Learning Objectives:

• Understand the role of economic decision making in companies.
• Understand the simplicity of payback period method as compared to other methods to evaluate projects.
• Understand payback period analysis concepts and terminology.
• Calculate payback period for a project.

The payback period (PP) is the number of years for the projects to break even, i.e. the number of years for which discounted annual net cash flows must be summed before the sum becomes positive (and remains positive for the remainder of the projects life).
The length of time required to recover the cost of an investment. The payback period of a given investment or project is an important determinant of whether to undertake the position or project, as longer payback periods are typically not desirable for investment positions.
Calculated as: \[\mathrm{Payback\ Period} = \dfrac{\mathrm{Cost\ of \ Project}}{\mathrm{Annual\ Cash\ Inflows}}\] Payback period, though is easy to understand and calculate, may not give you accurate results as it does not consider time value of money. Also, it gives you a time value but it does not tell you what happens after initial investment is recovered.

Solved Example: 17-1-01

Disadvantages of the payback method include:

A. It ignores all cash flows beyond the minimum acceptable payback period.

B. It discounts cash flows to present value.

C. It considers the effects of inflation.

D. All the above.

Payback ignores cash flows beyond the payback period, thereby ignoring the 'profitability' of a project. It does not account for the time value of money, risk, financing, or other important considerations, such as the opportunity cost.

Correct Answer: A

Solved Example: 17-1-02

In payback period analysis, one finds out:

A. The period necessary to invest the cost of the system

B. The time required for the full benefits to accrue

C. The time at which costs are fully recovered

D. Whether the system is able to payback amount invested.

The payback period method of capital budgeting calculates the time it takes to recover the initial cost of an investment.
Ref: http://www.unf.edu/~dtanner/dtch/dt_ch18.htm

Correct Answer: C

Solved Example: 17-1-03

In designing a system it is found that the cost of the system was \$1,50,000 and the benefit is \$10,000 per month. the payback period is:

A. 14 months

B. 17 months

C. 15 months

D. 20 months

\[\mathrm{Payback\ period} =\dfrac{150000}{10000} = 15 \mathrm{\ months}\]

Correct Answer: C

Learning Objectives:

• Perform cost-benefit analysis to justify whether a project is worthwhile or not.

Benefit-to-Cost Ratios:

\[\mathrm{Gross\ B/C\ ratio} = \mathrm{\dfrac{PV \ of \ benefits}{(PV \ of \ capital \ costs + PV \ of \ operating \ costs)}}\] \[\mathrm{Net\ B/C\ ratio = \dfrac{(PV \ of\ benefits -PV\ of \ operating\ costs)}{PV \ of \ capital \ costs}}\]

Steps in Cost-Benefit Analysis:

• Identify all projects or options that will be considered.
• Calculate net benefits for each one.
• Make decision.

Solved Example: 17-2-01

During a project analysis of a motorbike company FERO FONDA, following parameters were analyzed and reported as:

• Payback period = 18 months

• Benefit-to-cost ratio = 1.45

• Break-Even Point = 25000 units/ month

• Rate of Return = 7%

A. Producing 25000 motorbikes per month may require significant initial investment.

B. The rate of return 7% is way below the acceptable value as per the current market trends.

C. Payback period is 18 months, which may be acceptable, which will ensure relatively quick recovery of initial investment.

D. All of the above.

Let us see the options individually.

1. A vehicle assembly line will definitely require significant initial investment, irrespective of the quantity to be produced.

2. Considering the risks and the huge initial investment required, any business will expect more rte of return than what can normally be achieved by keeping it in bank or investing in stocks.

3. Payback period is the duration after which one can expect investment recovered. Considering the long term money making potential of a vehicle manufacturing company, 18 months maybe a reasonably acceptable time.

Correct Answer: D

Solved Example: 17-2-02

Which of the following statement is most accurate?

A. In general, if compound interest is calculated more frequently, you get less interest.

B. If Net Present Value (NPV) is positive, it is considered a liability for that project.

C. Simple and compound interest is same during first computational period.

D. In Benefit – Cost Ratio (BCR) analysis, if the ratio comes out to be exactly 1, you will have to abandon the project even if it causes positive impact on the society.

Let us see the options individually.

1. In compound interest, the interest is added to the principle amount. The shorter the computation period, sooner is the accumulation of interest in the principle. Hence, you get more benefit, if the interest is calculated more frequently in case of compound interest.

2. If NPV is positive, the perceived benefits of a projects outweigh the risk. Hence, it should be considered as an asset.

3. The difference in the calculation of simple and compound interest starts after the first computational period.

4. If Benefit-Cost Ratio (BCR) comes out to be exactly 1, still the project may be pursued for reasons such as it may provide jobs in the area, create sustainable development through generation of renewable energy, etc.

Correct Answer: C

Solved Example: 17-2-03

First Project:

• Costs: \$160 million
• Benefits: \$310 million

• Costs: $90 million
• Benefits: $211 million

Which project should the corporation select?

A. First

B. Second

C. Both are almost equivalent

D. Cannot be decided from the given information

For the first project: B/C Ratio = $\dfrac{310}{160}$ = 1.94

For the second project: B/C Ratio = $\dfrac{211}{90}$ = 2.34

The second project has higher B/C ratio, hence it must be preferred.

Correct Answer: B

Learning Objectives:

• Identify fixed and variable costs;
• Perform break-even analysis to calculate break-even quantity.
• Calculate required quantity to be manufactured to obtain certain profit (or to limit loss).

A breakeven analysis is used to determine how much sales volume your business needs to start making a profit.The breakeven analysis is especially useful when you’re developing a pricing strategy, either as part of a marketing plan or a business plan.

To conduct a breakeven analysis, use this formula:

\[\mathrm{BEQ} = \dfrac{\mathrm{Fixed\ Costs}}{(\mathrm{Revenue\ per\ unit - Variable\ costs \ per \ unit)}}\]

Fixed costs are costs that must be paid whether or not any units are produced. These costs are ’fixed’ over a specified period of time or range of production. e.g. cost of land, machinery and permits.

• Variable costs are costs that vary directly with the number of products produced. For instance, the cost of the materials needed and the labour used is directly proportional to the quantity manufactured.

• In the above diagram, the fixed costs will always be represented by horizontal straight line (parallel to quantity axis) as it is independent of quantity.
• The variable cost will always pass through the origin as no manufactured units means no variable cost.

• The total cost is addition of fixed cost and variable cost. It will be represented by a line having same slope as that of variable cost. However, it will be ’lifted up’ by an amount equal to fixed cost. Which means the y-intercept of total cost line is always equal to fixed cost.

• Revenue line will be similar to variable cost line, passing through origin. However, its slope will be greater that that of variable cost.

• Break-Even Point (BEP) is the intersection point of total cost and revenue.

Solved Example: 17-3-01

Before break-even point, a company will have:

A. Profit

B. Loss

C. No-profit no-loss

D. Profit = selling cost

Break-even point gives you minimum quantity to be manufactured so that the company will start earning profit. This means after break-even point, the company will have profit. Before that company will experience a loss.

Correct Answer: B

Solved Example: 17-3-02

The breakeven point is obtained at intersection of:

A. Total revenue and Total cost line

B. Total cost and variable cost line

C. Variable cost and fixed cost line

D. Fixed cost and total cost line

Refer the above figure. At break-even quantity, there is no profit or no loss, which means revenues are equal to total cost. Hence, break even point is at the intersection of total revenue and total cost.

Correct Answer: A

Solved Example: 17-3-03

At breakeven point:

A. Total expenses = Total revenue

B. Total expenses > Total revenue

C. Total expenses < Total revenue

D. Any of the above

At break-even quantity, there is no profit or no loss, which means revenues are equal to total cost.

Correct Answer: A

Solved Example: 17-3-04

Break-even analysis requires costs to be categorized as:

A. Either fixed or variable

B. Fixed, mixed, or variable

C. Product or period

D. Standard or actual

Depending upon whether the costs vary based upon quantity, the costs can be divided into two categories, fixed and variable.
Fixed cost (FC): It is a cost that does not change with an increase or decrease in the amount of goods or services produced. Fixed costs are expenses that have to be paid by a company, independent of any business activity. For example:

1. Initial investment made by the company in making plant and building, purchasing machinery and equipment etc. Rent. This is a periodic charge for the use of real estate owned by a landlord.

2. Salaries. This is a fixed compensation amount paid to employees, irrespective of their hours worked.

3. Utilities. This is the cost of electricity, gas, phones, and so forth. This cost has a variable element, but is largely fixed.

Variable Cost (VC): Variable cost line has a positive or upward slop starting from origin that indicates the effect of increasing variable expenses with the increase in production.
Variable costs are those that respond directly and proportionately to changes in product produced. For example:

1. Direct raw materials. The most purely variable cost of all, are the raw materials that go into a product.

2. Piece rate labor. This is the amount paid to workers for every unit completed.

3. Production supplies. Things like machinery oil are consumed based on the amount of machinery usage, so these costs vary with production volume.

4. Shipping cost: A business incurs a shipping cost only when it sells and ships out a product. Thus, freight out can be considered a variable cost.

Correct Answer: A

Solved Example: 17-3-05

In break-even analysis, if fixed costs are increased, then:

A. The total costs will increase and break – even point will shift towards right.

B. The total costs will increase and break – even point will shift towards left.

C. Variable costs will decrease and if they offset the increase, then the break- even point may remain practically same.

D. Break-even point is independent of fixed costs as long as revenues are constant.

If fixed costs are increased, then total costs will also increase. Hence the intersection point between total costs and sales revenue will also shift towards right.

Correct Answer: A

Solved Example: 17-3-06

In a graph of break even analysis, revenues are represented by:

A. An inclined straight line passing through origin.

B. A horizontal straight line having positive y-intercept.

C. An inclined straight line having positive y-intercept.

D. A vertical line having positive x-intercept.

In a graph of break-even analysis,

• Fixed costs are represented by a horizontal straight line with y-intercept equal to fixed costs.

• Variable costs are represented by an inclined straight line passing through origin.

• Total costs are represented by an inclined straight line having same slope as variable cost line but with a y-intercept equal to fixed costs.

• Sales revenues are represented by an inclined straight line passing through origin, but its slope is more than slope of variable cost line.

Correct Answer: A

Solved Example: 17-3-07

The quantity required to have desired profit is:

A. (Fixed cost + Desired profit)/ Contribution per unit

B. (Fixed cost - Desired profit)/ Contribution per unit

C. (Fixed cost x Desired profit)/ Contribution per unit

D. Fixed cost / (Desired profit x Contribution per unit)

The contribution is defined as how much net money that goes into your pocket when you sell one additional unit.

So, contribution = sales price - variable cost

Ideally if you just want to recover your investment (i.e. Fixed cost) then you need to produce less quantity, and that quantity will be break-even quantity. The break even quantity can be calculated as FIXED cost/contribution.

However, any company aims for profit, that means now they will have to manufacture more than break-even quantity.

So, not only they would like to receive initial fixed cost investment plus they want to have some profit. (So they want to receive Fixed cost plus profit)

This is possible only when they sell quantity equivalent of (Fixed cost + profit)/contribution, which is the answer.

Correct Answer: A

Solved Example: 17-3-08

An industry is selling a product for \$10 per unit. The fixed cost for assets is \$40000 with variable cost of \$6 per unit. How many units should be produced to break even?

A. 8,000

B. 10,000

C. 12,000

D. 14,000

Break Even Quantity (BEQ) is given by, \begin{align*} \mathrm{BEQ} &= \dfrac{\mathrm{Fixed\ Costs}}{(\mathrm{Revenue\ per\ unit - Variable\ costs \ per \ unit)}}\\ &= \dfrac{40000}{10-6}\\ &=10000 \end{align*}

Correct Answer: B

Solved Example: 17-3-09

You are opening a whiteboard marker factory, which requires fixed cost of \$14,500. Each marker will cost you \$0.60, and would sell for \$1.5 each. How many markers must be sold to realize a profit of \$1,450?

A. 1611

B. 26583

C. 17722

D. 9667

\begin{align*} \mathrm{BEQ} &= \dfrac{\mathrm{Fixed\ Costs}}{(\mathrm{Revenue\ per\ unit - Variable\ costs \ per \ unit)}}\\ &= \dfrac{14500}{1.5-0.60}\\ &= 16111 \end{align*} Any sales after break even quantity generates profit. To get \$1450 profit, $\dfrac{1450}{1.5-0.6}$ = 1611 additional markers must be sold. Hence, total quantity to be sold = 16111+1611= 17722

Correct Answer: C

Solved Example: 17-3-10

Consider the following data projected for the year:

• Selling price/unit: $14

• Variable Cost/unit: $5 (this was for labor, materials and overhead required)

• Fixed Costs: $100,000/year (rent, insurance, and other costs that do not depend on volume)

• Projected volume: 70,000 units (sales based on previous year sales)

A. 11111

B. 20000

C. 7143

D. 5263

BEP = $\dfrac{100000}{14-5}= 11111$

Correct Answer: A

Solved Example: 17-3-11

A graphical device used to determine the break-even point and profit potential under varying conditions of output and costs, is known as:

A. Gantt chart

B. Flow chart

C. Break-even chart

D. PERT chart

Let us look at the options individually.

• A Gantt chart is a type of bar chart, that illustrates a project schedule. Gantt charts illustrate the start and finish dates of the terminal elements and summary elements of a project.

• A flow chart is a graphical representation of a computer program in relation to its sequence of functions (as distinct from the data it processes).

• A break-even chart calculated the break-even point, that is the point at which revenue is exactly equal to costs. At this point, no profit is made and no losses are incurred.

• PERT:(Program Evaluation and Review Technique) A Project Management technique is a means of projecting task and project completion and organizing complex sequences of tasks. PERT is based on the probability of an event occurring at a specified time.

Correct Answer: C

Solved Example: 17-3-12

Break-even analysis consists of:

A. Fixed cost

B. Variable cost

C. Fixed and variable costs

D. Operation costs

Break-even analysis consists of fixed cost, which do not change with quantity manufactured, such as cost of land, machinery, license and registration, etc, as well as variable cost, which are directly proportional to the quantity manufactured, such as raw material cost and utility costs.

Correct Answer: C

Solved Example: 17-3-13

Break-even analysis shows profit when:

A. Sales revenue > total cost

B. Sales revenue = total cost

C. Sales revenue < total cost

D. Variable cost < fixed cost

Break-even analysis shows profit after break even point, when sales exceed total costs.

Correct Answer: A

Solved Example: 17-3-14

The break-even point represents:

A. The most economical level of operation of any industry

B. The time when unit can run without loss and profit

C. Time when industry will undergo loss

D. The time when company can make maximum profits

Break-even point represents no profit no loss scenario. Before break-even point there is loss and after it, there is a profit.

Correct Answer: B

Examples of some overhead costs are: Defective Work, Depreciation, Employee Fringe Benefits Fuel, Heat and Light, Indirect Labor, Indirect Materials, Insurance, Janitorial Service Overtime Premium, Plant Security, Power, Property Tax, Rent, Repairs, Small Tools, Spoilage, Supplies, Lubricants, Maintenance, Materials Handling, Telephone/Fax, Water, Workers’ Compensation Insurance (Ref: http://www.mccc.edu/~horowitk/documents/Chapter04_000.pdf)

Solved Example: 17-4-01

Which of the following cost is also known as overhead cost or on cost:

A. Cost of direct labour

B. Cost of indirect labour

C. Direct expenses

D. Indirect expenses

Correct Answer: D