Chapter Twenty-Four: Analytics for Managerial Decision Making

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Delete Button Clip ArtVirtually everyone can think of things they wish they could do over. Mistakes and fumbled execution seem to be unavoidable. Business persons experience similar feelings. Perhaps inventory was shipped using costly overnight express when less-expensive ground shipping would have worked as well. Perhaps parking lot lights were unnecessarily left on during daylight hours. Hundreds of examples can be cited, and management must be diligent to control against these types of business execution errors.

Earlier chapters discussed numerous methods for monitoring and controlling against waste. Remember, each dollar of wasted expense comes right off the bottom line. For a public company that is valued based on a multiple of reported income, a dollar wasted can translate into many times that in lost market value.

On a broader scale, business plans and decisions might be faulty from the outset. There is really no excuse for stepping into a business plan when it has little or no chance for success. This is similar to going into a tough exam without preparing. Regret is perhaps the only lasting outcome.

The overall theme of this chapter is to impart knowledge about sound principles and methods that can be employed to make sound business decisions. These techniques won’t eliminate execution errors, but they will help avoid many of the judgment errors that are all too common among failing businesses.


One of the first things to understand about sound business judgment is that a distinction must be made between sunk costs and relevant costs. There is an old adage that cautions against "throwing good money after bad." This has to do with the concept of a sunk cost, and it is an appropriate warning.

A sunk cost relates to the historical amount that has already been expended on a project or object. For example, one may have purchased an expensive shirt that was hopelessly shrunk in the dryer. There would be no reason to buy a matching pair of pants because so much was invested in the shirt. The amount previously spent on the shirt is no longer relevant; it is a sunk cost and should not influence future actions.

relevant COSTS

Link to Excel ExerciseIn business decision making, sunk costs should be ignored. Instead, the focus should be on relevant costs. Relevant items are future costs and revenues expected to differ among the alternative decisions under consideration. The objective is to identify the decision yielding the best incremental outcome as it relates to relevant costs/benefits.

case study

During a recent ice storm, Dillaway Company’s delivery truck was involved in a traffic accident. The truck originally cost $60,000, and was 40% depreciated. An insurance company has provided Dillaway $30,000 for the damages that were incurred. Dillaway took the truck to a local dealer who offered two options: (a) repair the truck for $24,000 or (b) buy the truck “as is, where is” for $10,000. Dillaway has found an undamaged, but otherwise identical, used truck for sale on the internet for $32,000. What decision is in order?

The truck’s cost of $60,000 is sunk and irrelevant. The degree to which it is depreciated is equally irrelevant. The financial statement “gain” reported on a sale is irrelevant. The $30,000 received from insurance is the same whether the truck is sold or repaired; because it does not vary between the two alternatives, it is irrelevant (i.e., it is not necessary to consider it in the decision process). All that matters is that the truck can be repaired for $24,000, or the truck can be sold for $10,000 and a similar one purchased for $32,000. In the former case, Dillaway is back in operation for $24,000; in the later, Dillaway is back in operation for $22,000 ($32,000 - $10,000). It seems clear that the better option is to sell the damaged truck.

The logic implied by the preceding discussion is to focus on incremental items that differ between the alternatives. The same conclusion can be reached by a more comprehensive analysis of all costs and benefits:

Factual Analysis of Truck

Income Analysis of Truck

Cash Flow Analysis of Truck

The preceding analysis also supports sale and replacement because the income and cash flow impacts are $2,000 better than with the repair option. Although the detailed analysis may be more descriptive of the entirety of the two alternatives, it can become unnecessarily burdensome. It bears repeating that decision making should be driven only by relevant costs/benefits that differ among the alternatives! To toss in the extraneous data may help describe the situation, but it is of no benefit in attempting to guide decisions.

In one sense, Dillaway was lucky. The insurance proceeds were more than enough to put Dillaway back in operation. Many times, a favorable outcome cannot be identified. Each potential decision leads to a negative result. Nevertheless, decisions must be made. As a result, proper incremental analysis often centers on choosing the option of least incremental harm or loss.


Relevant costs/benefits are rarely so obvious as illustrated for Dillaway. Suppose the local truck dealer offered Dillaway a third option: a $27,000 trade-in allowance toward a new truck costing $80,000. The incremental cost of this option is $53,000 ($80,000 - $27,000). This is obviously more costly than either of the other two options. But, Dillaway would have a brand new truck. As a result, Dillaway must now begin to consider other qualitative factors beyond those evident in the incremental cost analysis. This is often the case in business decision making. Rarely are two (or more) options under consideration driven only by quantifiable mathematics. Managers must be mindful of the impacts of decisions on production capacity, customers, employees, and other qualitative factors. Consider that qualitative factors can heavily influence long-run quantitative outcomes.

Remember that the analytical techniques presented throughout this chapter are based on concrete illustrations and logic. However, success in business depends upon much more than just adapting these sound conceptual approaches to a business world that is filled with uncertain and abstract problems. Do not assume that analytical methods can be used to solve all business problems, but do not abandon them in favor of wild guesswork! Analytics support decision making, but they do not supplant judgment.


Business Decision Logic

It is virtually impossible to develop a listing of every type of business decision that will be confronted. Classic examples include whether or not to outsource, when to accept special orders, and whether to discontinue a product or project. Although each of these examples will be considered in more detail, it is most important to develop a general frame of reference for business decision making.

In general, business decision making requires identification of decision alternatives, logging relevant costs/benefits of each choice, evaluating qualitative issues, and selecting the most desirable option based on judgmental balancing of quantitative and qualitative factors. Recognize that this process begins with judgment (what are the alternatives?) and ends with judgment (which alternative presents the best blend of quantitative and qualitative factors?).

Identifying Alternatives Illustration


Companies must frequently choose between using outside vendors/suppliers or producing a good or service internally. Outsourcing occurs across many functional areas. For instance, some companies outsource data processing, tech support, payroll services, and similar operational aspects of running a business. Manufacturing companies may also find it advantageous to outsource certain aspects of production (frequently termed the “make or buy” decision).

Further, some companies (e.g., certain high-profile sporting apparel companies) have broad product lines, but actually produce no tangible goods. They instead focus on branding/marketing and outsource all of the actual manufacturing. Outsourcing has been around for decades, but it has received increased media/political attention with the increase in global trade. Tax, regulation, and cost factors can vary considerably from one global region to another. As a result, companies must constantly assess the opportunities for improved results via outsourcing.

The outsourcing decision process should include an analysis of all relevant costs and benefits. Items that differ between the “make” alternative and the “buy” alternative should be studied. As usual, avoid the temptation to consider sunk costs as part of the decision analysis.

Generally, one would compare the variable production/manufacturing cost of a service/product with the purchase price of the service/product. Unless the outsourcing option results in a complete elimination of a factory or facilities, the fixed overhead is apt to continue whether the service/product is purchased or produced. As a result, unavoidable fixed overhead does not vary between the alternatives and can be disregarded. On the other hand, if some fixed factory overhead can be avoided by outsourcing, it should be taken into consideration as a relevant item.


Pilot Corporation produces software for handheld global positioning systems. The software provides a robust tool for navigational support and mapping. It is used by airline pilots, mariners, and others. Because these applications are often of critical importance, Pilot maintains a tech support department that is available around the clock to answer questions. The annual budget for the tech support department is shown below.

Outsourcing Case Study Table

Direct labor to staff the tech support department consists of 3 persons always available during each 8-hour shift, at an hourly rate of $12 per hour (3 persons per shift X 8 hours per shift X 3 shifts per day X 365 days per year X $12 per hour = $315,360). The utilities and maintenance are fixed, but would be avoided if the unit were shut down. The building is leased under a long-term contract, and the rent is unavoidable. Phone and computer equipment are leased under a flat-rate contract, but the agreement is cancelable without penalty. The annual depreciation charge on furniture and fixtures reflects a cost allocation of expenditures made in prior years.

Pilot has been approached by Chandra Corporation, a leading provider of independent tech support services, to provide a turn-key tech support solution at the rate of $12 per support event. Pilot estimates that it generates about 50,000 support events per year. Chandra’s proposal to Pilot notes that the total expected cost of $600,000 (50,000 events X $12 per event) is less than the $635,360 currently budgeted for tech support. However, a correct analysis for Pilot focuses only on the relevant items (following). Even if Chandra is engaged to provide the support services, building rent will continue to be incurred (it is not relevant to the decision). The cost of furniture and fixtures is a sunk cost (it is not relevant to the decision). The total cost of relevant items is much less than the $600,000 indicated by Chandra’s proposal. Therefore, the quantitative analysis suggests that Pilot should continue to provide its own tech support in the near future. After all, why spend $600,000 to avoid $415,360 of cost? Once the building lease matures, when the furniture and fixtures are in need of replacement, or if tech support volume drops off, Chandra’s proposal might be worthy of reconsideration.

Outsourcing Case Study Table


Link to Excel ExerciseOutsourcing analysis is made more complicated if a business is operating at capacity. If outsourcing will free up capacity to be used on other services or products, then the contribution margin associated with the additional services or products also becomes a relevant item in the decision process. In other words, if a company continues to manufacture a product in lieu of outsourcing, it foregoes the chance to produce the alternative product. The loss of this opportunity has a cost that must be considered in the final decision. Accountants (and economists and others) may use the term opportunity cost to describe the cost of foregone opportunities. It is appropriate to factor opportunity costs into any outsourcing analysis.

case study

Mueller Building Systems manufactures customized steel components that are sold in kits for the do-it-yourself rancher. The kits include all of the parts necessary to easily construct metal barns of various shapes and sizes. Mueller’s products are very popular, and its U.S. manufacturing plants have been running at full capacity.

In an effort to free up capacity, Mueller contracted with Zhang Manufacturing of China to produce all roof truss components to be included in the final kits. The capacity that was released by the outsourcing decision enabled a 10% increase in the total number of kits that were produced and sold. Mueller’s accounting department prepared the following analysis that was used as a basis for negotiating the contract with Zhang:

Capacity Issues Analysis

Notice that the analysis reveals that Mueller Building Systems will reduce costs by only $10,800,000 via outsourcing, but can easily spend more than this on purchasing the same units from Zhang. This results because the freed capacity will be used to produce additional contribution margin that would otherwise be foregone.

One must be very careful to fully capture the true cost of outsourcing. Oftentimes, the costs of placing and tracking orders, freight, customs fees, commissions, or other costs can be overlooked in the analysis. Likewise, if outsourcing results in employee layoffs, expect increases in unemployment taxes, potential acceleration of pension costs, and other costs that should not be ignored in the quantitative analysis. Finally, a situation like that faced by Mueller may indicate the need for additional capital expenditures to increase overall capacity.


Global Clip ArtCompanies must be very careful to consider qualitative issues in making decisions about outsourcing. Outsourcing places quality control, production scheduling, and similar issues in the hands of a third party. One must continually monitor the supplier’s financial health and ability to continue to deliver quality products on a timely basis. If goods are being moved internationally, goods may be subject to high freight costs, customs fees, taxes, and other costs. Delays are often associated with the uncertain logistics of moving goods through brokers, large sea ports, and homeland security inspections.

Hopefully rare, but not to be ignored, are risks associated with relying on suppliers in politically unstable environments; significant disruptions are not without precedent. Language barriers can be problematic. Although global trade is increasingly reliant on English, there are still many miscues brought about by a failure to have full and complete communication.

Additionally, some global outsourcing can be met with customer resistance. Examples include frustrations with call centers and tech support lines where language barriers become apparent, and customer protest/rejection because of perceived unfair labor practices in certain global regions. Despite the potential problems, there are decided trends suggesting that the most successful businesses learn to utilize logical outsourcing opportunities in both local and global markets.


Link to Excel ExerciseA business may receive a special order at a price that is significantly different from the normal pricing scheme. The quantitative analysis will focus on the contribution margin associated with the special order. In other words, it must be determined whether the special order sales price exceeds the variable production and selling costs associated with the special order.

Fishing Lure Clip ArtTo illustrate, assume that Lunker Lures Company produces the popular Rippin’ Rogue. The “cost” to produce a Rippin’ Rogue is $1.10, consisting of $0.20 direct materials, $0.40 direct labor, and $0.50 factory overhead. The overhead is 30% variable and 70% fixed cost allocation. Rippin’ Rogues are sold to retailers across the country through an established network of manufacturers’ representatives who are paid $0.10 for each lure sold in their respective territories.

Lunker Lures has been approached by Walleye Pro Fishing World to produce a special run of 1,000,000 units. These lures would be sold under the Walleye Wiggler brand name and would not otherwise compete with sales of Rippin’ Rogues. Walleye Pro Fishing World’s offer is priced at $1.00 per unit. Lunker Lures is obligated to pay its representatives half of the normal rep fee for such private label transactions.

On the surface it appears that Lunker Lures should not accept this order. After all, the offer is priced below the noted cost of production. However, so long as Walleye Wigglers do not compete with sales of Rippin’ Rogues, and Lunker Lures has enough capacity to produce lures without increasing fixed costs, profit will be enhanced by $200,000 ($0.20 X 1,000,000) by accepting the order. The following analysis focuses on the relevant items in reaching this conclusion:

Special Order Analysis


A potential error in special order pricing is acceptance of special orders offering the highest contribution margin per dollar of sales, while ignoring capacity constraints. Notice that the special order for Walleye Wigglers offered a 20% contribution margin ($0.20/$1.00). Suppose Fishing Town also placed a special order for a Bass Buzzer lure, and that special order afforded a 30% margin on a $1.00 per unit selling price.

Fishing Rod Clip ArtAt first glance, one would assume that the Fishing Town order would represent the better choice. But, what if one were also informed that remaining plant capacity would allow production of either 1,000,000 Walleye Wigglers or 600,000 Bass Buzzers? Now, the total contribution margin on the Wiggler is $200,000 (1,000,000 units X $0.20) while the total contribution on the Buzzer is $180,000 (600,000 X 30%).

The better choice is to go with the Wiggler, as that option maximizes the total contribution margin. This important distinction gives consideration to the fact that producing a few units (with a high per-unit contribution margin) may be less profitable than producing many units (with a low per-unit contribution margin). Contribution margin analysis should never be divorced from consideration of factors that limit its generation.


Link to Excel ExerciseIt is difficult to decide when to abandon a business unit that is performing poorly. Such decisions can have far-reaching effects on the company, shareholders, employees, and suppliers. What analytical methods should be employed to support a final decision to discontinue a business unit?

Management should not merely conclude that any unit generating a net loss is to be eliminated. This is an all-too-common error made by those who lack sufficient accounting knowledge. Sometimes, eliminating a unit with a loss can actually reduce overall performance.

Consider that some fixed costs identified with a discontinued unit may continue and must be absorbed by other units. This creates a potential domino effect where each failing unit pushes down the next. Instead, the appropriate analysis is to compare company-wide net income “with” and “without” the unit targeted for elimination.

Casa de Deportes is a mega sporting goods store occupying 80,000 square feet of space in a rented retail center. Each department is evaluated for profitability based on the following information:

Profitability Analysis

Management is concerned about the Golf Department. If Golf is discontinued, only 70% of the general and administrative costs would be eliminated, rent and depreciation would continue to be incurred, and utilities would be reduced by only half. The selling costs would be completely eliminated. The unavoidable costs are shifted equally to the other departments (although other allocation methods could be used, the overall conclusions would not change). The income report “without golf” appears as follows:

Discontinuation Analysis

Discontinuing Golf will not help. The reallocation of unavoidable costs not only reduces overall profitability, but it also moves Camping in a precarious direction. Further, this analysis does not take into account potential sales reductions in other departments that might occur from reductions in overall store traffic or incremental costs from closing a department (e.g., inventory write-offs). The decision to discontinue a product, department, or project can become quite complex.


A business may have a broad product line and large customer base. However, a significant portion of its success may be centered around a narrow set of products, customers, and services. As a result, it may prove beneficial to adopt the 80/20 concept.

The 80/20 business process focuses on what is most important (the 20% of the items that account for 80% of the value) and spends less effort on low-value drivers. The 80/20 process is used to simplify and focus on key parts of a business and reduce complexity that can often disguise what is most important.

Some contend that this approach results in sacrificing long-term opportunities to enhance short-term profitability. For instance, a “small and inexperienced” customer that is abandoned today might eventually grow to be a major player. As a result, the 80/20 philosophy is not always the optimum strategy, and good business judgment should always be exercised in the decision-making process.


Capital Expenditure Decisions

Much of the discussion has focused on decisions relating to near-term operations and activities. But, managers must also ponder occasional big-ticket expenditures that will impact many years to come.

Architect Clip ArtSuch capital expenditure decisions relate to construction of new facilities, large outlays for vehicles and machinery, embarking upon new product research and development, and similar items where the upfront cost is huge and the payback period will span years to come.

Although the tendency is to focus on the financial dimensions, such decisions are made even more complex because they usually involve a number of nonfinancial components as well. Thus, the final decision may involve consideration of architectural, engineering, marketing, regulatory, and numerous other variables.

These types of decisions involve considerable risk because they usually involve large amounts of money and extended durations of time. In addition, capital expenditure decisions (also called capital budgeting) are usually accompanied by a number of alternatives from which to choose. Sometimes, an option that is best in the long term may be the least desirable in the near term, and vice versa.

For instance, a student may currently invest time and money in an education; probably the student could make more money in the near term by working more hours in a paying job and devoting less time to study. However, the long term is frequently better served by investing in education. The same challenge often faces managers. For example, should a new computer information system be installed? In the near term, the business might appear more profitable by not buying a new system, but the long run may be better served by making the investment.


Capital expenditure planning requires managers to effectively evaluate and rank alternatives. This process must be matched/tempered by reasonable assessment of resource limitations and willingness to assume risk. In addition, managers must understand the goals of business owners: What is to be optimized, short-run or long-run performance goals? How much risk is to be undertaken in pursuit of an opportunity?

Managers naturally feel pressure to deliver in the near term, for fear of not keeping their jobs in the long term. Be on guard, as this behavioral issue can potentially foster an environment where the best long-run decisions are not always selected.


Fortunately, a number of analytical tools are available to bring logical and rationale decision-making processes to bear on capital expenditure decisions. The remainder of this chapter will focus on these tools. A good manager is well advised to understand and utilize these tools. They can be most helpful in evaluating capital expenditure decisions. In addition, managers can use these tools to clearly convey justification for making certain decisions, even if they appear to be illogical in the near-term.

The capital budgeting tools covered in the remainder of this chapter are net present value, accounting rate of return, internal rate of return, and payback method. These tools require foundational knowledge in compound interest and present value techniques, as provided in the next section.


Compound Interest and Present Value

Video LectureTime Clip ArtThere is an expression that “time is money.” In capital budgeting, this concept is actually measured and brought to bear on the decision process. The fundamental idea is that a dollar received today is worth more than a dollar to be received in the future. This result occurs because a dollar in hand today can be invested to generate additional immediate returns.

Link to Excel ExerciseIn the context of capital budgeting, assume two alternative investments have the same upfront cost. Investment Alpha returns $100 per year for each of the next 5 years. Investment Beta returns $50 per year for each of the next 10 years. Based solely on this information, one should conclude that Alpha is preferred to Beta. Although the total cash returns are the same, the time value of money is better for Alpha than Beta. With Alpha, the money is returned sooner, allowing for enhanced reinvestment opportunities. Of course, very few capital expenditure choices are as clear cut as Alpha and Beta. Therefore, accountants rely on precise mathematical techniques to quantify the time value of money.


The starting point for understanding the time value of money is to develop an appreciation for compound interest. Albert Einstein is quoted as saying: “The most powerful force in the universe is compound interest.” Very simply, money can be invested to earn money.

In this context, consider that when one spends a dollar on a soft drink, that person is actually foregoing $0.10 per year for the rest of their life (assuming a 10% interest rate). And, as will be shown, that annual dime of savings builds to much more because of interest that is earned on the interest.

Compound interest calculations can be used to compute the amount to which an investment will grow in the future. Compound interest is also called future value. If one invests $1 for one year, at 10% interest per year, how much will he or she have at the end of the year? The answer, of course, is $1.10. This is calculated by multiplying the $1 by 10% ($1 X 10% = $0.10) and adding the $0.10 to the initial dollar. If the resulting $1.10 is invested for another year at 10%, it will grow to $1.21. That is, $1.10 X 110%. This process will continue, year after year.

Compound Interest Calculation Illustration

The annual interest each year is larger than the year before because of “compounding.” Compounding simply means that an investment is growing with accumulated interest and earning interest on previously accrued interest that becomes part of the total investment pool. This formula expresses the basic mathematics of compound interest:


Where “i” is the interest rate per period and “n” is the number of periods

future value of lump sum

Link to Excel ExerciseHow much would $1 grow to in 25 years at 10% interest? The answer can be determined by taking 1.10 to the 25th power [(1.10)25], and the answer is $10.83. Future value tables provide predetermined values for a variety of such computations (see the companion website for a complete set of tables). To experiment with a future value table, determine how much $1 would grow to in 10 periods at 5% per period. The answer to this question is $1.63 and can be found by reference to the value in the “5% column/10-period row.” If the original investment was $5,000 (instead of $1), the investment would grow to $8,144.45 ($5,000 X 1.62889).

In using the tables, be sure to note that the interest rate is the rate per period. The “period” might be years, quarters, months, etc. It all depends on how frequently interest is to be compounded. For instance, a 12% annual interest rate, with monthly compounding for two years, would require reference to the 1% column (12% annual rate equates to a monthly rate of 1%) and 24-period row (2 years equates to 24 months). If the same investment involved annual compounding, then one would refer to the 12% column and 2-period row. The frequency of compounding makes a difference in the amount accumulated. For the given example, monthly compounding returns 1.26973, while annual compounding returns only 1.25440.


Annuities are level streams of payments. Each payment is the same amount and occurs at a regular interval. Annuities are common in business. They can arise in loans, retirement plans, leases, insurance settlements, tax-related calculations, and so forth. Sometimes, one may be curious to learn how much a recurring stream of payments will grow to after a number of periods. This is called the future value of an annuity.


An annuity due (also known as an annuity in advance) involves a level stream of payments, with the payments being made at the beginning of each time period. For instance, perhaps one plans on saving for retirement by investing $5,000 at the beginning of each year for the next five years. If the annual interest rate is 10% per year, how much will accumulate by the end of the 5-year period? The following graphic shows how each of the five individual payments would grow, and the accumulated total would reach $33,578:

Future Value of an  Annuity Due Illustration

Although the graphic provides a useful explanatory tool, it is a bit cumbersome to implement. The same conclusion can be reached by reference to a future value of an annuity due table. The table reveals a value of 6.71561 (10% column/5-period row). Multiplying the $5,000 annual payment by this factor yields $33,578 ($5,000 X 6.71561). This means that the annuity will grow to $33,578.


Sometimes an annuity will be based on “end of period” payments. These annuities are called ordinary annuities (also known as annuities in arrears). The next graphic portrays a 5-year, 10%, ordinary annuity involving level payments of $5,000 each.

Notice the similarity to the preceding graphic, except that each year’s payment is shifted to the end of the year. This means that each payment will accumulate interest for one less year, and the final payment will accumulate no interest! Be sure to note the striking difference between the accumulated total under an annuity due versus an ordinary annuity ($33,578 vs. $30,526).

Future Value of an Ordinary Annuity Illustration

There are also tables that reflect the future value of an ordinary annuity. Review a table to become satisfied about the $30,526 amount ($5,000 X 6.10510).


Future value calculations provide useful tools for financial planning. But, many decisions and accounting measurements will be based on a reciprocal concept known as present value. Present value (also known as discounting) determines the current worth of cash to be received in the future.

For instance, how much would one be willing to take today, in lieu of $1 in one year? If the interest rate is 10%, presumably he or she would accept the sum that would grow to $1 in one year if it were invested at 10%. This happens to be $0.90909. In other words, invest 90.9¢ for a year at 10%, and it will grow to $1 ($0.90909 X 1.1 = $1). Thus, present value calculations are simply the reciprocal of future value calculations. In formula terms this would be 1/(1+i)n.

A present value of $1 table reveals predetermined values for calculating the present value of $1, based on alternative assumptions about interest rates and time periods. A $25,000 lump sum amount to be received at the end of 10 years, at 8% annual interest, with semiannual compounding, would have a present value of $11,410 (recall the earlier discussion, and use the 4% column/20-period row: $25,000 X 0.45639).


Present value calculations are applicable to annuities also. Perhaps one is considering buying an investment that returns $5,000 per year for five years, with the first payment to be received immediately. What should be paid for this investment if the target rate of return is 10%? This scenario relates to the present value of an annuity due:

Present Value of an Annuity Due Illustration

The graphic shows that the annuity has a present value of $20,849. Of course, there is a present value of an annuity due table to ease the burden of this calculation ($5,000 X 4.16897 = $20,849).


Many times, the first payment in an annuity occurs at the end of each period. The present value of an ordinary annuity table provides the necessary factor to determine that $5,000 to be received at the end of each year for a 5-year period is worth only $18,954, assuming a 10% interest rate ($5,000 X 3.79079 = $18,954). The following graphic confirms this conclusion:

Present Value of an Ordinary Annuity Illustration


Present Value Function ExampleBe aware that most electronic spreadsheets also include functions for calculating present and future value amounts by simply completing a set of predetermined queries.

These spreadsheet functions can prove to be very efficient and effective in performing the calculations illustrated in this chapter.




Many scenarios represent a combination of lump sum and annuity cash flow amounts. There are a variety of approaches to calculating the future or present value for such scenarios. Perhaps the safest approach is to diagram the anticipated cash flows and apply logical manipulations.

To illustrate, assume that Markum Real Estate is considering buying an office building. The building will be vacant for two years while it is being renovated. Then, it will produce annual rents of $100,000 at the beginning of each of the next three years. The building will be sold in five years for $700,000. Markum desires to know the present value of the anticipated cash inflows, assuming a 5% annual interest rate.

The rental stream has a present value of $285,941 as of the beginning of Year 3. That value is discounted back to the beginning of Year 1 value ($259,357) by treating it as a lump sum. The sales price is separately discounted to its present value of $548,471. The present value of the rents and sales price are combined to produce the total present value for all cash inflows ($807,828). This type of cash flow manipulation is quite common in calculating present values for many investment decisions.

Markum Real Estate Illustration

An alternative way to value the rental stream would be to subtract the value for a 2-year annuity from the value for a 5-year annuity (4.54595 - 1.95238 = 2.59357; $100,000 X 2.59357 = $259,357). This result occurs because it assumes a 5-year annuity and backs out the amount relating to the first two years, leaving only the last three years in the resulting present value factor.


Evaluation of Long-Term Projects

Video LectureThe basic principles about how dollars are impacted by compound interest and present value calculations can be used to make better business decisions. There are a number of alternative methods for evaluating capital budgeting decisions. These include net present value, accounting rate of return, internal rate of return, and payback.


Link to Excel ExerciseThe net present value (NPV) method offsets the present value of an investment’s cash inflows against the present value of the cash outflows. Present value amounts are computed using a firm’s assumed cost of capital. The cost of capital is the theoretical cost of capital incurred by a firm. This cost may be determined by reference to interest rates on debt or a blending of debt/equity costs.

In the alternative, management may simply adopt a minimum required threshold rate of return that must be exceeded before an investment will be undertaken. If a prospective investment has a positive net present value (i.e., the present value of cash inflows exceeds the present value of cash outflows), then it clears the minimum cost of capital and is deemed to be a suitable undertaking. On the other hand, if an investment has a negative net present value (i.e., the present value of cash inflows is less than the present value of cash outflows), the investment opportunity should be rejected.

To illustrate NPV, return to the illustration for Markum Real Estate. Assume that the firm’s cost of capital is 5%. Recall that the present value of the cash inflows is $807,828. Additionally assume that the up-front purchase price for the building is $575,000. The remodel effort will require $60,000 to be spent at the end of Year 1 and Year 2. Maintenance, insurance, and taxes on the building will amount to $10,000 per year, payable at the end of each of the five years. The present value of the cash outflows is $729,859:

Present Value of Cash Outflows Illustration

This project has a positive net present value of $77,969 ($807,828 - $729,859). This suggests that the project’s returns exceed the 5% cost of capital threshold. Had the up-front investment been $675,000 (instead of $575,000), the project would have a negative net present value of $22,031 ($807,828 - $829,859).


Carefully consider the mathematics (or table values), and observe that:

Higher interest rates produce lower present value factors, and vice versa.

Thus, the logic of making certain investments changes with interest rates. Perhaps one has considered buying a house or car on credit. In considering the decision, the interest rates on the deal likely made a big difference in how the proposed transaction was viewed.

Even a casual observer of macroeconomic trends knows that government policies about interest rates influence investment activity and consumer behavior. In simple terms, lower rates can stimulate borrowing and investment, and vice versa.

To illustrate the impact of shifting interest rates, consider that Greenspan is considering a $500,000 investment that returns $128,000 at the end of each year for five years. The following spreadsheet shows how the net present value shifts from a positive net present value of $39,183 (when interest rates are 6%), to positive $11,067 (when interest rates are 8%), to negative $14,779 (when interest rates rise to 10%). This means that the investment would make sense if the cost of capital was 6%, but not 10%.

Changes in Rates Comparison Spreadsheet

In the preceding spreadsheet, formulas were used to determine present value factors. For example, cell E15 includes the formula: 1/(1+$A$10)^3. This formula draws the interest rate from cell A10. This simple approach allows rapid recalculation of net present value by simply changing the value in the interest rate cell.


In computing NPV, notice that the focus is on cash flows, not “income.” Items like depreciation do not impact the cash flows and are not included in the present value calculations. That is why the illustration for Markum Real Estate did not include deductions for depreciation. However, when applying net present value considerations in practice, one must be well versed in tax effects. Some noncash expenses like depreciation can reduce taxable income, which in turn reduces the amount of cash that must be paid for taxes. Therefore, cash inflows and outflows associated with a particular investment should be carefully analyzed on an after-tax basis. This often entails the preparation of pro forma cash flow statements and consultation with professionals well versed in the details of specific tax rules.

Annual Income and Cash Flows TableAs a simple illustration, assume that Mirage Company purchases a tract of land with a prolific spring-fed creek. The land cost is $100,000, and $50,000 is spent to construct a water bottling facility. Net water sales amount to $40,000 per year (for simplicity, assume this amount is collected at the end of each year and is net of all cash expenses). The bottling plant has a 5-year life and is depreciated by the straight-line method. Recall that land is not depreciated. At the end of five years, it is anticipated that the land will be sold for $100,000. Mirage has an 8% cost of capital, and is subject to a 35% tax rate on profits. The table shows the calculation of annual income and cash flows.

The annual cash flow from water sales (not the net income) is incorporated into the following spreadsheet. The annual net cash flows are then multiplied by the appropriate present value factors corresponding to an 8% discount rate. The project has a positive net present value of $35,843. Interestingly, had the annual net income of $19,500 been erroneously substituted for the $29,500 annual cash flow, this analysis would have produced a negative net present value. One cannot underestimate the importance of considering tax effects on the viability of investment alternatives.

Tax Effects Spreadsheet


The accounting rate of return is an alternative evaluative tool that focuses on accounting income rather than cash flows. This method divides the average annual increase in income by the amount of initial investment. For Mirage’s project, the accounting rate of return is 13% ($19,500/$150,000). The accounting rate of return is simple and easy. The decision rule is to accept investments that exceed a particular accounting rate of return. But, the method ignores the time value of money, the duration of cash flows, and terminal returns of invested dollars (e.g., notice that Mirage plans to get the $100,000 back at the end of the project). As a result, by itself, the accounting rate of return can easily misidentify the best investment alternatives. It should be used with extreme care.


The internal rate of return (also called the time-adjusted rate of return) is similar to NPV. But, rather than working with a predetermined cost of capital, this method calculates the actual discount rate that equates the present value of a project’s cash inflows with the present value of the cash outflows. In other words, it is the interest rate that would cause the net present value to be zero.

IRR is a ranking tool, calculated for each investment opportunity. The decision rule is to accept the projects with the highest internal rates of return, so long as those rates are at least equal to the firm’s cost of capital. This contrasts with NPV, which has a general decision rule of accepting projects with a “positive NPV,” subject to availability of capital. Fundamentally, the mathematical basis of IRR is not much different than NPV.

The manual calculation of IRR using present value tables is challenging. One would repeatedly try rates until the rate that caused the present value of cash inflows to equal the present value of cash outflows is isolated. If the available tables are not sufficiently detailed, some interpolation would be needed. However, spreadsheet routines are much easier. Reconsider the illustration for Greenspan. The following spreadsheet uses an interest rate of 8.8361%. Notice that this rate caused the net present value to be zero and is the IRR. This rate was selected by a higher-lower guessing process (trying each interest rate guess in cell A2). This does not take as many guesses as one might think; with a little logic, the exact correct rate can be found rather quickly.

Internal Rate of Return Spreadsheet


The payback method is a popular and easy method, and can be valuable when the key investment goal is to find projects where the initial investment is quickly recovered. But, it is not very strong in otherwise pinpointing the best capital investment decisions.

Payback is calculated by dividing the initial investment by the annual cash inflow. The earlier illustration for Greenspan has a payback of approximately 3.9 years ($500,000/$128,000 = 3.9). If an investment involves uneven cash flows, the computation requires scheduling cash inflows and outflows. The payback period is the point at which the cumulative net cash inflows begin to exceed the cumulative net cash outflows.

The method is deficient in that it does not take into account the time value of money. It also fails to reveal what happens after the payback period. For example, some investments may pay back rapidly, but have little residual cash flow after the payback period. Other investments may take years to pay back and then continue to generate future returns for many more years to come. Although the investment with the shorter payback may be viewed as favorable, it could easily turn out to be the worst choice. All in all, be very cautious using the payback method for making business decisions.


Capital budgeting decisions are not much different than the whole of managerial accounting. There are many tools one should understand and utilize. But, in the final analysis, good decision making will be driven by reasoned judgment.