the discount rate
 
  Ct - the net cash flow (the amount of cash) at that point in time.
 
  C0 - the capital outlay at the beginning of the investment time ( t = 0 )
 

The Discount Rate

Choosing an appropriate discount rate is crucial to the NPV calculation. A good practice of choosing the discount rate is to decide the rate which the capital needed for the project could return if invested in an alternative venture. If, for example, the capital required for Project A can earn five per cent elsewhere, use this discount rate in the NPV calculation to allow a direct comparison to be made between Project A and the alternative. Obviously, NPV value obtained using variable discount rates with the years of the investment duration is more reflecting to the real situation than that calculated from a constant discount rate for the entire investment duration.

For some professional investors, their investment funds are committed to target a specified rate of return. In such cases, that rate of return should be selected as the discount rate for the NPV calculation. In this way, a direct comparison can be made between the profitability of the project and the desired rate of return.

The interest rate used to discount future cash flows to their present values is a key input of this process. Most firms have a well defined policy regarding their capital structure. So the weighted average cost of capital (after tax) is appropriate for use with all projects. Alternately, higher discount rates can be used for more risky projects. Another method is to apply higher discount rates to cash flows occurring further along the time span, to reflect the yield curve premium for long-term debt.

Reinvestment Rate

There are assumptions made about what rate of return is realized on cash that is freed-up before the end of the project. In the NPV model it is assumed to be reinvested at the discount rate used. This is appropriate in the absence of capital rationing. In the IRR model, no assumption is made about the reinvestment rate of free cash, which tends to exaggerate the calculated values. Some people believe that if the firm’s reinvestment rate is higher than the Weighted Average Cost of Capital, it becomes, in effect, an opportunity cost and should be used as the discount rate.

What NPV Tells

With a particular project, if Ct is a positive value, the project is in the status of cash inflow in the time of t. If Ct is a negative value, the project is in the status of cash outflow in the time of t. Appropriately risked projects with a positive NPV should be accepted. This does not necessarily mean that they should be undertaken since NPV at the cost of capital may not account for opportunity cost, i.e. comparison with other available investments. In financial theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected. The following sums up the NPV’s various situations.

If... It means... Then...
NPV > 0 the investment is profitable the project should be accepted
NPV < 0 the investment is at loss the project should be rejected
NPV < 0 the investment amount is unchanged the project should be neither accepted nor rejected

Example

X corporation must decide whether to introduce a new product line. The new product will have startup costs, operational costs, and incoming cash flows over six years. This project will have an immediate (t=0) cash outflow of $100,000 (which might include machinery and employee training costs). Other cash outflows for years 1-6 are expected to be $5,000 per year. Cash inflows are expected to be $30,000 per year for years 1-6. All cash flows are after-tax, and there are no cash flows expected after year 6. The required rate of return is 10%. The present value (PV) can be calculated for each year:

T=0 -$100,000 / 1.10^0 = -$100,000 PV.
T=1 ($30,000 - $5,000)/ 1.10^1 = $22,727 PV.
T=2 ($30,000 - $5,000)/ 1.10^2 = $20,661 PV.
T=3 ($30,000 - $5,000)/ 1.10^3 = $18,783 PV.
T=4 ($30,000 - $5,000)/ 1.10^4 = $17,075 PV.
T=5 ($30,000 - $5,000)/ 1.10^5 = $15,523 PV.
T=6 ($30,000 - $5,000)/ 1.10^6 = $14,112 PV.

The sum of all these present values is the net present value, which equals $8,882. Since the NPV is greater than zero, the corporation should invest in the project.

More realistic problems would need to consider other factors, generally including the calculation of taxes, uneven cash flows, and salvage values as well as the availability of alternate investment opportunities.


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