As explained in earlier chapters, the present value of a future cash flow is the amount that a knowledgeable investor would pay today for the right to receive that future amount.

Arriving at a present value figure depends on (1) the amount of the future cash flow, (2) the length of time that the investor must wait-to.receive the cash flow, and (3) the rate of return required by the investor. Discounting’ is the process by which the present value of cash flows (the discounted cash flows) is determined.

The use of present value tables to discount future cash flows is demonstrated in Appendix C (at the end of this text). Those who are not familiar with the concept of present value or with present value tables should read the appendix before continuing with this chapter.

For your convenience, the two present value tables presented in the appendix are repeated on the following page.

Table shows the present value of a single lump-sum payment of $1 to be received in n periods’ (years) in the future. Table 2 shows the present value of a $1 annuity-that is, $1′ to be received each year for n consecutive years. For illustrative purposes, both tables have’ been kept short. They include only selected discount rates and extend only for a Limited number of periods.,

However, they contain the appropriate rates and periods for all of the problem material in this . IA firm’s cost of capital refers to the cost of financing investments. In situations where an investment is entirely financed with debt, the cost of capital is the interest rate paid by the on borrowed funds, For investments that are financed all or in part with equity, the computation is more complex. Approaches for determining a cost of capital are addressed in a corporate finance course

**The discount rate may be viewed as an investor’s required rate of return. The present **value of art investment’s future cash flows is the maximum amount that an investor’ should be willing to pay for the investment and still expect to earn the required rate of return. Therefore, an investment is considered desirable when its cost is less than the present value of its future cash flows. In such cases, the expected rate of return exceeds the rate of return required by the investor, Conversely, when the cost of an investment exceeds the present value of its future cash flows; its expected return is less than that required by the investor

The higher the discount rate being used, the lower the resulting present value figure will be.

Built the higher the required rate of return for a particular investment, the less an investor will be willing to pay for the investment. The appropriate discount rate (or required rate of return) for determining the present value of a specific investment depends on the nature of the investment, the alternative investment opportunities available, and the investor’s cost of capital.

Let us do apply the concept of discounting cash flows to our example. We shall assume that the Stars require a 15% annual rate of return on all capital investments. The 10 vending machines are expected to generate annual net cash flows of $24,000 for five years. Table 2 shows that the present value of $1 to be received annually for five years, . discounted at 15%, is 3.352. Therefore, the present value of $24;000 received annually for five years “is $24,000 X 3.352, or $80,448.

In addition to these annual cash flows, Wilson expects that Vindicator will repurchase the machines from the Stars at the end of five years for $5.000 (their salvage value). Referring to Table 1, we see that the present value of $1 to be received in five years, discounted at 15%, is .497. Thus the present value of $5,000 dollars to be received at the end of five years is $5,000 X .497, or $2,485. We may now analyze the proposal to invest in the 10 vending machines in the following manner:

This analysis indicates that the present value of the vending machines’ future cash .flows, discounted at a “rate of 15%, amounts to $82,933. This is the maximum amount that the Stars could invest in these machines and still expect to earn’ the required annual return of 15%. As the actual cost of the investment is only $75,000, the machines have the potential ‘to earn a rate of return in excess 0(15%.

The net present value of Vindicator’s proposal is the difference between the total present value of the net cash flows·and the cost of the investment. If the net present value is equal to zero, the rate of return is equal to the”discount rate.

A positive net present value means that the investment is expected to provide a rate of return greater than.the discussant rate, whereas a negative net present value means that the investment is likely to yield a return fess than the discount rate.

In financial terms, proposals’ with a positive net present value are considered acceptable and those with a negative net present value are viewed as unacceptable. These relationships may be summarized as follows: