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Cost Benefit Analysis Formula

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Benefit Cost Ratio is profitability indicator used in cost-benefit analysis to determine the viability of cash flows generated from a project or asset. Check FAQs

BCR = \frac{\sum (x, 0, n, (\frac{CF B}{{(1 + (0.01 \cdot DR))}^{x}}))}{\sum (x, 0, n, (\frac{CF C}{{(1 + (0.01 \cdot DR))}^{x}}))}

BCR - Benefit Cost Ratio?n - Number of Periods?CF_B - Cash Flow of Benefits?DR - Discount Rate?CF_C - Cash Flow of Costs?

Cost Benefit Analysis Example

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Here is how the Cost Benefit Analysis equation looks like with Values.

Here is how the Cost Benefit Analysis equation looks like with Units.

Here is how the Cost Benefit Analysis equation looks like.

2 = \frac{\sum (x, 0, 6, (\frac{200000}{{(1 + (0.01 \cdot 12))}^{x}}))}{\sum (x, 0, 6, (\frac{100000}{{(1 + (0.01 \cdot 12))}^{x}}))}

2 = \frac{\sum (x, 0, 6, (\frac{200000}{{(1 + (0.01 \cdot 12))}^{x}}))}{\sum (x, 0, 6, (\frac{100000}{{(1 + (0.01 \cdot 12))}^{x}}))}

2 = \frac{\sum (x, 0, 6, (\frac{200000}{{(1 + (0.01 \cdot 12))}^{x}}))}{\sum (x, 0, 6, (\frac{100000}{{(1 + (0.01 \cdot 12))}^{x}}))}

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Cost Benefit Analysis Solution

Follow our step by step solution on how to calculate Cost Benefit Analysis?

FIRST Step Consider the formula

BCR = \frac{\sum (x, 0, n, (\frac{CF B}{{(1 + (0.01 \cdot DR))}^{x}}))}{\sum (x, 0, n, (\frac{CF C}{{(1 + (0.01 \cdot DR))}^{x}}))}

Next Step Substitute values of Variables

∴

BCR = \frac{\sum (x, 0, 6, (\frac{200000}{{(1 + (0.01 \cdot 12))}^{x}}))}{\sum (x, 0, 6, (\frac{100000}{{(1 + (0.01 \cdot 12))}^{x}}))}

Next Step Prepare to Evaluate

∴

BCR = \frac{\sum (x, 0, 6, (\frac{200000}{{(1 + (0.01 \cdot 12))}^{x}}))}{\sum (x, 0, 6, (\frac{100000}{{(1 + (0.01 \cdot 12))}^{x}}))}

LAST Step Evaluate

∴

BCR = 2

Cost Benefit Analysis Formula Elements

Variables

Functions

Benefit Cost Ratio

Benefit Cost Ratio is profitability indicator used in cost-benefit analysis to determine the viability of cash flows generated from a project or asset.

Symbol: BCR

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Benefit Cost Ratio

Number of Periods

The Number of Periods is the periods on an annuity using the present value, periodic payment, and periodic rate.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Periods

Cash Flow of Benefits

Cash Flow of Benefits is the cash inflow for an asset or a project.

Symbol: CF_B

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cash Flow of Benefits

Discount Rate

Discount Rate is the interest rate charged to commercial banks and other depository institutions for loans received from the Federal Reserve Bank’s discount window.

Symbol: DR

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Discount Rate

Cash Flow of Costs

Cash Flow of Costs is the cash outflow for an asset or a project.

Symbol: CF_C

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Cash Flow of Costs

sum

Summation or sigma (∑) notation is a method used to write out a long sum in a concise way.

Syntax: sum(i, from, to, expr)

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How to Evaluate Cost Benefit Analysis?

Cost Benefit Analysis evaluator uses Benefit Cost Ratio = (sum(x,0,Number of Periods,(Cash Flow of Benefits/(1+(0.01*Discount Rate))^x)))/(sum(x,0,Number of Periods,(Cash Flow of Costs/(1+(0.01*Discount Rate))^x))) to evaluate the Benefit Cost Ratio, The Cost Benefit Analysis determines the viability of cash flows generated from an asset or project. The BCR compares the present value of all benefits generated from a project/asset to the present value of all costs. Benefit Cost Ratio is denoted by BCR symbol.

How to evaluate Cost Benefit Analysis using this online evaluator? To use this online evaluator for Cost Benefit Analysis, enter Number of Periods (n), Cash Flow of Benefits (CF_B), Discount Rate (DR) & Cash Flow of Costs (CF_C) and hit the calculate button.

FAQs on Cost Benefit Analysis

What is the formula to find Cost Benefit Analysis?

The formula of Cost Benefit Analysis is expressed as Benefit Cost Ratio = (sum(x,0,Number of Periods,(Cash Flow of Benefits/(1+(0.01*Discount Rate))^x)))/(sum(x,0,Number of Periods,(Cash Flow of Costs/(1+(0.01*Discount Rate))^x))). Here is an example- 2 = (sum(x,0,6,(200000/(1+(0.01*12))^x)))/(sum(x,0,6,(100000/(1+(0.01*12))^x))).

How to calculate Cost Benefit Analysis?

With Number of Periods (n), Cash Flow of Benefits (CF_B), Discount Rate (DR) & Cash Flow of Costs (CF_C) we can find Cost Benefit Analysis using the formula - Benefit Cost Ratio = (sum(x,0,Number of Periods,(Cash Flow of Benefits/(1+(0.01*Discount Rate))^x)))/(sum(x,0,Number of Periods,(Cash Flow of Costs/(1+(0.01*Discount Rate))^x))). This formula also uses Summation Notation (sum) function(s).

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Cost Benefit Analysis Formula

Cost Benefit Analysis Example

Cost Benefit Analysis Solution

Cost Benefit Analysis Formula Elements

Other formulas in Public Finance category

How to Evaluate Cost Benefit Analysis?

FAQs on Cost Benefit Analysis

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