BenefitCost Ratio Formula (Table of Contents)
What is the BenefitCost Ratio Formula?
The benefitcost ratio is the ratio that gives the relationship between the benefits and costs of a proposed project or investment. The long term benefits of the proposed project are compared to the costs relating to the project. It has two factors – One is the associated benefits and the other is the associated costs. The BenefitCost Ratio (BCR) Formula is represented as below,
Where,
 PV is Present Value
The present value of costs and benefits is calculated as the value of money today is not the same as the value of money in the future due to inflation. If the Benefitcost ratio of the project is greater than 1, then the project should be undertaken. If the benefitcost ratio is less than 1, then the project should not be carried out.
Explanation of the BenefitCost Ratio Formula (BCR)
In order to calculate the BCR, use the following steps:
Step 1: Calculate the present value of benefit expected from the project. The formula 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 present value of costs as there is no PV factor.
Step 3: Calculate the benefitcost ratio using the formula:
BenefitCost Ratio Formula = PV of Benefit Expected from the Project / PV of the Cost of the Project
Step 4: In certain cases, we have to evaluate the proposed investment on the basis of the benefitcost ratio. The rules for selecting the project are as under:
 If the benefitcost ratio is less than 1, you should not proceed with the proposed project
 If the benefitcost ratio is greater than 1, proceed with the proposed project.
Examples of BenefitCost Ratio Formula (BCR)
Let’s see some simple to advanced examples of BCR formula to understand it better.
Example #1
The present value of the proposed benefits of a project is $17,80,000. The costs which are incurred upfront are $10,00,000. Calculate the benefitcost ratio. Should this project be undertaken based on a benefitcost ratio?
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Solution
Use the following data for calculation of the benefitcost ratio.
Therefore, the calculation of benefitcost ratio is as follows,
 =1780000/1000000
BenefitCost Ratio will be –
 BenefitCost Ratio = 1.78
Since the benefitcost ratio is greater than 1, the project should be undertaken.
Example #2
A company is engaged in the business of manufacturing shoes. It wants to evaluate whether to replace manufacturing equipment. The new manufacturing equipment is expected to generate the following profits: An upfront cost of $4,00,000 will be incurred on replacing the equipment. Evaluate whether the manufacturing equipment should be replaced on the basis of the benefitcost ratio. Use the discounting rate of 4%.
Solution
PV Factor and PV of Benefit Expected from Project
Therefore, the calculation of benefitcost ratio is as follows,
 =626209/400000
BenefitCost Ratio will be –
 BenefitCost Ratio = 1.5655
Since the benefitcost ratio is greater than 1, the manufacturing equipment should be replaced.
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 benefitcost ratio and evaluate which project should be undertaken.
Solution
Project A
Use the following data for calculation of the benefitcost ratio.
Therefore, the calculation of benefitcost ratio is as follows,
 =4000000/2000000
BenefitCost Ratio will be –
 BenefitCost Ratio = 2
Project B
Use the following data for calculation of the benefitcost ratio.
Therefore, the calculation of benefitcost ratio is as follows,
 =6000000/2000000
BenefitCost Ratio will be –
 BenefitCost Ratio = 3
Since the benefitcost ratio 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 benefitcost ratio of the proposed investment.
Solution:
Step 1: Calculate the Present Value Factor. Insert the formula =1/((1+0.03))^1 in cell C9.
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
Calculator
You can use these benefitcost ratio formula calculator
PV of Benefit Expected from the Project  
PV of the Cost of the Project  
BenefitCost Ratio Formula  
BenefitCost Ratio Formula = 


Relevance and Uses
The benefitcost ratio is one of the tools of strategic planning. The benefitcost ratio is simple to calculate. It helps determine which projects have a higher benefit in relation to the investment made in the project. The benefitcost ratio gives the positives and negatives of investing in different projects, which enables businesses and governments to make decisions. Once the benefitcost ratio is calculated, it needs to be interpreted to determine whether to go ahead with the proposed investment.
If the benefitcost ratio is greater than 1, it implies that the benefits of the proposed investment exceed the costs. The entity should go ahead with the project as the benefits significantly outweigh the costs. If the benefitcost ratio is less than 1, it implies that the costs are greater than the benefits. The costs are equal to the benefits if the benefitcost ratio is equal to 1.
A benefitcost ratio of say 1.8 means that for every dollar spent on the project, the benefits would be $1.8. Similarly, a benefitcost ratio of 0.7 means that for every dollar spent on the project, the enterprise will recover only $0.7. While calculating the benefitcost ratio, it is important to discount the benefits and costs in order to adjust for the effects of inflation. If we don’t discount the costs and benefits, the results would be erroneous and the wrong decision would be taken.
The benefitcost ratio depends upon future estimates of costs and benefits. Since it is extremely difficult to predict the future, the calculations may not be accurate. For example, let’s take a transportation project. It may take more time to acquire land for the project, which may lead to cost overruns. This may lead to underestimation of the costs of the project. Another limitation is that certain benefits may be qualitative in nature and it may be difficult to quantify these benefits. For instance, if a center for senior citizens is developed in a city, it will end up keeping senior citizens engaged and active. Quantifying engagement and activity in monetary terms may be a difficult job.
Recommended Articles
This has been a guide to the BenefitCost Ratio Formula. Here we discuss the calculation of benefitcost ratio along with practical examples and downloadable excel template. You can learn more about financing from the following articles –
 Calculate Velocity of Money
 Top 4 Capital Budgeting Methods
 Meaning of NPV Profile
 Incremental IRR Calculation
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