Question

Topic: Time Value money

Subject: Engineering economics

Explain the need for the consideration of Benefit to Cost (BC) ratio as oppose to only taking the Present Worth (PW) into account. Provide a case study to justify your answer.

Answer 1

A benefit-cost ratio (BCR) is a ratio used in a cost-benefit analysis to summarize the overall relationship between the relative costs and benefits of a proposed project. BCR can be expressed in monetary or qualitative terms. If a project has a BCR greater than 1.0, the project is expected to deliver a positive net present value to a firm and its investors.The BCR is calculated by dividing the proposed total cash benefit of a project by the proposed total cash cost of the project. Prior to dividing the numbers, the net present value of the respective cash flows over the proposed lifetime of the project – taking into account the terminal values, including salvage/remediation costs – are calculated.

If a project has a BCR that is greater than 1.0, the project is expected to deliver a positive net present value (NPV) and will have an internal rate of return (IRR) above the discount rate used in the DCF calculations. This suggests that the NPV of the project’s cash flows outweighs the NPV of the costs, and the project should be considered.

the BCR is equal to 1.0, the ratio indicates that the NPV of expected profits equals the costs. If a project's BCR is less than 1.0, the project's costs outweigh the benefits, and it should not be considered.

Example of How to Use BCR

As an example, assume company ABC wishes to assess the profitability of a project that involves renovating an apartment building over the next year. The company decides to lease the equipment needed for the project for $50,000 rather than purchasing it. The inflation rate is 2%, and the renovations are expected to increase the company's annual profit by $100,000 for the next three years.

The NPV of the total cost of the lease does not need to be discounted, because the initial cost of $50,000 is paid up front. The NPV of the projected benefits is $288,388, or ($100,000 / (1 + 0.02)^1) + ($100,000 / (1 + 0.02)^2) + ($100,00 / (1 + 0.02)^3). Consequently, the BCR is 5.77, or $288,388 divided by $50,000.

In this example, our company has a BCR of 5.77, which indicates that the project's estimated benefits significantly outweigh its costs. Moreover, company ABC could expect $5.77 in benefits for each $1 of costs.

Limitations of BCR

The primary limitation of the BCR is that it reduces a project to a simple number when the success or failure of an investment or expansion relies on many factors and can be undermined by unforeseen events. Simply following a rule that above 1.0 means success and below 1.0 spells failure is misleading and can provide a false sense of comfort with a project. The BCR must be used as a tool in conjunction with other types of analysis to make a well-informed decision.

Cost benefit analysis is a process used primarily by businesses that weighs the sum of the benefits, such as financial gain, of an action against the negatives, or costs, of that action. The technique is often used when trying to decide a course of action, and often incorporates dollar amounts for intangible benefits as well as opportunity cost into its calculations.

Although CBA can be used for short-term decisions, it is most often used when a company or individual has a long-term decision.

CBA is an easy tool to determine which potential decision would make the most financial sense for the business or individual. The process also takes indirect benefits or costs into consideration, like customer satisfaction or even employee morale. And opportunity cost often plays a big role when deciding between several options. When listing potential costs and benefits, companies or analysts will often factor in things like labor costs, social benefits and other factors that may not be immediately obvious.

The first thing to do when running a cost benefit analysis is to compile a comprehensive list of all the costs and benefits associated with the potential action or decision.

Consider not only the obvious costs (like the cost of installation for new software, or for the software itself) but also possible intangible costs like the opportunity cost of picking one software over another, or over another option like hiring a new employee.

Additionally, consider all the possible benefits of the course of action or decision - how much might it add to your revenue? What other benefits may be inherent in the action that would make it outweigh the costs? For example, would a new software improve efficiency or capabilities that could promote new business or make current operations run smoother? Be sure to also consider intangible benefits as well as obvious, fiscal ones.

Once you have two comprehensive lists of costs and benefits for the action, assign monetary values to each individual cost or benefit.

For some, the values will be obvious - like the cost of installing the software might be $500. However, it is also important to try to assign monetary values to direct or indirect and tangible and intangible costs or benefits if possible. For example, installing a new software may render an employee's computer inaccessible for a couple hours, costing that employee working time or productivity and therefore money generated for the company.

Once you assign monetary values for each cost and benefit, add all the costs and benefits respectively and set up the equation.

Take the sum of the benefits (the sum of all the monetary values assigned to the benefits of the action) and the sum of the costs (all the monetary values of the costs of the action) and plug them into the b/c equation.

The equation should be a numerical equation, and if the numerical benefits (the sum of the fiscal values for the benefits of the action) outweigh the costs, it is advisable to proceed with the decision. If not, the company or individual should re-examine the potential action and make adjustments accordingly.

This equation can also be set up for multiple different options or projects and can help companies compare options side by side.

In our first example, a financial technology startup is expanding and adding two new programmers. The CEO of the company decides to run a cost benefit analysis to determine whether the decision will be beneficial to the company - and to what degree.

The company is analyzing a time horizon of one year, and estimates that revenue would increase some 50% if the two programmers were hired.

On the cost side of the equation, the CEO must examine the cost of the two programmer's salaries - estimated at $75,000. Additionally, there is the cost of recruitment, which might be around $3,000. Training could add an additional $4,000.

Additionally, there is the cost of new work areas and computers, totaling $5,000, and the cost of additional licensing for software and the like, around $2,000.

The total direct and indirect costs would total around $89,000.

When calculating benefits, the CEO would examine the benefit of additional revenue within a 12 month period, estimated around $100,000. Additionally, the increase in product quality resulting from the new programmers (and therefore presumed customer satisfaction) would increase by 10%, adding an estimated $10,000 in value to the company.

In total, the benefits would be $110,000. Using the benefit-cost ratio equation, that would be BCR = $110,000/$89,000, or 1.24. Given that the value is positive (and the total benefits are greater than the total costs), the cost benefit analysis indicates the decision to hire two additional programmers would be a beneficial move for the company.

Construction costs for option 1 would be $80,000 per house, which would sell for $100,000 each. The cost of a sales office would be $1,000,000 and the salaries of sales staff would be $200,000 each year. The project would last 2 years, with a financing cost of $2,000,000 per year.

For option 2, the construction company could build 200 houses, renting 25 of them for 5 years at $3,500 per year. The 25 units could be sold after 5 years for $70,000.

Construction costs for option 2 would be $70,000 per house, and the rest of the homes would sell for $110,000 each. The cost of a sales office would be $2,000,000 and sales staff salaries would be $150,000 each year. The project would last 1 year, with a financing cost of $1,500,000 per year.

For option 1, costs would include:

Construction cost = $24,000,000

Sales office cost = $1,000,000

Cost of sales staff = $400,000

Financing cost = $4,000,000

Total costs would therefore be $29,400,000.

For option 1, benefits would include:

Income from rentals = $1,500,000

Income from sales = $25,000,000

Income from sales after rental = $3,000,000

Total benefits would therefore be $29,500,000. Using the cost benefit analysis formula b/c, the ratio would be 29,500,000/29,400,000, or 1.0. Since the equation is possible, the benefits for option 1 outweigh the costs. However, since the developer is trying to decide between two projects, the same analysis needs to be performed for option 2.

For option 2, costs would include:

Construction cost = $14,000,000

Sales office cost = $2,000,000

Cost of sales staff = $150,000

Financing cost = $1,500,000

Total costs would therefore be $17,650,000.

For option 2, benefits would include:

Income from rentals = $437,500

Income from sales = $19,250,000

Income from sales after rental = $1,750,000

So, the total benefits for option 2 would be $21,437,500. The b/c ratio for option 2 would therefore be 21,437,500/17,650,000, or 1.2.

Comparing both options together, it is clear that option 2 has a higher benefit-to-cost ratio (and costs less to execute) and would therefore be the most fiscally resourceful option for the developer to pick.