# Selection of Purchase Alternatives under NPV

In the past, the company has always purchased its cars from a dealer and then sold the cars after three years of use. The company's present fleet of cars is three years old and will be sold very shortly.

To provide a replacement fleet, the company is considering two alternatives as follows Purchase Alternative. The company can purchase the cars, as in the past, and sell the cars after three years of use. The company can lease the cars under a three-year lease contract. Excluding such cases, for investment projects, where the pattern of cash flows is such that the higher the IRR, the higher the NPV, for mutually exclusive projects, the decision rule of taking the project with the highest IRR will maximize the return, but it may select a project with a lower NPV.

The IRR exists and is unique if one or more years of net investment negative cash flow are followed by years of net revenues. But if the signs of the cash flows change more than once, there may be several IRRs. The IRR equation generally cannot be solved analytically but only via iterations.

IRR is the return on capital invested, over the sub-period it is invested. It may be impossible to reinvest intermediate cash flows at the same rate as the IRR. Accordingly, a measure called Modified Internal Rate of Return MIRR is designed to overcome this issue, by simulating reinvestment of cash flows at a second rate of return. Despite a strong academic preference for maximizing the value of the firm according to NPV, surveys indicate that executives prefer to maximize returns [ citation needed ].

The equivalent annuity method expresses the NPV as an annualized cash flow by dividing it by the present value of the annuity factor.

### Net present value method

It is often used when assessing only the costs of specific projects that have the same cash inflows. In this form it is known as the equivalent annual cost EAC method and is the cost per year of owning and operating an asset over its entire lifespan. It is often used when comparing investment projects of unequal lifespans. For example, if project A has an expected lifetime of 7 years, and project B has an expected lifetime of 11 years it would be improper to simply compare the net present values NPVs of the two projects, unless the projects could not be repeated.

Alternatively the chain method can be used with the NPV method under the assumption that the projects will be replaced with the same cash flows each time. To compare projects of unequal length, say 3 years and 4 years, the projects are chained together , i.

## Net Present Value as a Capital Budgeting Method

The chain method and the EAC method give mathematically equivalent answers. The assumption of the same cash flows for each link in the chain is essentially an assumption of zero inflation , so a real interest rate rather than a nominal interest rate is commonly used in the calculations. Real options analysis has become important since the s as option pricing models have gotten more sophisticated.

The discounted cash flow methods essentially value projects as if they were risky bonds, with the promised cash flows known. But managers will have many choices of how to increase future cash inflows, or to decrease future cash outflows. When the analysis concerns a series of cash inflows or outflows coming at different future times, the series is called a cash flow stream.

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Each future cash flow has its value today its present value. The sum of these "present values" is the "net present value" for the cash flow stream. The future values and present values of these cash flow events might look like this:.

## Net present value method

The next section explains the role of the discount rate a percentage and time periods in determining NPV. The size of the discounting effect depends on two things: the amount of time between now and each future payment the number of discounting periods and an interest rate called the discount rate. The example shows that:.

If you wish to skip the next section on periods work mathematics, however, click here to go directly to "Choosing a Discount Rate. Future Value Definition Formula. M any if not most business people outside of finance, are unfamiliar with "time value of money" terms and calculations.

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The subject becomes approachable, however, if the explanation begins by noting that DCF mathematics are very closely related to that is familiar to most people: calculations for interest growth and compounding. Remember briefly how interest calculations work. Interest earned in earlier periods begins to "earn interest on itself," in addition to interest on the original PV.

Compound interest growth is delivered by the exponent in the FV formula, showing the number of periods. The same formula can be rearranged to deliver a "present value" given a "future value" and "interest rate" for input, as shown. When the FV is more than one period into the future, as most people know, interest compounding takes place. Interest earned in earlier periods begins to compound, in addition to interest on the original PV.