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

Let your net returns be N = G-E where G is gross returns and E is expenditure. The ratio N/E = (G/E)-1. So you can use either N/E or G/E because they are closely related. But your decision rule will be different. If you use G/E then the project passes the test of acceptability if G/E > 1. If you use N/E then the project passes the acceptability test if N/E > 0. In either case you are using the rule that a project passes the acceptability test if G-E>0. One final point: if you are using gross returns to measure benefits and expenditure to measure costs, it doesn't sound like you are really doing cost-benefit analysis. It's a profitability analysis.

However for accurate results you can use discounted benefits and costs by taking their net present value.

b The fallacy in this method is that it takes in to account direct costs not discounted one.Besides the method gives inaccuarte results because here costs exceed the total investment made by investor.

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