- 38.1 Purpose
- 38.2 Strengths, weaknesses, and limitations
- 38.3 Inputs and related ideas
- 38.4 Concepts
- 38.4.1 Costs and benefits
- 38.4.2 Discounting
- 38.4.3 Payback period

- 38.4.4 Net present value
- 38.4.5 The internal rate of return

- 38.5 Key terms
- 38.6 Software
- 38.7 References

Developing a system is a form of investment. The purpose of cost/benefit analysis is to give management a reasonable picture of the costs, benefits, and risks associated with a given system development project so they can compare it to other investment opportunities. Cost/benefit analysis is the de facto standard for demonstrating economic feasibility and for comparing and selecting among investment opportunities.

The values generated by cost/benefit analysis resemble standard accounting and financial measures. Consequently, they are meaningful to management and non-technical personnel, and can be used to compare a system development project to other types of investment opportunities.

The accuracy of a cost/benefit analysis can be no better than the accuracy of the underlying cost and benefit estimates. The standard cost/benefit models consider only tangible benefits. Using the tools described in this # to compare investment opportunities of substantially different duration can yield misleading results.

Before performing a cost/benefit analysis, the analyst must generate or otherwise obtain estimates of system development costs, tangible benefits by time period, and operating costs by time period. The discount rate varies from organization to organization and from time to time. It might reflect the prime rate, a business concern’s typical profit rate, and/or perceived risk. Additionally, many organizations specify a standard system or project life; five years is common.

Cost/benefit analysis is the de facto standard for demonstrating economic feasibility in a feasibility study (# 13) and is an important element in project planning and project management (Part III).

The purpose of cost/benefit analysis is to give management a reasonable picture of the costs, benefits, and risks associated with a given system development project so they can compare it to other investment opportunities. Cost/benefit analysis is the de facto standard for demonstrating economic feasibility and for comparing and selecting among investment opportunities.

An investment opportunity represents a string of cash flows that occur over time. Development costs are one-time costs that occur before the system is released to the user. They include the personnel, hardware, and software costs accumulated from the time the project is initially approved until the system is released to the user. Benefits are advantages generated by or derived from the system after it is released. Some systems reduce operating costs. Others generate new revenues. The net benefit for any given time period is computed by subtracting the new costs associated with achieving the benefits from the related cost savings or new revenues.

Because money has time value, the best way to compare cash flows that occur at different times is to convert all those cash flows to their present values. Most cost/benefit models assume that interest is compounded. The future value (*FV*) of a sum of money invested today (the present value, or *PV*) at a fixed interest rate (*i*) for a known number of time periods (*n*) is:

FV = PV(1+i).
^{n} | (38.1) |

To compute the present value of a future sum of money, solve that equation for the present value:

PV = FV/(1+i).
^{n} | (38.2) |

Computing the present value of a future sum of money is called discounting. The interest rate is called the discount rate.

When performing interest computations, unless otherwise stated always assume that the interest rate is expressed in annual terms. Also, make sure the interest rate and the time period are consistent. For example, if time is measured in months, divide the annual interest rate by 12 to get the equivalent monthly interest rate.

The payback period is a measure of the time it takes for accumulated benefits to exactly match the development cost. The process of computing the payback period is best shown by example.

In the Excel worksheet reproduced as Figure 38.1, the development cost ($100,000) is shown as a negative cash flow occurring at time zero and a series of annual benefits are shown as positive cash flows. The discount rate is 5 percent.

To compute the payback period, discount the benefits to their present values, compute cumulative discounted costs and benefits, and determine when accumulated benefits exceed the development cost (or when the cumulative cash flow becomes positive). (*Note:* Some organizations compute the payback period without discounting costs or benefits.) In this example, accumulated cash flows total $14,163 at the end of year 4, so payback occurs sometime during year 4.

To compute the point at which the accumulated benefits exactly match development costs, extrapolate. At the end of year 3, accumulated cash flows were $18,745 short of $100,000. During year 4, discounted benefits totaled $32,908. Divide: (18,745)/(32,908) is 0.57, or 57 percent. Payback occurs at a time 57 percent into year 4, so the payback period is 3.57 y.

Figure 38.1 This Excel worksheet illustrates payback period and net present value. |

Generally, system development costs (*C*) are assumed to occur at time zero (0). Annual benefits (*B*_{1}, *B*_{2}, *B*_{3}, ...) are assumed to occur at the end of year 1, year 2, year 3, and so on, throughout the system’s life. To compute the net present value (*NPV*), those benefits are discounted back to their present values and added to the development cost (a negative cash flow):

NPV = –C + [B_{1}/(1+i)^{1}] + [B_{2}/(1+i)^{2}] + ... + [B/(1+_{n}i)],
^{n} | (38.3) |

where *n* is the system’s life (the last period) and *i* is the discount rate. Note that the accumulated totals used to illustrate the payback period in Figure 38.1 are equivalent to the net present value at the end of each year.

Most popular spreadsheet programs contain built-in functions to compute net present value. For example, the general form of Excel’s net present value (*NPV*) function is:

- =NPV(rate, value1, value2, ...)

where *rate* is the discount rate and *value1, value2*, . . . represent a series of future cash flows (negative payments and positive incomes). Note that the first cash flow (*value1*) occurs one time period from the present, the second cash flow (*value2*) occurs two time periods from the present, and so on. Note also that because the first cash flow in the function occurs at time 1, any current (time 0) cash flows must be added to (or subtracted from) the value returned by the NPV function.

In Figure 38.1, the development cost ($100,000) is shown as a negative cash flow occurring at time 0 and a series of annual benefits are shown as positive cash flows. The discount rate is 5 percent.

Look carefully at the formula in the formula bar (just above the column identifiers near the top of Figure 38.1). It reads:

- =(B5)+NPV(C1,B6:B10)

B5 is the development cost ($100,000); it is a cash outflow and thus is recorded as a negative number. NPV is the Excel function name. C1 is the discount rate. B6:B10 (B6 to B10) is the range that holds the benefits. Note (in cell C13) that the computed net present value is $49,422, which matches the value in cell D10.

Generally, the higher the net present value the better the investment, but comparing the NPVs of projects with significantly different magnitudes can be misleading. Consequently, many organizations use the internal rate of return to rank their investment opportunities.

To compute the internal rate of return (IRR), start with the net present value equation (38.3) and set NPV = 0:

0 = –C + [B_{1}/(1+i)^{1}] + [B_{2}/(1+i)^{2}] + . . . + [B/(1+_{n}i)].
^{n} | (38.4) |

The initial investment cost (*C*) and the future benefits (*B*_{1}, *B*_{2}, *B*_{3}, . . .) are known. Solve for the internal rate of return (*i*), the interest rate that yields a zero net present value. Generally, the higher the internal rate of return, the better the investment.

Most popular spreadsheet programs contain built-in functions to compute the internal rate of return. For example, the general form of Excel’s internal rate of return (IRR) function is:

- =IRR(values,guess)

where *values* is a series of cash flows and *guess* is an initial estimate of the internal rate of return. The list of values must include at least one negative cash flow and at least one positive cash flow. If the initial guess is not coded, 0.1 is assumed.

In Figure 38.2, the development cost ($100,000) is shown as a negative cash flow occurring at time 0 and a series of annual benefits are shown as positive cash flows. The discount rate is 5 percent.

Figure 38.2 This Excel worksheet illustrates internal rate of return. |

Look carefully at the formula on the formula bar (just above the column identifiers near the top of Figure 38.2). It reads:

- =IRR(B5:B10,0.1)

The range B5:B10 (B5 to B10) holds the series of cash flows. The first cash flow (the negative value in cell B5) is assumed to occur at time 0. The value 0.1 is an initial guess. The computed internal rate of return (cell C15) is 20 percent.

Polynomials such as the formula for computing the internal rate of return have one possible solution for each sign change. If the string of benefits contains one or more negative values in addition to the development cost, the built-in function might return an incorrect answer.

**Benefits —**- Advantages generated by or derived from the system.
**Development costs —**- One-time costs that occur before the system is released to the user; they include the labor, hardware, and software costs accumulated from the time the project is initially approved until the system is released to the user.
**Discount rate —**- The interest rate used to discount a sum of money.
**Discounting —**- The act of computing the present value of a future sum of money.
**Future value —**- The value of a sum of money at some future time.
**Intangible benefits —**- Benefits that cannot be measured in financial terms, such as improved morale or employee safety.
**Interest rate —**- A charge for a loan or a payment for the use of money; usually expressed as a percentage.
**Internal rate of return —**- The interest rate that yields a zero net present value.
**Life —**- The number of time periods (usually years) during which the system is expected to be in use.
**Net benefit —**- Cost savings or new revenues minus the new cost associated with achieving the benefit.
**Net present value —**- The sum of discounted benefits minus the development costs.
**Operating costs —**- Continuing costs that begin after the system is released and last for the life of the system; they include personnel, supplies, maintenance, utilities, insurance, and similar costs.
**Payback period —**- A measure of the time it takes for accumulated benefits to exactly match the development costs.
**Present value —**- The value of a (current or future) sum of money in today’s dollars.
**Risk —**- The likelihood that an investment will fail to return the expected benefits.
**Tangible benefits —**- Benefits that can be measured in financial terms, such as reduced operating costs or enhanced revenues.

The standard cost/benefit criteria are incorporated in most spreadsheet programs as built-in functions. In Excel, the net present value function is = NPV and the internal rate of return function is = IRR. In Lotus 1-2-3, the net present value function is @NPV and the internal rate of return function is @IRR.

**1.**Boehm, B.W.,*Software Engineering Economics*, Prentice-Hall, Englewood Cliffs, New Jersey, 1981.**2.**Davis, W. S.,*Business Systems Analysis and Design*, Wadsworth, Belmont, CA, 1994.