Benefit-Cost Ratio

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A benefit-cost ratio (BCR) is an indicator, used in the formal discipline of cost-benefit analysis, which attempts to summarize the overall value for money of a project or proposal. A BCR is the ratio of the benefits of a project or proposal, expressed in monetary terms, relative to its costs, also expressed in monetary terms.

All benefits and costs should be expressed in discounted present values. Benefits and costs are adjusted for the time value of money, so that all flows of benefits and flows of project costs over time (which tend to occur at different points in time) are expressed on a common basis in terms of their “present value.” (Please see our article below on discounted cash flows for the details on “present” and “future” values).

When we talk about the benefits, we are talking about all of the revenues the project is expected to return. Please note that we will consider the total revenue and not the profit when calculating the BCR. Also the costs must include every costs involved such as resource cost, equipment costs and quality costs etc. Also, the accuracy of the outcome of a benefit-cost analysis depends on how accurately costs and benefits have been estimated.

Discounted Cash Flows

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The “Discounted Cash Flow” technique is used to perform cost-benefit analysis for a project which is spread for a big period of time. Please note that this accounting technique is used during project initiation and once the project is rolling, we switch to the “Earned Value Management” technique for project costing and performance evaluations.

The “Discounted Cash Flow” technique is based on time-value of the money. The money we earn earlier is better than the same amount earned later. Before getting into the technical details, let me present two very basic examples. These examples are not directly related to the “Discounted Cash Flow” technique, but it will set the foundation I need to explain the concept.

First, consider that I hire your company to construct a house for me and we agree that I will pay an X amount for this service in lump sump. Now consider you finish constructing my house in three months and now the X amount is due for payment. What would be your preference, would you like to receive the payment as soon as you finish the construction or would you prefer to receive the payment later, say one year later? Obviously the early the better, right?

Another example will consider the opportunity costs. The opportunity cost is the “benefit” you forgo in pursuit of some other project or benefit. Consider you have $10,000 in your bank account and you want to invest this amount. The bank is already paying you 10% per annum. Would you invest in a project or business that will return you 8% per annum? No? Why? Because the opportunity cost is higher than the benefit.

Let’s combine these ideas, we know that the early we earn the money is better. However “better” is very qualitative figure and cannot be measured. We can quantify it by “discounting” the project cash flows by a “discount factor” (that is usually determined by the company keeping various factors in mind, including the opportunity costs). Suppose my discount factor is 20% and my project is yielding $10,000 per year. The first payment I will receive after the end of the first year will be $10,000. After discounting it by 20% factor, I get $8,333. Please note that I not calculating the discount by multiplying the future value by 20% (otherwise the discount would have been $2,000 and the discounted value would have been $8,000). Here the formula is reverse, if X is my present value (that I want to calculate for the first year), then X + X*20% = $10,000 ($10,000 is the return I will get after one year). Solving this equation will give X = $8,333.

The relation of Present Value (PV) to the Future Value (FV) is given by:

FV = PV (1+i)^n

Where “i” is the interest rate or the discount factor, and “n” is the number of elapsed year after the investment when the return is coming.

I hope this answer’s the question.

Regards,

Exam Support Team

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