Accounting: The Language of Business - Vol. 1 (Part 157)

Anyone with an engineering frame of mind will look at [accounting standards] and want to throw up.

Charlie Munger

 Capital Investment Analysis (Part C)

by

Charles Lamson 

Net Present Value Method

The net present value method analyzes capital investment proposals by comparing the initial cash investment with the present value of the net cash flows. It is sometimes called the discounted cash flow method. The interest rate (return) used in net present value analysis is set by management. This rate, sometimes termed the hurdle rate, is often based upon such factors as the nature of the business, the purpose of the investment, the cost of securing funds for the investment, and the minimum desired rate of return. If the net present value of the cash flows expected from all proposed investment equals or exceeds the amount of the initial investment, the proposal is desirable.

To illustrate, assume a proposal to acquire $200,000 of equipment with an expected useful life of five years [no residual value ( the estimated value of a fixed asset at the end of its lease term or useful life)] and a minimum desired rate of return of 10%. The present value of the net cash flow for each year is computed by multiplying the net cash flow for the year by the present value factor of $1 for that year. For example, the $70,000 net cash flow to be received on December 31, 2023, is multiplied by the present value of $1 for one year at 10% (0.826) to yield $48,560, and so on. The amount to be invested, $200,000, is then subtracted from the total percent value, $2,900, as shown below. The net present value indicates that the proposal is expected to recover the investment and provide more than the minimum rate of return of 10%.

When capital investment funds are limited and the alternative proposals involve different amounts of investment, it is useful to prepare ranking of the proposals by using a present value index. The present value index is calculated by dividing the total present value of the net cash flow by the amount to be invested. The present value index for the investment in the previous illustration is calculated as follows:

If a business is considering three alternative proposals and has determined their net present values, the present value index for each proposal is as follows:

Although Proposal A has the largest net present value, the present value indices indicate that it is not as desirable as Proposal B. That is, Proposal B returns $1.08 present value per dollar invested, whereas Proposal A returns only $1.07. Proposal B requires an investment of $80,000, compared to an investment of $100,000 for Proposal A. Management should consider the possible use of the $20,000 difference between Proposal A and Proposal B investments before making a final decision.

An advantage of the net present value method is that it considers the time value of money. A disadvantage is that the computations are more complex than those for the methods that ignore present value. In addition, The net present value method assumes that the cash received from the proposal during its useful life can be reinvested at the rate of return used in computing the present value of the proposal. Because of changing economic conditions, this assumption may not always be reasonable.

Internal Rate of Return Method

The internal rate of return method uses present value concepts to compute the rate of return from the net cash flows expected from capital investment proposals. This method is sometimes called the time adjusted rate of return method. It is similar to the net present value method, in that it focuses on the present value of the net cash flows. However, the internal rate of return method starts with the net cash flows and, in a sense, works backwards to determine the rate of return expected from the proposal.

EXHIBIT 2 Partial Present Value of an Annuity Table

To illustrate, assume that management is evaluating a proposal to acquire equipment costing $35,530. The equipment is expected to provide annual net cash flows of $10,000 per year for five years. If we assume a rate of return of 12%, we can calculate the present value of the net cash flows, using the present value of an annuity table in Exhibit 2, from part 156 and reintroduced above. These calculations are shown in Exhibit 3.

EXHIBIT 3  Net Present Value Analysis at 12%

In Exhibit 3, the $36,050 present value of the cash inflows, based on a 12% rate of return, is greater than the $33,530 to be invested. Therefore, the internal rate of return must be greater than 12%. Through trial and error procedures, the rate of return that equates the $33,530 cost of the investment with the present value of the net cash flows is determined to be 15%, as shown below.

Such trial and error procedures are time consuming. However, when equal annual net cash flows are expected from a proposal, as in the illustration, the calculations are simplified by using the following procedures (Equal annual net cash flows are assumed in order to simplify the illustration. If the annual net cash flows are not equal, the calculations are more complex, but the basic concepts are the same.)

1. Determine a present value factor for an annuity of $1 by dividing the amount to be invested by the equal annual net cash flows, as follows: Present value factor for an annuity of $1 = Amount to be invested / Equal annual net cash flows.

2. In the present value of an annuity of $1 table, locate the present value factor determined in (1). First locate the number of years of expected useful life of the investment in the Year column, and then proceed horizontally across the table until you find the present value factor computed in (1).

3. Identify the internal rate of return by the heading of the column in which the present value factor in (2) is located.

To illustrate, assume that management is considering a proposal to acquire equipment costing $97,360. The equipment is expected to provide equal annual net cash flows of $20,000 for seven years. The present value factor for an annuity of $1 is 4.868, calculated as follows:

For a period of seven years, the partial present value of an annuity of $1 table indicates that the factor 4.868 is related to a percentage of 10%, as shown below. Thus, 10% is the internal rate of return for the proposal. 

If the minimum acceptable rate of return for similar proposals is 10% or less, then the proposed investment should be considered acceptable. When several proposals are considered, management often ranks the proposals by their internal rates of return. The proposal with the highest rate is considered the most desirable.

The primary advantage of the internal rate of return method is that the present values of the net cash flows over the entire useful life of the proposal are considered. In addition, by determining a rate of return for each proposal, all proposals are compared on a common basis. The primary disadvantage of the internal rate of return method is that the computations are more complex than for some of the other methods. However, spreadsheet software programs have internal rate of return functions that simplify the calculation. Also, like the net present value method, this method assumes that the cash received from a proposal during its useful life will be reinvested at the internal rate of return. Because of changing economic conditions, the assumption may not always be reasonable. 

*WARREN, REEVE, & FESS, 2005, ACCOUNTING, 21ST ED., PP. 1040-1044*

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