Foundations of Financial Management: An Analysis (part 46)

“Money cannot buy peace of mind. It cannot heal ruptured relationships, or build meaning into a life that has none.” 

– Richard M. DeVos

The Capital Budgeting Decision (Part B)

by

Charles Lamson

Methods of Ranking Investment Proposals

Three widely used methods for evaluating Capital expenditures will be considered, along with the shortcomings and advantages of each. 

1. Payback method.

2.  internal rate of return.

3.  Net Present Value.

The first method, while not conceptually sound, is often used. Approaches 2 and 3 are more acceptable, and one or the other should be applied to most situations.

Payback Method

Under the payback method, we compute the time required to recoup the original investment. Assume we are called on to select between investments A&B in Table 3.

Table 3 Investment alternatives

The payback period for Investment A is two years, while Investment B requires 3.8 years. In the latter case, we recovered $6,000 in the first three years, leaving us with a need for another $4,000 to recoup the full $10,000 investment. Since the fourth year has a total inflow of $5,000, $4,000 represents 0.8 of that value. Thus the payback period for Investment B is 3.8 years.

In using the payback method to select Investment A, two important considerations are ignored. First there is no consideration of inflows after the cutoff period. The $2,000 in year 3 for Investment A in Table 3 is ignored, as is the $5,000 in year 5 for Investment B. Even if the $5,000 were $50,000, it would have no impact on the decision under the payback method.

Second, the method fails to consider the concept of the time value of money. If we had two $10,000 investments with the following inflow patterns, the payback method would rank them equally. 

Although both investments have a payback period of two years, the first alternative is clearly superior because the $9,000 comes in the first year rather than the second.

The payback method does have some features that help to explain its use by U.S. corporations. It is easy to understand, and it emphasizes liquidity. An investment must recoup the initial investment quickly or it will not qualify (most corporations use a maximum time horizon of three to five years). A rapid payback may be particularly important to firms in industries characterized by rapid technological developments.

Nevertheless the payback method, concentrating as it does on only the initial use of investment, fails to discern the optimum or most economic solution to a capital budgeting problem. The analyst is therefore required to consider more theoretically correct methods.

Internal Rate of Return

The internal rate of return (IRR) calls for determining the yield on an investment, that is, calculating the interest rate that equates the cash outflows (cost) of an investment with the subsequent cash flows. The simplest case would be an investment of $100 that provides $120 after 1 year, or a 20 percent internal rate of return. For more complicated situations, we use Table 2 from part 31 of this analysis (present value of a single amount) and Table 1 from part 31 (present value of an annuity, and the techniques described in parts 26-38 of this analysis dealing with the time value of money and valuation and rates of return. For example, a $1,000 investment returning an annuity of $244 per year for five years provides an internal rate of return of 7 percent, as indicated by the following calculations.

The solution at 10% is $177 away from $10,000. Actually the solution is ($177/$303) percent of the way between 10 and 12 percent.Since there is a two percentage-point difference between the two rates used to evaluate the cash inflows, we need to multiply the fraction by 2% and then add our answer to 10% for the final answer of:

10% + ($177/$303)(2%) = 11.17% IRR

In Investment B the same process will yield an answer of 14.33%.

The use of the internal rate of return calls for the prudent selection of Investment B in preference to Investment A, the exact opposite of the conclusion reached under the payback method.

The final selection of any project under the internal rate of return method will also depend on the yield exceeding some minimum cost standard, such as the cost of capital to the firm.

Net Present Value

The final method of investment selection is to determine the net present value of an investment. This is done by discounting back the inflows over the life of the investment to determine whether they equal or exceed the required investment. The basic discount rate is usually the cost of capital to the firm. Thus inflows that arrive in later years must provide a return that at least equals the cost of financing those returns. If we once again evaluate Investments A and B using an assumed cost of capital, or a discount rate, of 10 percent---we arrive at the following figures for net present value. 

While both proposals appear to be acceptable, Investment B has a considerably higher net present value than Investment A. Under most circumstances the net present value and internal rate of return methods give theoretically correct answers, and the subsequent discussion will be restricted to these two approaches. A summary of the various conclusions reached under the three methods is presented in Table 4.

Table 4 Capital budgeting results

*MAIN SOURCE: BLOCK & HIRT, 2005, FOUNDATIONS OF FINANCIAL MANAGEMENT, 11TH ED., PP. 354-358*

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