# The Use of Net Present Value(NPV) Method in Capital Budgeting Decisions – Discounted Cash Flows:

Learning Objectives:

1. Define and explain the net present value method.
2. Evaluate the acceptability of an investment project using the net present value (NPV) method.
3. What are the advantages and disadvantages of NPV method?

Two approaches to making capital budgeting decisions use discounted cash flows. One is the net present value method (NPV), and other is the internal rate of return method (also called the time adjusted rate of return method). The net present value method is discussed on this page.

## Definition and Explanation of Net Present Value (NPV) Method:

Under the net present value method, the present value of a project’s cash inflows is compared to the present value of the project’s cash outflows. The difference between the present value of these cash flows is called “the net present value”. This net present value determines whether or not the project is an acceptable investment. To illustrate consider the following data.

### Example 1:

Harper company is contemplating the purchase of a machine capable of performing certain operations that are now performed manually. The machine will cost \$5,000, and it will last for five years. At the end of five-years period the machine will have a zero scrap value. Use of the machine will reduce labor costs by \$1,800 per year. Harper company requires a minimum pretax return of 20% on all investment projects.

Should the machine be purchased? Harper company must determine whether a cash investment now of \$5,000 can be justified if it will result in an \$1,800 reduction in cost each year over the next five years. It may appear that the answer is obvious since the total cost savings is \$9,000 (5 × \$1800). However, the company can earn a 20% return by investing its money elsewhere. It is not enough that the cost reductions cover just the original cost of the machine. they must also yield at least 20% return or the company would be better off investing the money elsewhere.

To determine whether the investment is desirable, the stream of annual \$1,800 cost savings is discounted to its present value and then compared to the cost of the new machine. Since Harper company requires a minimum return of 20% on all investment projects, this rate is used in the discounting process and is called the discount rate. This analysis is shown below.

 Initial Cost Life of the project (year) Annual cost savings Salvage value Required rate of return \$5,000 5 \$1,800 0 20% Item Years Amount of cash flows 20% Factor Present value of cash flows Annual cost savings Initial investmentNet present value 1―5 Now \$1,800 (5,000) 2.991* 1,000 \$ 5,384 (5,000) ——— \$  384 ======

*Present value of an annuity of \$1 in arrears. (From Future Value and Present Value Tables page – Table 4)

According to this analysis, Harper company should purchase the new machine. The present value of the cost savings is \$5,384, as compared to a present value of only \$5,000 for the required investment (cost of the machine). Deducting the present value of the required investment from the present value of the cost savings a net value of \$384. Whenever the net present value is zero or greater, as in our example, an investment project is acceptable. Whenever the net present value is negative an investment project is not acceptable. In sum:

 If the net present value is Then the project is Positive Acceptable since it promises a return greater than the required rate of return Zero Acceptable, since it promises a return equal to the required rate of return. Negative Not acceptable, since it promises a return less than the required rate of return

### A full interpretation of the solution is as follows:

The new machine promises more than the required 20% rate of return. This is evident from the positive net present value of \$384. Harper company could spend up to \$5,384 for the new machine and still obtain the minimum 20% required rate of return. The net present value of \$384, therefore, shows the amount of “cushion” or “margin of error“. One way to look at this is that the company could underestimate the cost of the new machine by up to \$384, or overestimate the net present value of the future cash savings by up to \$384, and the project would still be financially attractive.

## Emphasis on Cash Flow:

In capital budgeting decisions, the focus is on cash flows and not on accounting net income. The reason is that accounting net income is based on accruals that ignore the timing of cash flows into and out of an organization. From a capital budgeting standpoint, the timing of cash flows is important, since a dollar received today is more valuable than a dollar received in the future. Therefore, even though accounting net income is useful for many things, it is not ordinarily used in discounted cash flow analysis. Instead of determining accounting net income, the manager concentrates on identifying the specific cash flows of the investment project.

What kind of cash flows should the manager look for? Although the specific cash flows will vary from project to project, certain type of cash flows tend to recur as explained in the following paragraphs.

### Typical Cash Out Flows:

Most projects will have an immediate cash outflows in the form of an initial investment or other assets. Any salvage value realized from the sale of the old equipment can be recognized as a cash inflow or as a reduction in the required investment. In addition, some projects require that a company expand its working capital. When a company takes on a new project, the balances in the current assets will often increase. For example, opening a new Nordstrom’s department store would require additional cash in sales registers, increased accounts receivable for new customers, and more inventory to stock the shelves. These additional working capital needs should be treated as part of the initial investment in a project. Also, many projects require periodic outlays for repairs and maintenance and for additional operating costs. These should all be treated as cash outflows for capital budgeting purposes.

### Typical Cash Inflows:

On the cash inflow side, a project will normally either increase revenues or reduce costs. Either way, the the amount involved should be treated as a cash inflow for capital capital budgeting purposes. Notice that so for as cash flows are concerned, a reduction in costs is equivalent to an increase in revenues. Cash inflows are also frequently realized from salvage of equipment when a project ends, although the company may actually have to pay to dispose of some low – value or hazardous items. In addition, any working capital that was tied up in the project can be released for use elsewhere at the end of the project and should be treated as a cash inflow at that time. Working capital is released, for example, when a company sells off its inventory or collects its receivables.

The following types of cash flows are common in business investment projects.

 Cash out flows: Cash inflows: Initial investment (including installation costs). Increased working capital needs for project. Repairs and maintenance. Incremental operating costs. Incremental revenues Reduction in costs Salvage value Release of working capital

## Recovery of the Original Investment:

When computing the present value of a project, depreciation is not deducted for two reasons. First, depreciation is not a current cash outflow. As discussed above, discounted cash flow methods of making capital budgeting decisions focus on cash flows. Although depreciation is used to compute not income for financial statements, it is not relevant in an analytical framework that focuses on cash flows.

A second reason for not deducting depreciation is that discounted cash flow methods automatically provide for return of the original investment, thereby making a deduction for depreciation unnecessary. To demonstrate this point, consider the following example:

### Example 2:

Carver Hospital is considering the purchase of an attachment for its X-ray machine that will cost \$3,170. The attachment will be usable for four years, after which time it will have no salvage value. It will increase net cash inflows by \$1,000 per year in the X-ray department. The hospital’s board of directors has instructed that no investments are to be made unless they have an annual return of at least 10%.

A present value analysis of the desirability of purchasing the X-ray attachment is presented below:

 Initial cost Life of the project (years) Annual net cash inflow Salvage value Required rate of return \$3,170 4 \$1,000 0 10% Item Year(s) Amount of Cash Flow 10% Factor Present Value of Cash Flows Annual net cash inflow Initial investmentNet present value 1 – 4 Now \$1,000 (3,170) 3.170* 1.000 \$3,170 (3,170) ——— \$ 0 ======

Notice that the attachment promises exactly a 10% return on the original investment, since the net present value is zero at a 10% discount rate.

Each annual \$1,000 cash inflow arising from use of the attachment is made up of two parts. One part represents a recovery of a portion of the original \$3,170 paid for the attachment, and the other part represents a return on this investment. The breakdown of each year’s \$1,000 cash inflow between recovery of investment and return on investment is shown below:

Carver Hospital – Breakdown of Annual Cash Inflows

 (1) (2) (3) (4) (5) Year Investment outstanding during the year Cash Inflow Return on investment (1) × 10% Recovery of investment during the year (2) – (3) Un-recovered investment at the end of the year (1) – (4) 1 \$3,170 \$1,000 \$317 \$683 \$2,487 2 2,487 1,000 249 751 1,736 3 1,736 1,000 173 827 909 4 909 1,000 91 909 0 ——- ——- ——- ——- ——- Total investment recovered \$3,170

The first year’s \$1,000 cash inflow consists of a \$317 interest return (10%) on the \$3,170 original investment, plus a \$683 return of that investment. Since the amount of unrecovered investment decreases over the four years, the dollar amount of the interest return also decreases. By the end of the fourth year, all \$3,170 of the original investment has been recovered.

## Simplifying Assumptions:

Two simplifying assumptions are usually made in net present value analysis:

1. The first assumption is that all cash flows other than the initial investment occur at the end of the period. This is somewhat unrealistic in that cash flows typically occur throughout a period rather than just at its end. The purpose of this assumption is just to simplify computations.
2. The second assumption is that all cash flows generated by an investment project are immediately reinvested at a rate of return equal to the discount rate. Unless these conditions are met, the net present value computed for the project will not be accurate. To illustrate, we used a discount rate of 10% for Carver Hospital in example 2. Unless the funds released each period are immediately reinvested at a 10% return, the net present value computed for the X-ray attachment will be misstated.

## Choosing a Discount Rate in Capital Budgeting Decisions:

A positive net present value means that the project’s return exceeds the discount rate. A negative net present value means that the project’s return is less than the discount rate. Therefore, if the company’s minimum required rate of return is used as the discount rate, a project with a positive net present value is accepted and a project with a negative net present value is unacceptable.

What should be a company’s rate of return? The company’s cost of capital is usually regarded as the minimum required rate of return. The cost of capital is the average rate of return the company must pay to its long term creditors and to shareholders for the use of their funds. The cost of the capital is the minimum requirement of return because if a project’s rate of return is less than the cost of capital, the company does not earn enough to compensate its creditors and shareholders. Therefore any project with a rate of return less than the cost of capital should not be accepted.

The cost of capital serves as a screening device in net present value analysis. When the cost of capital is used as the discount rate, any project with a negative net present value does not cover the company’s cost of capital and should be discarded as unacceptable.

## An Extended Example of the Net Present Value Method:

To conclude our discussion of the net present value method, we present below an extended example of how it is used to analyze investment proposals. This example will also help to tie together (and to reinforce) many of the ideas developed thus far.

### Example 3:

Under a special arrangement, Swinyard company has an opportunity to market a new product in the western united states for a five-year period. The product would be purchased from the manufacturer, with Swinyard company responsible for all costs of  promotion and distribution. The licensing arrangement could be renewed at the end of the five-year period. After careful study, Swinyard company has estimated the following costs and revenues for the new product:

 Cost of equipment needed \$60,000 Working capital needed 100,000 Overhaul of the equipment in four years 5,000 Salvage value of the equipment in five years 10,000 Annual revenues and costs: Sales revenue 200,000 Cost of goods sold 125,000 Out of pocket operating costs (for salaries, advertising, and other direct costs) 35,000

At the end of five year period, the working capital would be released for investment elsewhere if Swinyard decides not to renew the licensing arrangement. Swinyard company uses a 14% discount rate.

Would you recommend the new product be introduced?

This example involves a variety of cash inflows and cash outflows. The solution is given below:

 Sales revenues \$200,000 Less cost of goods sold 125,000 Less out of pocket costs for salaries, advertising etc. 35,000 ——— Annual net cash inflows 40,000 ====== Item Years Amount of Cash Flows 14% Factor Present Value of Cash Flows Purchase of equipment Now \$ (60,000) 1.000 \$ (60,000) Working capital needed Now (100,000) 1.000 (100,000) Overhaul of equipment 4 (5,000) 0.592* (2,960) Annual net cash inflows from sales of the product line 1 – 5 40,000 3.433** 137,320 Salvage value of the equipment 5 10,000 0.519* 5,190 Working capital released 5 100,000 0.519* 51,900 ———- Net present value \$31,450 ======

*From Future Value and Present Value Tables page – Table 3
**From Future Value and Present Value Tables page – Table 4

Notice particularly how the working capital is handled in this example. It is counted as a cash outflow at the beginning of the project and as a cash inflow when it is released at the end of the project. Also notice how the sales revenues, cost of goods sold, and out of pocket costs are handled. Out of pocket costs are actual cash outlays for salaries, advertising, and other operating expenses. Depreciation would not be an out of pocket cost, since it involves no current cash outlay.

Since the overall net present value is positive, the new product should be added assuming the company has no better use for the investment funds.

### You may also be interested in other articles from “capital budgeting decisions” chapter:

Learning Objectives:

1. Define and explain the net present value method.
2. Evaluate the acceptability of an investment project using the net present value (NPV) method.
3. What are the advantages and disadvantages of NPV method?

Two approaches to making capital budgeting decisions use discounted cash flows. One is the net present value method (NPV), and other is the internal rate of return method (also called the time adjusted rate of return method). The net present value method is discussed on this page.

## Definition and Explanation of Net Present Value (NPV) Method:

Under the net present value method, the present value of a project’s cash inflows is compared to the present value of the project’s cash outflows. The difference between the present value of these cash flows is called “the net present value”. This net present value determines whether or not the project is an acceptable investment. To illustrate consider the following data.

### Example 1:

Harper company is contemplating the purchase of a machine capable of performing certain operations that are now performed manually. The machine will cost \$5,000, and it will last for five years. At the end of five-years period the machine will have a zero scrap value. Use of the machine will reduce labor costs by \$1,800 per year. Harper company requires a minimum pretax return of 20% on all investment projects.

Should the machine be purchased? Harper company must determine whether a cash investment now of \$5,000 can be justified if it will result in an \$1,800 reduction in cost each year over the next five years. It may appear that the answer is obvious since the total cost savings is \$9,000 (5 × \$1800). However, the company can earn a 20% return by investing its money elsewhere. It is not enough that the cost reductions cover just the original cost of the machine. they must also yield at least 20% return or the company would be better off investing the money elsewhere.

To determine whether the investment is desirable, the stream of annual \$1,800 cost savings is discounted to its present value and then compared to the cost of the new machine. Since Harper company requires a minimum return of 20% on all investment projects, this rate is used in the discounting process and is called the discount rate. This analysis is shown below.

 Initial Cost Life of the project (year) Annual cost savings Salvage value Required rate of return \$5,000 5 \$1,800 0 20% Item Years Amount of cash flows 20% Factor Present value of cash flows Annual cost savings Initial investmentNet present value 1―5 Now \$1,800 (5,000) 2.991* 1,000 \$ 5,384 (5,000) ——— \$  384 ======

*Present value of an annuity of \$1 in arrears. (From Future Value and Present Value Tables page – Table 4)

According to this analysis, Harper company should purchase the new machine. The present value of the cost savings is \$5,384, as compared to a present value of only \$5,000 for the required investment (cost of the machine). Deducting the present value of the required investment from the present value of the cost savings a net value of \$384. Whenever the net present value is zero or greater, as in our example, an investment project is acceptable. Whenever the net present value is negative an investment project is not acceptable. In sum:

 If the net present value is Then the project is Positive Acceptable since it promises a return greater than the required rate of return Zero Acceptable, since it promises a return equal to the required rate of return. Negative Not acceptable, since it promises a return less than the required rate of return

### A full interpretation of the solution is as follows:

The new machine promises more than the required 20% rate of return. This is evident from the positive net present value of \$384. Harper company could spend up to \$5,384 for the new machine and still obtain the minimum 20% required rate of return. The net present value of \$384, therefore, shows the amount of “cushion” or “margin of error“. One way to look at this is that the company could underestimate the cost of the new machine by up to \$384, or overestimate the net present value of the future cash savings by up to \$384, and the project would still be financially attractive.

## Emphasis on Cash Flow:

In capital budgeting decisions, the focus is on cash flows and not on accounting net income. The reason is that accounting net income is based on accruals that ignore the timing of cash flows into and out of an organization. From a capital budgeting standpoint, the timing of cash flows is important, since a dollar received today is more valuable than a dollar received in the future. Therefore, even though accounting net income is useful for many things, it is not ordinarily used in discounted cash flow analysis. Instead of determining accounting net income, the manager concentrates on identifying the specific cash flows of the investment project.

What kind of cash flows should the manager look for? Although the specific cash flows will vary from project to project, certain type of cash flows tend to recur as explained in the following paragraphs.

### Typical Cash Out Flows:

Most projects will have an immediate cash outflows in the form of an initial investment or other assets. Any salvage value realized from the sale of the old equipment can be recognized as a cash inflow or as a reduction in the required investment. In addition, some projects require that a company expand its working capital. When a company takes on a new project, the balances in the current assets will often increase. For example, opening a new Nordstrom’s department store would require additional cash in sales registers, increased accounts receivable for new customers, and more inventory to stock the shelves. These additional working capital needs should be treated as part of the initial investment in a project. Also, many projects require periodic outlays for repairs and maintenance and for additional operating costs. These should all be treated as cash outflows for capital budgeting purposes.

### Typical Cash Inflows:

On the cash inflow side, a project will normally either increase revenues or reduce costs. Either way, the the amount involved should be treated as a cash inflow for capital capital budgeting purposes. Notice that so for as cash flows are concerned, a reduction in costs is equivalent to an increase in revenues. Cash inflows are also frequently realized from salvage of equipment when a project ends, although the company may actually have to pay to dispose of some low – value or hazardous items. In addition, any working capital that was tied up in the project can be released for use elsewhere at the end of the project and should be treated as a cash inflow at that time. Working capital is released, for example, when a company sells off its inventory or collects its receivables.

The following types of cash flows are common in business investment projects.

 Cash out flows: Cash inflows: Initial investment (including installation costs). Increased working capital needs for project. Repairs and maintenance. Incremental operating costs. Incremental revenues Reduction in costs Salvage value Release of working capital

## Recovery of the Original Investment:

When computing the present value of a project, depreciation is not deducted for two reasons. First, depreciation is not a current cash outflow. As discussed above, discounted cash flow methods of making capital budgeting decisions focus on cash flows. Although depreciation is used to compute not income for financial statements, it is not relevant in an analytical framework that focuses on cash flows.

A second reason for not deducting depreciation is that discounted cash flow methods automatically provide for return of the original investment, thereby making a deduction for depreciation unnecessary. To demonstrate this point, consider the following example:

### Example 2:

Carver Hospital is considering the purchase of an attachment for its X-ray machine that will cost \$3,170. The attachment will be usable for four years, after which time it will have no salvage value. It will increase net cash inflows by \$1,000 per year in the X-ray department. The hospital’s board of directors has instructed that no investments are to be made unless they have an annual return of at least 10%.

A present value analysis of the desirability of purchasing the X-ray attachment is presented below:

 Initial cost Life of the project (years) Annual net cash inflow Salvage value Required rate of return \$3,170 4 \$1,000 0 10% Item Year(s) Amount of Cash Flow 10% Factor Present Value of Cash Flows Annual net cash inflow Initial investmentNet present value 1 – 4 Now \$1,000 (3,170) 3.170* 1.000 \$3,170 (3,170) ——— \$ 0 ======

Notice that the attachment promises exactly a 10% return on the original investment, since the net present value is zero at a 10% discount rate.

Each annual \$1,000 cash inflow arising from use of the attachment is made up of two parts. One part represents a recovery of a portion of the original \$3,170 paid for the attachment, and the other part represents a return on this investment. The breakdown of each year’s \$1,000 cash inflow between recovery of investment and return on investment is shown below:

Carver Hospital – Breakdown of Annual Cash Inflows

 (1) (2) (3) (4) (5) Year Investment outstanding during the year Cash Inflow Return on investment (1) × 10% Recovery of investment during the year (2) – (3) Un-recovered investment at the end of the year (1) – (4) 1 \$3,170 \$1,000 \$317 \$683 \$2,487 2 2,487 1,000 249 751 1,736 3 1,736 1,000 173 827 909 4 909 1,000 91 909 0 ——- ——- ——- ——- ——- Total investment recovered \$3,170

The first year’s \$1,000 cash inflow consists of a \$317 interest return (10%) on the \$3,170 original investment, plus a \$683 return of that investment. Since the amount of unrecovered investment decreases over the four years, the dollar amount of the interest return also decreases. By the end of the fourth year, all \$3,170 of the original investment has been recovered.

## Simplifying Assumptions:

Two simplifying assumptions are usually made in net present value analysis:

1. The first assumption is that all cash flows other than the initial investment occur at the end of the period. This is somewhat unrealistic in that cash flows typically occur throughout a period rather than just at its end. The purpose of this assumption is just to simplify computations.
2. The second assumption is that all cash flows generated by an investment project are immediately reinvested at a rate of return equal to the discount rate. Unless these conditions are met, the net present value computed for the project will not be accurate. To illustrate, we used a discount rate of 10% for Carver Hospital in example 2. Unless the funds released each period are immediately reinvested at a 10% return, the net present value computed for the X-ray attachment will be misstated.

## Choosing a Discount Rate in Capital Budgeting Decisions:

A positive net present value means that the project’s return exceeds the discount rate. A negative net present value means that the project’s return is less than the discount rate. Therefore, if the company’s minimum required rate of return is used as the discount rate, a project with a positive net present value is accepted and a project with a negative net present value is unacceptable.

What should be a company’s rate of return? The company’s cost of capital is usually regarded as the minimum required rate of return. The cost of capital is the average rate of return the company must pay to its long term creditors and to shareholders for the use of their funds. The cost of the capital is the minimum requirement of return because if a project’s rate of return is less than the cost of capital, the company does not earn enough to compensate its creditors and shareholders. Therefore any project with a rate of return less than the cost of capital should not be accepted.

The cost of capital serves as a screening device in net present value analysis. When the cost of capital is used as the discount rate, any project with a negative net present value does not cover the company’s cost of capital and should be discarded as unacceptable.

## An Extended Example of the Net Present Value Method:

To conclude our discussion of the net present value method, we present below an extended example of how it is used to analyze investment proposals. This example will also help to tie together (and to reinforce) many of the ideas developed thus far.

### Example 3:

Under a special arrangement, Swinyard company has an opportunity to market a new product in the western united states for a five-year period. The product would be purchased from the manufacturer, with Swinyard company responsible for all costs of  promotion and distribution. The licensing arrangement could be renewed at the end of the five-year period. After careful study, Swinyard company has estimated the following costs and revenues for the new product:

 Cost of equipment needed \$60,000 Working capital needed 100,000 Overhaul of the equipment in four years 5,000 Salvage value of the equipment in five years 10,000 Annual revenues and costs: Sales revenue 200,000 Cost of goods sold 125,000 Out of pocket operating costs (for salaries, advertising, and other direct costs) 35,000

At the end of five year period, the working capital would be released for investment elsewhere if Swinyard decides not to renew the licensing arrangement. Swinyard company uses a 14% discount rate.

Would you recommend the new product be introduced?

This example involves a variety of cash inflows and cash outflows. The solution is given below:

 Sales revenues \$200,000 Less cost of goods sold 125,000 Less out of pocket costs for salaries, advertising etc. 35,000 ——— Annual net cash inflows 40,000 ====== Item Years Amount of Cash Flows 14% Factor Present Value of Cash Flows Purchase of equipment Now \$ (60,000) 1.000 \$ (60,000) Working capital needed Now (100,000) 1.000 (100,000) Overhaul of equipment 4 (5,000) 0.592* (2,960) Annual net cash inflows from sales of the product line 1 – 5 40,000 3.433** 137,320 Salvage value of the equipment 5 10,000 0.519* 5,190 Working capital released 5 100,000 0.519* 51,900 ———- Net present value \$31,450 ======

*From Future Value and Present Value Tables page – Table 3
**From Future Value and Present Value Tables page – Table 4

Notice particularly how the working capital is handled in this example. It is counted as a cash outflow at the beginning of the project and as a cash inflow when it is released at the end of the project. Also notice how the sales revenues, cost of goods sold, and out of pocket costs are handled. Out of pocket costs are actual cash outlays for salaries, advertising, and other operating expenses. Depreciation would not be an out of pocket cost, since it involves no current cash outlay.

Since the overall net present value is positive, the new product should be added assuming the company has no better use for the investment funds.