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# Net Present Value Method:

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1. Define and explain the net present value method of evaluating capital investment proposals.
2. How is it calculated?

Contents:

## Definition and Explanation:

Capital investment analysis is concerned with comparing the initial cash investment with a future cash flow stream. To make this comparison, cash flows at different points in time must be made equivalent. As a result, cash flows in the future must be brought back to the present and compared with the cash outflow for the investment. This method is also known as discounted cash flow method.

The net present value method uses present value concepts to compute the net present value of the cash flows expected from a proposed investment. The rate of return or interest factor, used in present value analysis is determined by management. The rate is often based upon such factors as the nature of the business enterprise and its relative profitability, the purpose of the capital investment, the cost of securing funds for the investment, and the minimum desired rate of return . If the net present value of the net cash flow expected from a proposed investment at the selected rate equals or exceeds the amount of the initial investment, the proposal is desirable.

## Example:

Management is considering to acquire equipment costing \$2,00,000. The expected useful life of the equipment is five years with no residual value.  The minimum desired rate of return is 10%.

The expected net cash flow for each of the five years and the net present value of the proposal is as follows:

 Present 1 2 3 4 5 \$(20,000) \$70,000 \$60,000 \$50,000 \$40,000 \$40,000 63,630 × .909 49,560 × .826 37,530 × .751 27,230 × .683 24,840 × .621 Net present value \$2,900

 Year Present Value of \$1 at 10% Net Cash Flow Present Value of net cash flow 1 .909 \$70,000 \$63,630 2 .826 \$60,000 \$49,560 3 .751 \$50,000 \$37,550 4 .683 \$40,000 \$27,320 5 .621 \$40,000 \$24,840 Total \$260,000 \$202,900 Amount to be invested \$200,000 Net present value \$2,900

### Explanation:

The present value of the net cash flow for each year is calculated by multiplying the net cash flow for the year by the present value factor of \$1 for that year. In above example, the net cash flow of \$70,000 to be received at the end of year 1 is multiplied by the present value of \$1 for one year at 10% (.909). Thus, the present value of the \$70,000, \$63,630. Likewise, the net cash flow at the end of the second year, \$60,000, is multiplied by the present value of \$1 for two years at 10% (.826) to yield \$49,560, and so on. The amount to be invested, \$200,000, is then subtracted from the total present value of the net cash flows, \$202,900, to determine the net present value, \$2,900. The net present value indicates that the proposal is expected to recover the investment and provide more than the minimum rate of return of 10%.

## Choosing From Several Alternative Investment Proposals:

When many alternative capital investments of the same amount are proposed and the funds are limited, the proposal with the highest net present value is preferred. If the alternative proposals involve different amounts of investment, it is useful to prepare a relative ranking of the proposals by using a present value index. The present value index is computed by dividing the total present value of the net cash flow by the amount to be invested. The present value index for above example is computed as follows:

 Present Value Index = Total Present Value of Net Cash Flow / Amount to Be Invested = \$202,900 / \$2300,000 = 1.01

To further illustrate, assume that the total present value of the net cash flow and the amounts to be invested for three alternative proposals are as follows:

 Proposal A Proposal B Proposal C Total present value of net cash flow \$107,000 \$86,400 \$93,600 Amount to be invested 100,000 80,000 90,000 Net present value \$7,000 \$6,400 \$3,600

The present value index for each proposal is as follows:

 Present Value Index Proposal A 1.07 (\$107,000 / \$100,000) Proposal B 1.08 (\$86,400 / \$80,000) Proposal C 1.07 (\$93,600 / \$90,000)

Although Proposal A has the largest net present value, the present value indexes indicate that it is not as desirable as Proposal B. Proposal B returns 1.08 present value per dollar invested, whereas Proposal A returns 1.07. Proposal B requires an investment of \$80,000, compared to an investment of \$100,000 for Proposal A. Management should consider the possible use of the \$20,000 difference between Proposal A and Proposal B investments before making a final decision.

An advantage of this method is that it considers the time value of money. A disadvantage is that the computations are more complex than those for the methods that ignore present value. The net present value method assumes that the cash received from the proposal during its useful life can be reinvested at the rate of return used in computing the present value of the proposal. This assumption may not always be reasonable due to the changing economic conditions.

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## More study material from this topic: Methods for the evaluation of capital investment analysis Average rate of return or accounting rate of return method Cash payback method Net present value method Internal rate of return method Simple interest Future value of a single sum Future value of an annuity Present value of a single sum Present value of an annuity Qualitative consideration in capital investment analysis Capital investment analysis and unequal proposal lives Capital rationing decision process Difference between simple interest and compound interest Difference between nominal and effective interest rate Future value of \$1 table Present value of \$1 table Present value of ordinary annuity table Future value of ordinary annuity table

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