Somebody computed the benefit cost ratio by summing of all the benefits and divi

Question

Somebody computed the benefit cost ratio by summing of all the benefits and dividing by the sum of all the costs. Why would such a computation produce an incorrect answer? How should this computation be performed? $1000 can be invested in Alternative A or Alternative B. Alternative A produces $500 at the end of Year 1 and $500 at the end of Year 2. Alternative B produces $250 per year for 5 years. The payback period for Alternative A is 2 years, whereas the payback period for Alternative B is four years. Therefore, according to the payback method, A is the better alternative. What is the fallacy of this analysis?

Explanation / Answer

1) Jules Dupuit, an engineer from France, first introduced the concept of benefit cost ratio in 1848. Alfred Marshall, a British economist further enhanced the formula that became the basis for benefit cost ratio.

In its simplest form, benefit cost ratio is a figure that is used to define the value of a project versus the money that will be spent in doing the project in the overall assessment of a cost-benefit analysis. This ratio provides a value of benefits and costs that are represented by actual dollars spent and gained. By definition the benefit cost ratio should be expressed using present values that are discounted.

2) 1. Asset life span. If an asset’s useful life expires immediately after it pays back the initial investment, then there is no opportunity to generate additional cash flows. The payback method does not incorporate any assumption regarding asset life span.

2. Additional cash flows. The concept does not consider the presence of any additional cash flows that may arise from an investment in the periods after full payback has been achieved.

3. Cash flow complexity. The formula is too simplistic to account for the multitude of cash flows that actually arise with a capital investment. For example, cash investments may be required at several stages, such as cash outlays for periodic upgrades. Also, cash outflows may change significantly over time, varying with customer demand and the amount of competition.

4. Profitability. The payback method focuses solely upon the time required to pay back the initial investment; it does not track the ultimate profitability of a project at all. Thus, the method may indicate that a project having a short payback but with no overall profitability is a better investment than a project requiring a long-term payback but having substantial long-term profitability.

5. Time value of money. The method does not take into account the time value of money, where cash generated in later periods is work less than cash earned in the current period. A variation on the payback period formula, known as the discounted payback formula, eliminates this concern by incorporating the time value of money into the calculation.

6. Individual asset orientation. Many fixed asset purchases are designed to improve the efficiency of a single operation, which is completely useless if there is a process bottleneck located downstream from that operation that restricts the ability of the business to generate more output. The payback period formula does not account for the output of the entire system, only a specific operation. Thus, its use is more at the tactical level than at the strategic level.

7. Incorrect averaging. The denominator of the calculation is based on the average cash flows from the project over several years - but if the forecasted cash flows are mostly in the part of the forecast furthest in the future, the calculation will incorrectly yield a payback period that is too soon. The following example illustrates the problem.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.