Objectives:

Define and understand primary variable and fixed costs

Understand the relevance of other types of costs and how they behave under certain circumstances and conditions relevant to time

Define and understand the interrelationships between NPV, BCR, Discount Ratios, and IRR methods of project/investment feasibility

Basic methods and calculations for determining a project or investment selection, or reinvestment strategy
Cost analysis is a comparison of costs. Costs used to prepare financial statements are not the same as those used to control operations. Costs may be controllable or noncontrollable and are subject to time periods and constraints. For example, controllable costs are those the manager may authorize. However, costs that may be able to be controlled over the longterm, may not be controllable in the shortterm.
Total cost is the relationship between production quantity and costs, expressed as:
Total cost = Fixed Cost + Variable Cost * Output
COST CLASSIFICATIONS
Costs are classified according to their behavior. A cost's behavior is how the cost responds to changes in the level of the business activity.
Costs are broadly divided into variable costs and fixed costs. For example, the total variable cost increases and decreases in relation to the changes in business activity levels. Conversely, fixed costs are not affected by business activity level changes, remaining the same throughout.
 Absolute cost quantifies an asset's loss in value.
 Relative cost compares the selected action or decision, and the alternative action or decision that was not selected.
 Opportunity cost is the cost or sacrifice (loss) incurred as a result of selecting one activity or action over another.
 Differential cost is a cost that is present under one kind of alternative or set of conditions, but not under another. Differential costs may be variable or fixed.
 Incremental costs (sometimes referred to as "differential costs") are increases or decreases in cost, when moving from one alternative to another.
 Sunk costs are those that have already been incurred and cannot be changed, now, or in the future.
VARIABLE COSTS
"For a cost to be variable, it must be variable with something"  which happens to be its activity base. A variable cost's activity base is a cost driver, which is a measure of effort that influences what causes the cost to change. The type and quantity of variable costs a firm has depends on the nature of the firm's structure.
A variable cost's total variance is directly proportional to changes in the level of business activity. A variable cost changes in accordance with the particular unit of production. But it remains constant per unit, such as:

cost per cubic meter

cost per cubic yard, or

cost per square foot
Variable costs incurred during a stated time period may be calculated using the following formula:
Total Variable Cost = Total Output Quantity * Variable Cost Per Unit of Output
FIXED COSTS
Fixed costs are only incurred once and remain constant in total dollar amount, regardless of the level of activity. Fixed costs are timerelated. For example, indirect costs and overhead  such as salaries, rent, insurance, and advertising  are considered fixed costs because
 they remain unchanged, regardless of increases or decreases in production output, and
 they do not depend on the level of goods or services produced by the business.
However, fixed costs do decrease per unit as the business activity level increases, and increase per unit as the business activity level decreases. For example, when additional units are produced, there is a decline in unit cost.
Total fixed costs may be:
 Committed, which are longterm and cannot be reduced to zero at any point, or
 Discretionary, which are managed and based on periodic spending/investing decisions
Committed fixed costs are plant and equipment investments. Discretionary fixed costs are research and development, advertising, or development program costs.
Benefit Cost Analysis (BCA)
Benefit Cost Analysis (BCA) is a decisionmaking tool used to determine the feasibility of a project or investment, or the probability of its success. BCA allows the manager to compare the ultimate cost(s) and benefit(s) of a proposed business activity or investment, prior to committing time and resources.
Performing a Benefit Cost Analysis allows management to identify the best cost alternative by:
ASSESSING BENEFIT COST FEASIBILITY
Commonly used methods for measuring BCA, or economic feasibility, include the:

Payback Method, which determines when an investment will pay for itself.

Return on Investment (ROI), which compares the "lifetime profitability" of project or investment options or projects, using a percentage rate that represents the correlation between the invested amount and the return, expressed as:
(Estimated lifetime benefits  Estimated Lifetime Costs)
Lifetime ROI = Estimated lifetime costs

Net Present Value, which compares the benefits of available options and annual discounted costs
THE BENEFIT COST ANALYSIS PROCESS
The actual applicable BCA process includes:

Listing all options and stakeholders

Calculating and evaluating all costs/benefits over the projected time period

Quantify all costs and benefits into currency

Add the applicable discount rate

Estimate the net present value (time value of money) of all options

Perform a sensitivity analysis and present the recommended selection
BENEFIT COST ANALYSIS ADVANTAGES
BCA is a systematic, quantifiable approach that exposes strengths, weaknesses, and benefits of available options that might satisfy a specific business activity.
BCA provides method that allows management to evaluate qualitative arguments using quantitative data that supports the analysis.
All options are compared using the same method, which makes rejection of certain weak or impractical alternatives obvious.
BENEFIT COST ANALYSIS DRAWBACKS
BCA requires all costs and benefits be assigned monetary values. Intangible costs and benefits are difficult to value.
Some calculated results are sensitive to the discount rate chosen. Different discount rates should be tried before eliminating any option.
Most current benefits and costs are known. Future costs that arise can only be speculated at best. Information may be limited which injects an element of uncertainty, which is not uncommon in decisionmaking.
Net Present Value (NPV)Investments can be viewed in terms of the future or at their present value. The Net Present Value (NPV) is the sum of benefits minus costs, or the current value of all project net benefits. This sum is discounted at the discount rate. A project appears to be a good choice when the project has a NPV greater than zero. If an investment has a positive net present value, it will also have a yield in excess of the cost of capital.
The Net Present Value (NPV) formula is written and expressed as:
Where:
t = the time of the cash flow
i = the opportunity cost of capital
R_{t }= the net cash flow = Cash Inflow – Cash Outflow (at time t)
N = total number of periods
NPV is based on inflation and any lost return on investment:

Inflation dictates that the current purchasing power of a dollar will be less 12 months from today. For example, the value of one dollar today will be worth only 97 cents one year from today, give that inflation increases 3 percent over that time.

Lost ROI typically stems from being overly cautious. Conservative investments can end up costing the firm money in the longterm. For example, if inflation is flat and $1.00 is deposited in a 2.75percent interest account today, 12 months from today, the investment value will be just $1.03.
When known, variable discount rates used to calculate the NPV may better reflect the nature of the situation than an NPV calculated using a constant discount rate for the entire investment period.
D. Discounting and Discount Rate
Discounting is the process used to change benefits and costs into their present values, or essentially, determine the future cash flow. Discounting assumes that a dollar received in the future is worth less than that dollar today. In effect, the future value of the dollar is discounted.
Discounting and compounding are opposites. The rate at which a future value is discounted is the interest rate, which is closely related to the present values compounded rate. A dollar invested today at a compound interest rate of 3 percent will be worth $1.03 a year from now. However, $1.03 today will only be worth $1.00 a year from today if the discount interest rate is 3 percent.
Future benefits and costs used in a BCA calculation must be discounted to justify their present value when they occur in the future. The Present Value can be found using the following formula:
Where:
PV = present value of the invested amount
P_{t} = dollar value of the future amount in time t
r = the discount rate
t = the year P_{t} is realized
Definitively, the Discount Rate is "the rate used to discount future cash flows to the present value." Essentially it is the interest factor used to determine the NPV, or, the future value of today's dollar. Typically, it is the cost of capital to the firm. The Discount Rate takes into account the effects of inflation and any lost return on investment.
E. BenefitCost Ratio (BCR)The BenefitCost Ratio (BCR), used in costbenefit analysis, summarizes the project's proposed value, expressed monetarily, relative to its costs. All benefits and costs are expressed in their discounted present value, which is the value of an expected income stream that is less, or equal to, the future value.
Simplified, the BCR defines the value of a project compared to the capital invested to complete it, as determined from the BCA. The BenefitCost Ratio is calculated as the Net Present Value of benefits divided by the Net Present Value of costs:
Where:
B_{t} = the benefit in time t
C_{t} = the cost in time t
SIMPLIFIED: Discounted value of incremental benefits
BCR = Discounted value of incremental costs
1. The higher the BCR, the better the investment.
2. If the BCR > 1, the project qualifies as a good investment candidate.
3. Projects having the highest NPV are the best risks.
4. The NPV should be evaluated over the servicelife of the project.
F. Internal Rate of Return (IRR)The Internal Rate of Return (IRR) is a probability metric used to determine desirability of a project or investment. The calculated result indicates the degree of efficiency, yield, or quality of investment. Corporations employ the IRR method to compare feasibility of capital projects.
The IRR equates the maximum interest paid for cash outflows (project, investment, and operating costs), with cash inflows, that still allow the investor to break even. Simply put, the present value of inflows equals the present value of outflows.
PV (Benefits)  PV(Costs) = ZERO
A project is acceptable for selection when the IRR exceeds the project discount rate.
Generally, Internal Rate of Return and Net Present Value calculation methods produce similar results when projects are mutually exclusive. Probability, calculated in both the internal rate of return and the net present value methods, must equal or exceed the cost of capital for the projects to be potentially reasonable selection decisions.
An assumption of the IRR is that all inflows can be reinvested at the yield from a given investment. If an investment has a positive NPV, it will also have a yield that exceeds the cost of capital.
A Modified Internal Rate of Return (MIRR) uses the cost of capital to determine the probability of project success. Initial positive cash flow is followed by negative cash flow which, in turn, is followed by positive cash flow resulting in multiple IRRs. When a project has multiple IRRs, the Internal Rate of Return may be more easily computed using reinvested benefits. MIRR, whose assumed reinvestment rate is equal to the project's cost of capital, is used.
DRAWBACKS OF USING THE IRR METHOD
It is not advisable to use the Internal Rate of Return method to compare mutually exclusive projects. The IRR should also not be used to equate projects of different durations.
Another erroneous assumption is that all cash flows continue until the end of the project. The reinvestment of all cash flows does not continue until the project is completed. The calculated IRR does not assume they do.