## 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**

- 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., net present value 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 present valuePresent ValuePresent Value (PV) is the today's value of money you expect to get from future income. It is computed as the sum of future investment returns discounted at a certain rate of return expectation.read more 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

#### 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 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 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 escrow accountEscrow AccountThe escrow account is a temporary account held by a third party on behalf of two parties in a transaction. It reduces the risk of failing to oblige the transaction by either of the parties. It operates until a transaction is completed and all the conditions are met.read more 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 3^{rd }year to the contract employees.

Further, the cost of production that will be incurred in the 1^{st} year will be $6,500. In the 2^{nd} 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.

Year | Cash Outflow | Cash Inflow | Interest Earned | Total Cash Flows |
---|---|---|---|---|

0 | – | – | – | – |

1 | -6500.00 | 10000.00 | 700.00 | 4200.00 |

2 | -24000.00 | 32000.00 | 700.00 | 8700.00 |

3 | -450000.00 | 500000.00 | 700.00 | 50700.00 |

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.

Particulars | Amount |
---|---|

Present Value of Benefit Expected from Project | 4000000 |

Present Value of Cost of the Project | 2000000 |

- =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:**

Year | Profit |
---|---|

2016 | $40,000 |

2017 | $50,000 |

2018 | $50,000 |

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

**Solution: **

**Step 1:** Calculate 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. 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**

### Advantages

- 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.

### Disadvantages

- 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, IRR, 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.

### Recommended Articles

This article has been a guide to Benefit-Cost Ratio and its definition. Here we discuss the formula to calculate Benefit-Cost Ratio (BCR) along with examples. Advantages and limitations. You can learn more about excel modeling from the following articles –

- Advantages of Net Present Value
- Cost-Benefit Analysis Examples
- Mutual Fund Expense Ratio
- Calculate Benefit-Cost Ratio