# Benefit Cost Ratio Article byHarsh Katara ## Benefit-Cost Ratio Definition

The benefit-cost ratio indicates the relationship between the cost and benefit of project or investment for analysis as it is shown by the present value of benefit expected divided by present value of cost which helps to determine the viability and value that can be derived from investment or project.

### Formula

Benefit-Cost Ratio Formula = PV of Benefit Expected from the Project / PV of the Cost of the Project

For eg:
Source: Benefit Cost Ratio (wallstreetmojo.com)

• If that investment or the project has a BCR value that is greater than one, than the project can be expected to return or deliver a positive NPV, i.e.,  to the business or the firm and their investors.
• If BCR value is less than 1, then the project cost can be expected to higher than the returns, and therefore, it should be discarded.

### Steps to Calculate Benefit-Cost Ratio (BCR)

To calculate the BCR formula, use the following steps:

• Step 1: Calculate the present value of the benefit expected from the project. The procedure to determine the present value is:
• The amount for each year = Cash Inflows*PV factor
• Aggregate the amounts for all the years.
• Step 2: Calculate the present value of costs. If the costs are incurred upfront, the cost incurred is the of the expenses as there is no PV factor.
• Step 3: Calculate the benefit-cost ratio using the formula:
• BCR formula = PV of Benefit Expected from the Project / PV of the Cost of the Project

### Examples

You can download this Benefit Cost Ratio Excel Template here – Benefit Cost Ratio Excel Template

#### Example #1

EFG ltd is working upon the renovation of its factory in the upcoming year, and for they expect an outflow of \$50,000 immediately, and they expect the benefits out of the same for \$25,000 for the next three years. The inflation rate that is currently prevailing is 3%. You are required to assess whether the decision to renovate will be profitable by using a BCR.

Solution

To do the first, we need to bring both costs and benefit in today’s value. Since the outflow of \$50,000 is immediate and hence that would remain the same.

Since the gains are in future value, we need to discount them back by using a discount rate of 3%.

Therefore, the Benefit-Cost Ratio can be calculated as using the below formula as,

The formula for Calculating BCR = PV of Benefit expected from the Project / PV of the cost of the Project

= 70715.28 /-50,000.00

BCR =1.41

Since the Benefit-Cost ratio is greater than 1, the renovation decision appears to be beneficial.

#### Example #2

Sunshine private limited has recently received an order where they will sell 50 tv sets of 32 inches for \$200 each in the first year of the contract, 100 air condition of 1 tonne each for \$320 each in the second year of the contract, and the third year they will sell 1,000 smartphones valuing at \$500 each. But to fulfill this requirement, they need to increase the production, and for that, they are looking for a cash flow of \$35,000 to hire people on contract. All this will be deposited in a separate explicitly created for this purpose and cannot be withdrawn for any other purpose. Still, the company will earn a 2% rate on the same for the next three years as the same will be paid at the end of 3rd year to the contract employees.

Further, the cost of production that will be incurred in the 1st year will be \$6,500. In the 2nd year, it will be 75% of the gross revenue earned, and in the last year will be 83% of the gross income as per the estimates. You are required to calculate the benefit-cost ratio and advise whether the order is worthful? Assume the cost of the project is 9.83%.

Solution

To do the cost-benefit analysis first, we need to bring both costs and benefit in today’s value. Since here the costs are also incurred in different years, we need to discount them as well.

Before discounting, we need to compute total cash flows for the entire project life.

There is no cash outflow or inflow in the 0 years as the company is making a deposit and its earning interest on the same at the rate of 3%, and in the final year, the company will make a payment of \$35,000, which has been included in the cash outflow.

Now we can discount the cash flows at 9.83% and arrive at the discounted benefit and discounted cost per below:

Therefore, the Benefit-Cost Ratio can be calculated as using the below formula as,

Benefit-cost ratio = PV of Benefit expected from the Project /PV of the cost of the Project

= 414783.70 / -365478.43

Benefit-Cost Ratio=1.13

Since it is greater than 1, the mega order appears to be beneficial.

#### Example #3

The Mayor of a city is evaluating two transportation projects – Project A and Project B. Project A – The present value of the benefits expected from the project is \$40,00,000. The present value of costs is \$20,00,000. Project B – The present value of benefit expected from the project is \$60,00,000. The present value of costs is \$20,00,000. Calculate the benefit-cost ratio and evaluate which project should be undertaken.

Solution

Project A

Use the following data for calculation of the benefit-cost ratio.

• =4000000/2000000

Project B

Use the following data for calculation of the benefit-cost ratio.

• =6000000/2000000
• BCR = 3

Since the BCR of Project B is higher, Project B should be undertaken.

#### Example #4

A company will have to incur a cost of \$1,00,000 if new machinery is purchased. It will lead to the following extra profits in the following years:

Assuming a discounting rate of 3%, calculate a benefit-cost ratio of the proposed investment.

Solution:

Step 2: Insert the relevant formula in cells C10 and C11.

Step 3: Insert formula =B9*C9 in cell D9.

Step 4: Drag the formula from cell D9 up to D11.

Step 5: Insert the formula =SUM(D9: D11) in cell D12

Step 6: Insert the formula =-D12/B8 in cell D13.

Step 7: Press Enter to get the Result

•  The benefit of using the benefit-cost ratio (BCR) is that it helps to compare various projects in a single term and helps to decide faster which projects should be preferred and which projects should be rejected.
• It compares benefit and cost at the same level that is it considers the time value of money before giving any outcome based on absolute figures as there could be a scenario that the project appears to be lucrative without considering time value and when we consider time value, the benefit-cost ratio goes less than 1.

• The major limitation of the BCR is that since it reduces the project to mere a number when the failure or success of the projector of expansion or investment etc. relies upon various variables and other factors, and those can be weakened by events which are unforeseen.

### Important Points

The following points must be noted before making a decision based upon the Benefit-Cost Ratio.

• Simply following a rule that success means above one and failure or reject decision would mean BCR below one can be misleading and lead to a misfit with the project in which heavy investment is made.
•  Hence, the BCR should be used as a conjunctive tool with different types of analysis as the use of NPV, , other qualitative factors, and then make a good decision.

### Conclusion

We can conclude that if the investment has a BCR which is greater than one, the investment proposal will deliver a positive NPV and on the other hand, it shall have an IRR that would be above the discount rate or the cost of project rate, which will suggest that the Net Present Value of the investment’s cash flows will outweigh the Net Present Value of the investment’s outflows and the project can be considered.

• If the Benefit-Cost Ratio (BCR) is equal to one, the ratio will indicate that the NPV of investment inflows will equal investment’s outflows.
•  Lastly, if the investment’s BCR is not more than one, the investment’s outflow shall outweigh the inflows or the benefits, and the project should not be taken into consideration.

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