Cost-Benefit Analysis Formula

What is Cost-Benefit Analysis Formula?

The cost-benefit analysisCost-benefit AnalysisCost-benefit analysis is the technique used by the companies to arrive at a critical decision after working out the potential returns of a particular action and considering its overall costs. Some of these models include Net Present Value, Benefit-Cost Ratio etc.read more involves comparing the costs to the benefits of a project and then deciding whether to go ahead with the project. The costs and benefits of the project are quantified in monetary terms after adjusting for the time value of money, which gives a real picture of the costs and benefits.

There are two popular models of carrying out cost-benefit analysis calculations – Net Present Value (NPV) and benefit-cost ratio.

The formula for Net Present ValueNet Present ValueNet Present Value (NPV) estimates the profitability of a project and is the difference between the present value of cash inflows and the present value of cash outflows over the project’s time period. If the difference is positive, the project is profitable; otherwise, it is not.read more (NPV) is

NPV = ∑ Present Value of Future Benefits – ∑ Present Value of Future Costs

The formula for benefit-cost ratio is:

Benefit-Cost Ratio = ∑ Present Value of Future Benefits / ∑ Present Value of Future Costs.
Cost-Benefit-Analysis-Formula

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Explanation of Cost-Benefit Analysis Formula

Net Present Value (NPV) and Benefit-Cost ratioBenefit-Cost RatioThe benefit-cost ratio measures the monetary or qualitative correlation of a project's or investment's cost with the benefits a company or individual will acquire from it. It is computed by dividing the present value of the project's expected benefits from the present value of the project's cost.read more are two popular models of carrying out a cost-benefit analysis formula in excel.

Net Present Value

For calculating Net Present Value, use the following steps:

Step 1: Find out the future benefits.

Step 2: Find out the present and future costs.

Step 3: Calculate the present value of future costs and benefits. The present value factorPresent Value FactorPresent value factor is factor which is used to indicate the present value of cash to be received in future and is based on time value of money. This PV factor is a number which is always less than one and is calculated by one divided by one plus the rate of interest to the power, i.e. number of periods over which payments are to be made.read more is 1/(1+r)^n. Here r is the rate of discounting, and n is the number of years.

The formula for calculating present value is:

Present Value of Future Benefits = Future Benefits * Present Value Factor.

Present Value of Future Costs = Future Costs * Present Value Factor

Step 4: Calculate the Net Present Value using the formula:

NPV = ∑ Present Value of Future Benefits – ∑ Present Value of Future Costs

Step 5: If the Net Present Value (NPV) is positive, the project should be undertaken. If the NPV is negative, the project should not be undertaken.

Benefit-Cost Ratio

For calculating the cost-benefit ratio, follow the given steps:

Step 1: Calculate the future benefits.

Step 2: Calculate the present and future costs.

Step 3: Calculate the present value of future costs and benefits.

Step 4: Calculate the benefit-cost ratio using the formula

Benefit-Cost Ratio = ∑ Present Value of Future Benefits / ∑ Present Value of Future Costs.

Step 5: If the benefit-cost ratio is greater than 1, go ahead with the project. If the benefit-cost ratio is less than 1, you should not go ahead with the project.

Examples of Cost-Benefit Analysis Formula

Let’s see some simple to advanced practical examples of the cost-benefit analysis equation to understand it better.

You can download this Cost-Benefit Analysis Formula Excel Template here – Cost-Benefit Analysis Formula Excel Template

Cost-Benefit Analysis Formula – Example #1

The present value of the future benefits of a project is $6,00,000. The present value of the costs is $4,00,000. Calculate the Net Present Value (NPV) of the project and determine whether the project should be executed.

Solution

Use below given data for the calculation of Net Present Value (NPV)

Cost Benefit Analysis Formula Example 1

Calculation of Net Present Value (NPV) can be done as follows-

Cost Benefit Analysis Formula Example 1.1
  • = $6,00,000 – $4,00,000

Net Present Value (NPV) will be –

Cost Benefit Analysis Formula Example 1.2
  • = $2,00,000

Since the NPV is positive, the project should be executed.

Cost-Benefit Analysis Formula – Example #2

The CFO of Briddles Inc. is considering a project. He wants to determine whether the project should be executed. He decides that he would use the NPV model to determine whether the company should be executing the project.

The upfront cost of $1,00,000 would be incurred. It is the given information relating to the benefits. Use the discounting rate of 6% to calculate the NPV of the project. Also, determine whether the project is viable.

Cost Benefit Analysis Formula Example 2

Solution

To calculate the net present value (NPV), we need to first calculate the present value of future benefits and the present value of future costs.

Calculation of PV Factor for Year 1

Cost Benefit Analysis Formula Example 2.1
  • =1/(1+0.06)^1
  • =0.9434

Similarly, we can calculate the PV Factor for the remaining years

Cost Benefit Analysis Formula Example 2.2

Calculation of present value of future costs

Cost Benefit Analysis Formula Example 2.3
  • =-100000*1.0000
  • =-100000.00
Cost Benefit Analysis Formula Example 2.4

Calculation of Total Value of Future Benefits

Cost Benefit Analysis Formula Example 2.5
  • =47169.81+26699.89+50377.16
  • =124246.86

Calculation of Net Present Value (NPV) can be done as follows-

Cost Benefit Analysis Formula Example 2.6
  • =124246.86-(-100000.00)

Net Present Value (NPV) will be –

Cost Benefit Analysis Formula Example 2.7
  • NPV =24246.86

Since the Net Present Value (NPV) is positive, the project should be executed.

Cost-Benefit Analysis Formula – Example #3

The CFO of Jaypin Inc. is in a dilemma. He has to decide whether to go for Project A or Project B. He decides to choose the project based on the benefit-cost ratio model. The data for both the projects is as under. Choose the project based on the benefit-cost ratio.

Example 3

Solution

Project A

Calculation of the Benefit-Cost Ratio can be done as follows,

Cost Benefit Analysis Formula Example 3.1
  • =78000/60000

Benefit-Cost Ratio will be –

Cost Benefit Analysis Formula Example 3.2
  • Benefit-Cost Ratio = 1.3

Project B

Calculation of the Benefit-Cost Ratio can be done as follows,

Cost Benefit Analysis Formula Example 3.3
  • =56000/28000

Benefit-Cost Ratio will be –

Example 3.4
  • Benefit-Cost Ratio = 2

Since the benefit-cost ratio for Project B is higher, Project B should be chosen.

Relevance and Uses

Cost-benefit analysis is useful in making decisions on whether to carry out a project or not. Decisions like whether to shift to a new office, which sales strategy to implement are taken by carrying out a cost-benefit analysis. Generally, it is used for carrying out long term decisions that have an impact over several years. This method can be used by organizations, government as well as individuals. Labor costsLabor CostsCost of labor is the remuneration paid in the form of wages and salaries to the employees. The allowances are sub-divided broadly into two categories- direct labor involved in the manufacturing process and indirect labor pertaining to all other processes.read more, other direct and indirect costs, social benefits, etc. are considered while carrying out a cost-benefit analysis. The costs and benefits need to be objectively defined to the extent possible.

The cost-benefit analysis formula in excel helps in comparing different projects and in finding out which project should be implemented. Under the NPV model, the project with a higher NPV is chosen. Under the benefit-cost ratio model, the project with a higher benefit-cost ratio is chosen.

Cost-Benefit Analysis Formula in Excel (with Excel Template)

The CFO of Housing Star Inc. gives the following information related to a project. Costs of $1,80,000 are to be incurred upfront at the start of 2019, which is the date of evaluation of the project. Use a discounting rate of 4% to determine whether to go ahead with the project based on the Net Present Value (NPV) method.

Example 4

Solution:

Step 1: Insert the formula =1/(1+0.04)^A9 in cell C9 to calculate the present value factor.

Cost Benefit Analysis Formula Example 4.1

Step 2: Press Enter to get Result

Cost Benefit Analysis Formula Example 4.2

Step 3: Drag the formula from cell C9 up to cell C12.

Example 4.3

Step 4:Press Enter to get Result

Cost Benefit Analysis Formula Example 4.4

Step 5: Insert the formula =B9*C9 in cell D9

Example 4.5

Step 6: Drag the formula up to cell D12.

Cost Benefit Analysis Formula Example 4.6

Step 7: Insert the formula =SUM(D9: D12) in B14 to calculate the sum of the present value of cash inflows.

Cost Benefit Analysis Formula Example 4.7

Step 8: Press Enter to get Result

Example 4.8

Step 9: Insert the formula =B14-B15 to calculate the Net Present Value.

Cost Benefit Analysis Formula Example 4.9

Step 10: Press Enter to get Result

Example 4.10

Step 11: If the NPV is greater than 0, the project should be implemented. Insert the formula =IF(D8>0, “Project should be implemented,” “Project should not be implemented”) in cell B17.

Example 4.11

Since NPV is greater than 0, the project should be implemented.

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