College of San Mateo

Accounting 131

Rosemary Nurre


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Chapter 14

Capital Budgeting Decisions

Learning Objectives

1. Evaluate the acceptability of an investment project using the net present value method.
2. Evaluate the acceptability of an investment project using the internal rate of return method.
3. Evaluate an investment project that has uncertain future cash flows..
4. Rank investment projects in order of preference.
5. Determine the payback period for an investment.
6. (Appendix 14A) Understand the concept of present value and make present value computations with and without the present value tables.

 Lecture Notes

A. The Concept of Present Value (Appendix 14A Money has a time value. A dollar today is worth more than a dollar in the future for the simple reason that a dollar can be invested today to yield more than a dollar in the future. When an investment involves cash flows over many years, this time value of money becomes important and should be taken into account in investment decisions. Simply adding together cash flows from different periods is like adding apples and oranges; dollars in different periods have different values.

 NOTE: As an example would you prefer to receive a gift of $100 today or a year from now? Almost everyone will respond they would prefer $100 today. Why is this? Some will say that the value of the dollar could decline due to inflation. Some will say that they would like to spend the money now. What if there is no inflation and the money can't be spent until the end of the year even if it is received now? Repeat the question in the first sentence. Hopefully, you will respond that it is always possible to put $100 in the bank today and wind up with more than $100 in a year. Therefore, the opportunity to take the money now is clearly attractive. This is the reasoning underlying present value; the value today of a dollar a year from now should depend upon the rate of return during the year.

 1. The mathematics of interest.
 a. The relation between an amount P, which is invested at the interest rate r, and the value of the investment after n periods, Fn, is given by:
 Fn = P(1+r) n (n referring to the nth power).

This formula assumes that the interest is compounded at the end of each period. For simplicity, we assume throughout the text and problem materials that interest is compounded annually.

 b. The difference between the present value, P, and the future value at any point in time, Fn, is the interest earned on the investment through time n. Exhibit 14A-1 in the text illustrates the relation between present value and future values and how future values grow over time.

2. Present value factors.

 a. Rather than making decisions based on future values, it is conventional to express the values of future cash flows in terms of present values. This can be done by rearranging the compound interest formula as follows:
P = Fn / (1 + r)n = Fn (1 / (1+r)n)

To find the present value of the amount Fn to be received n periods in the future, we just apply the formula using the appropriate interest rate r ( you may also see k or i designated for interest).

 b. The process of finding the present value of a future cash flow is called discounting. The interest figure that is used to find the present value is called the discount rate.

 c. The quantity in brackets in the above formula is called a "present value factor PVIF)."

PVIF = ( 1 / (1 + r )n)

Table 14C-3 provides present value factors for a wide range of values of r and n. The present value factors can also be easily computed using the power key on calculators.

 NOTE: It is worthwhile to go over the present value table, emphasizing some important points. Suggest to students that they think in terms of making a deposit in a bank. Ask them why the present value factors decrease as the interest rate gets larger. The answer is that as the interest rate gets larger, you can get the same future value with a smaller deposit today. Ask them why the present value factors get smaller as the number of periods increases. The answer is that if there are more periods for compounding to work, a smaller deposit today will yield the same amount in the future.

 3. Present value of a series of cash flows. Some investments involve a simple annuity, which is a series of identical cash flows that begin at the end of the first period and continue for a total of n periods into the future. The present value of such an annuity can be computed as the sum of individual present value factors, through the use of annuity tables, or using a formula.

 NOTE: Table 14C-4 in Appendix 14C was derived by simply adding the present value factors down each column from Table 14C-3. You should understand that the annuity table is valid only for a particular type of annuity - one that starts at the end of the first period and involves exactly the same cash flows every period until it ends.

B. Capital budgeting. The term capital budgeting is used to describe actions relating to planning and financing capital outlays for purposes such as purchase of new machines, introduction of new products, and modernization of facilities. Capital budgeting involves a commitment of funds now in order to receive cash flows in the future.

1. Typical capital budgeting decisions. Capital budgeting decisions tend to fall into two broad categories-screening decisions and preference decisions.
 a. Screening decisions relate to whether a proposed project meets some preset standard of acceptance. For example, does a particular investment generate at least a minimum desired return of, say, 20%? Screening involves grouping alternatives into acceptable and not acceptable categories.

 b. Preference decisions relate to selecting from among several competing courses of action. Preference decisions rank alternatives in order of desirability.

2. Characteristics of business investments. Most business investments involve depreciable assets that have little or no resale value at the end of their useful lives. Thus, the assets must generate sufficient cash to provide a return on the investment and to provide a return of the total amount of the original investment itself. Furthermore, since a dollar today is worth more than a dollar tomorrow, the future cash flows should be discounted to the present.

C. Discounted Cash Flows-The Net Present Value Method. The net present value of a project is the difference between the present value of all cash inflows and the present value of all cash outflows. If the net present value is positive, the investment project is acceptable. If the net present value is negative, the investment project is unacceptable. Both of these statements assume, of course, that there are no other important factors beyond the cash flows.

 1. Importance of the discount rate. This discount rate is typically the minimum required rate of return that a company sets on all investment projects and is often the company's cost of capital. The cost of capital is the overall cost to an organization of obtaining investment funds, including the cost of both debt and equity sources. A change in the discount rate can dramatically affect the decision of whether to accept or reject an investment project.

 2. Emphasis on cash flows. When computing the net present value of a project, cash flow-and not accounting net income-is ordinarily discounted. However, recent work by Ohlson and Feltham and others has shown that under specific conditions, it is also appropriate to discount carefully defined accounting net income. Nevertheless, the conditions are fairly stringent, so we only consider discounting cash flows in the text.

 a. Typical cash outflows include the initial investment, increased working capital requirements, repairs and maintenance, and incremental operating costs.

 b. Typical cash inflows include incremental revenues, reductions in costs, salvage value, and release of working capital.

 SUGGESTION: The role of working capital in capital budgeting sometimes confuses people.. The initial investment in working capital at the beginning of the project for items such as inventories is recaptured at the end of the project when the working capital is no longer required. Thus, working capital is recognized as a cash outflow at the beginning of the project and as a cash inflow at the end of the project.

 3. Recovery of the initial investment. The net present value method automatically provides for a return on the original investment in a project. This is illustrated in the text in Example B.

 4. Assumptions of the net present value method. The net present value method assumes that all cash flows are known with certainty and that all cash flows generated by the project are immediately reinvested at a rate of return equal to the discount rate.

 5. Additional simplifying assumptions. We make several additional assumptions that are not inherent characteristics of the Net Present Value Method but which simplify the material considerably.

 a. We assume that all cash flows either occur immediately or at the ends of periods. (Usually the periods are years.) In reality, most cash flows occur more or less uniformly throughout the period.

 b. We assume that there is no inflation. As discussed in Appendix 14B, inflation affects both the discount rate that should be used and the estimates of future cash flows. If there is inflation, then managers must take care to be consistent in their use of discount rates and cash flows. For simplicity, we assume in both this chapter and in the subsequent chapter that there is no inflation.

 c. We assume that there are no income taxes in Chapter 14. In appendix 14D, income taxes are introduced. Income taxes affect both the cash flows and the discount rate that should be used. If there are income taxes, an after-tax discount rate should be used.

 D. Discounted Cash Flows-The Internal Rate of Return Method. The internal rate of return (IRR) is the rate of return on an investment over its useful life. The internal rate of return of a project is the discount rate that will result in a zero net present value for the project.

 1. The case of even cash flows. When the cash flows associated with an investment are the same every year, the net present value of the project can be computed as follows:

 Net present value = Investment required (show as a negative number)

+ (Net annual cash flow times the PVIFA ). ( Present value factor for an annuity)

 The internal rate of return is the discount rate that results in a zero net present value. Setting the net present value equal to zero above and solving for the "Present value factor for an annuity" (PVIFA) yields the following formula:

Factor of the IRR = Investment required / Net annual cash inflow

To find the internal rate of return, locate the factor computed above in the present value table for an annuity in the row corresponding to the useful life of the project. In practice this often requires interpolation since the factor is likely to fall between two values in the present value table.

2. The problem of uneven cash flows. When cash flows are uneven, the above formula cannot be used to find the factor that results in a zero net present value. Instead, it may be necessary to resort to trial and error. Doing this by hand can be quite a chore, but is fairly easy if the problem is set up on a computer spreadsheet. Also, computer spreadsheets contain macros (such as "solver" in Excel) that can automate the trial and error process.

3. Using the internal rate of return. The internal rate of return of any investment is compared to whatever rate of return the organization requires on its investment projects. If the internal rate of return is equal to or greater than the required rate of return, then the project is acceptable. If the internal rate of return is less than the required rate of return, the project is rejected. Of course, non-financial factors may override these rules.

 E. Cost of Capital as a Screening Tool. The cost of capital can be used as a screening tool in both discounted cash flow methods. When the internal rate of return method is used, the cost of capital is the hurdle rate that a project must clear for acceptance. When the net present value method is used, the cost of capital is the discount rate.

 F. Net Present Value versus Internal Rate of Return. The net present value method of making capital budgeting decisions has several advantages over the internal rate of return method.

 1. The net present value method is simpler to use. It does not require trial-and-error methods.

 2. The internal rate of return method assumes that the cash flows can be reinvested at whatever the internal rate of return turns out to be-even if the internal rate of return is very high. The net present value method assumes that cash flows can be reinvested at the discount rate. The assumption made under the net present value method is usually more realistic.

G. Expanding the Net Present Value Approach. The net present value approach can be expanded to include two alternatives and to integrate the concept of relevant costs. Two approaches-the total-cost approach and the incremental-cost approach-are used to compare competing investment projects.

1. The Total-Cost Approach. In the total-cost approach to net present value, all cash inflows and all cash outflows are included in the computation of net present value for each alternative. The net present value figures for each of the two alternatives are compared and the alternative with the higher net present value is preferred.

2. The Incremental-Cost Approach. Under the incremental-cost approach, only those costs and revenues that differ between the alternatives are included in the discounted cash flow analysis. When only two alternatives are being considered, the incremental-cost approach offers a simpler, more direct route to a decision.

3. Evaluating an investment with uncertain cash flows. In practice, of course, future cash flows are seldom known with certainty. In principle, this complication can be incorporated into net present value analysis in a number of ways. We approach the problem from the perspective of using a sort of breakeven analysis. We ask how large would this particulare cash flow have to be to change the decision? The decision maker may not know exactly what the cash flow is going to be, but may be fairly confident that it will be larger (or smaller) than this critical value.

 H. Investments in Automated Equipment. Investments in automated equipment differ in several ways from investments in other types of equipment. These differences are discussed below.

1. Cost of automation. The cost involved in automating a process is often much greater than the cost of purchasing conventional equipment. Even more important, the front-end investment in robots and other hardware usually constitutes no more than half of the total cost to automate. Costs of engineering, software, and implementation can exceed the cost of the equipment itself.

 2. Benefits from automation. There are many benefits from automation including:

 a. Reduced labor cost, although the saving is seldom sufficient by itself to justify automation.

 b. Reduced inventory costs. Automated equipment is more reliable, more consistent, and faster than conventional equipment. As a result, work in process and finished goods inventories can be reduced.

 c. Fewer defects and higher quality. Due to greater reliability and consistency, defects are commonly reduced under automation. This results in less waste, scrap, rework, warranty work, and customer returns.

 d. Faster throughput time. The increased reliability and faster processing speeds reduce throughput time.

e. Increased manufacturing flexibility. Setup time can be greatly reduced, making it much easier to switch between products.

 Some of these benefits are intangible and difficult to estimate. One approach is to compute the net present value for a project based on the costs and benefits that can be easily estimated-omitting the difficult-to-estimate intangible benefits. If the net present value is positive with the intangible benefits excluded, it would be even more positive if they were included. If the net present value is negative, one can then ask whether the intangible benefits are likely to be big enough to turn the project into one with a positive net present value.

 I. Preference Decisions - The Ranking of Investment Projects. When making capital budgeting decisions, projects are first screened into acceptable and unacceptable groups. Projects in the acceptable group are then ranked in order of preference. Either the internal rate of return method or the net present value method can be used to make this ranking.

1. Internal Rate of Return Method. When using the internal rate of return method to rank competing investment projects, the preference rule is: The higher the internal rate of return, the more desirable the project.

 2. Net Present Value Method. Every project with a positive net present value is acceptable. However, if investment funds are limited, there needs to be some method of ranking acceptable projects in order of how well they utilize the available funds. If projects are not equal in size and there are limited investment funds, then it is necessary to compute each project's profitability index. The formula for the profitability index (PI) is:

PI = Present value of cash inflows / Investment required

This is actually an application of the idea from Chapter 13 that the possible uses of a scarce resource should be ranked in order of the contribution margin per unit of the scarce resource. In this case, the constrained resource is investment funds and the present value of the cash inflows is analogous to the contribution margin. When using the profitability index, the preference rule is: the higher the profitability index, the more desirable the project.

 J. Other Approaches to Capital Budgeting Decisions. One other approach to capital budgeting decisions is widely used: the payback period method.

1. The Payback Period Method. The payback period is defined as the length of time that it takes for an investment project to recoup its initial cost out of the cash inflows that it generates.
 a. When the net annual cash inflow is always the same, the payback period can be computed as follows:
Payback period = Investment required / Net annual cash inflow

b. When cash flows associated with an investment project are erratic or uneven, the payback period is computed by subtracting the net cash flow from the unrecovered investment each year until the unrecovered investment is zero.

 c. The basic criticisms of the payback period method are that it does not measure the profitability of an investment and it does not consider the time value of money. However, it does have value in situations where the useful life of the project is short and difficult to predict. Japanese firms, particularly in consumer electronics, use the payback method when evaluating new products since the product life cycle can be quite short and a new product can be made unexpectedly obsolete by changes in technology.

NOTE: Imagine you have to choose between two alternatives that each require an initial investment of $4,000. Option A returns $1,000 at the end of each of four years. Option B returns $4,000 at the end of the fourth year. Under the payback method, Option A and Option B are equally preferable. Note, however, that Option A is really better since the cash flows come earlier. Now add the information that in Year 5, Option A will produce an additional cash inflow of $500,000 but that Option B will never generate another dollar after the fourth year. Repeat the question of preference of Option A or Option B using only the payback method. The payback method ignores the time value of money and does not measure profitability; it just measures the time required to recapture the original investment.

K. Post-audit of Investment Projects. Post-audit of an investment project means a follow-up after the project has been approved to see whether or not expected results are being realized. In a post-audit, actual data (rather than estimated data) are used in computing the net present value. The net present value based upon actual data is compared to the net present value based upon estimated data as a way of gauging the accuracy of the estimated data. Such a post-audit may help refine planning models and also may help encourage managers to be forthright in their estimates of future cash flows