Chapter 13 Managerial Accounting
The Concept of Present Value
A dollar recieved today is more valuable than a dollar received a year from now for the simple reason that if you have a dollar today, you can put t in the bank and have more than a dollar a year from now Because dollars today are worth more than dollars in the future, cash flows that are received at different times must be valued differently
Choosing a Discount Rate
A positive net present value indicates that the project's return exceeds the discount rate A negative net present value indiciates that the project's return is less than the discount rate If the company's minimum required rate of return is used as the discount rate, a project with a positive net present value has a return that exceeds the minimum required rate of return and is acceptable Contrarily, a project with a negative net present value has a return that is less than the minimum required rate of return and is unacceptable The company's cost of capital is usually regarded as the minimum required rate of return The cost of capital is the average rate of return the company must pay ro its long-term creditors and its shareholders for the use of their funds If a project's rate of return is less than the cost of capital, the company does not earn enough to compensate its creditors and shareholders -Therefore, any project with a rate of return less than the cost of capital should be rejected The cost of capital serves as a screening device -when the cost of capital is used as the discount rate in net present value analysis, any project with a negative net present value does not cover the company's cost of capital and should be discarded as unacceptable
Annuity
A series of identical cash flows
Emphasis On Cash Flows
Accounting net income is based on accruals that ignore when cash flows occur However, in capital budgeting, the timing of cash flows is critical The present value of a cash flow depends on when it occurs For that reason, cash flow rather than accounting net income is the focus in capital budgeting
Postaudit of Investment Projects
After an investment project has been approved and implemented, a postaudit should be conducted A postaudit involves checking whether or not expected results are actually realized -this is a key part of the capital budgeting process because it helps keep managers honest in their investment proposals Any tendency to inflate the benefits or downplay the costs in a proposal should become evident after a few postaudits have been conducted The postaudit also provides an opportunity to reinforce and possibly expand successful projects and to cut losses on floundering projects The same capital budgeting method should be used in the postaudit as was used in orginal approval process -that is, if a project was approved on the baiss of a net present value analysis, then the same procedure should be used in preorming the postaudit -however, the data used in the postaudit analyssi should be actual observed data rather than estimated data. This gives management an opportunity to make side-by-side comparison to see how well the project has succeeded -it also helps assure that estimated data recieved on future proposals will be carefully prepapred because the persons submitting the data knows that their estimates will be comapred to actua results in the postaudit process Actual results that are far out of line with original estimates should be carefully reviewed
Present Value of a Series of Cash Flows
Although some investments involve a single sum to be received (or paid) at a single point in the future, other investments involve a series of cash flows A series of identical cash flows is known as an annuity Exhibit 13B-1- This table should be usd to find the present value of a single cash flow (such as a single payment or receipt) occuring in the future Exhibit 13B-2: This table should be used to find the present value of a series of identical cash flows beginning at the end of the current period and continuing into the future When a present value factor appears in an exhibit, you should take the time to trace it back into either Exhibit 13B-1 or E
Computation of Present Value
An investment can be viewed in two ways- either in terms of its future value or in terms of its present value If we know the present value of a sum, the future value in n years can be computed by using Fn=(1+r)^n But what if the situation is reversed and we know the future value of some amount but we do not know its present value? The present value of any sum to be received in the future can be computed by turning the above equation around and solving for P: P=Fn/(1+r)^n The process of finding the present value of a future cash flow is called discounting The interest rate that we used to find a present value is called the discount rate Discounting future sums to their present value is a common practice in business, particularly in capital budgeting decisions
Capital Budgeting- Planning Investments
Any decision that involves an outlay now in order to obtain a future return is a capital budgeting decision Typical capital budgeting decisions include: 1. Cost reduction decisions. 2. Expansion decisions 3. Equipment selection decisions 4. Lease or buy decisions 5. Equipment replacement decisions Capital budgeting decisions fall into two broad categories: screening decisions and preference decisions Screening decisions relate to whether a proposed project is acceptable- whether it passes a preset hurdle Preference decisions, by contrast, relate to selecting from among several acceptable alternatives
The Concept of After-Tax Cost
Businesses, like individuals, must pay income taxes In the case of businesses, the amount of income tax that must be paid is dtermined by the company's net taxable income Tax deductible expenses decrease the company's net taxable income and reduce the taxes the company must pay Expenses are often stated on an after-tax basis An expenditure net of its tax effect is known as after-tax cost After tax cost (net cash outflow)= (1- Tax rate) x Tax deductible cash expense This formula is very useful because it provides the actual amount of cash a company must pay after considering tax effects -it is this actual, after-tax, cash outflow that should be used in capital budgeting decisions Similar reasoning applies to revenues and other taxable cash inflows -because these cash receipts are taxable, the company must pay out a portion of them in taxes The after-tax benefit, or net cash inflow, realized from a particular cash receipt can be obtained by applying a simple variation of the cash expenditure formula used above: After tax benefit (net cash outflow)= (1-Tax rate) x Taxable cash receipt We emphasize the term taxable cash receipts because not all cash inflows are taxable
The Time Value of Money
Capital investments usually earn returns that extend over fairly long periods of time -consequently, it is important to recognize that the time value of money when evaluating investment proposals A dollar today is worth more than a dollar a year from now if for no other reason than you could put a dollar in the bank today and have more than a dollar a year from now -therefore, projects that promise earlier returns are preferable to those that promise later returns Capital budgeting techniques that recognize the time value of money include discounting cash flows
In summary, the following types of cash flows are common in business investment projects
Cash outflows: -Initial Investment (including installation costs) -Increased working capital needs -Repairs and maintenance -Incremental operating costs Cash inflows: -Incremental revenues -Reduction in costs - Salvage Value - Release of working capital
Depreciation Tax Shield
Depreciation is not a cash flow -depreciation does affect the taxes that must be paid and therefore, has an effect on company's cash flows The depreciation deduction reduces the compan's taxes Because depreciation deductions shield revenues from taxation, they are generally referred to as depreciation tax shiled The reduction in tax payments made possible by the depreciation tax shield is equal to the amount of the depreciation deduction, multipied by the tax rate as follows: Tax savings from the depreciation tax shield= Tax rate x Depreciation deduction When we estimate after-tax cash flows for capital budgetin decisions, we will include the tax savings provided by the depreciation tax shield We will assume in all of our examples and problem materials that depreciation reported for tax purposes is straight-line depreciation, with no deduction for salvage value In other words, we will assume that the entire original cost of the asset is written off evenly over its usefu life Because the net book value of the asset at the end of its useful life will be zero under this depreciation method, we will assume that any proceeds received on disposal of the asset at the end of its useful life will be taxed as ordinary income In actuality, the rules for depreciation are more complex than this and most companies take advantage of accelerated depreciation methods allowed under the tax code -these accelerated methods usually result in a reduction in current taaxes and an offsetting increase in future taxes the shifting of part ofthe tax burden from the current year to future years is advantageous from a present value point of view because a dollar today is worth more than a dollar in the future
Uncertain Cash Flows: An Example
Exxample: consider the case of investments in automated equipment The up front costs of automated equipment and the tangible benefits tend to be relatively easy to estimate -however, the intangible benefis are more difficult to quantify in terms of future cahs flows. These intangible benefits certainly impact future cash flows but the cash flow effects are difficult to estimate A fairly simple procedure ccan be followed when the intangible benefits are likely to be significant -if the intangible benefits are large enoug, they could turn this negative net present value into a positive net present value
The Mathematics of Interst
F1=P(1+r) F1= the balance at the end of one period P=the amount invested now r=the rate of interest per period
Compound Interest
Interest can be compounded on a semiannual, quarterly, monthly, or even more frequent basis The more frequently compounding is done, the more rapidly the balance will grow We can determine the balance in an account after n periods of compounding using the following equation: Fn=P(1+r)^n n=the number of period of compounding
Summary
Investment decisions should take into account the time value of money because a dollar today is more valuable than a dollar received in the future The net present value and internal rate of return methods both reflect this fact In the net present value method, future cash flows are discounted to their present value -the difference between the present value of the cash inflows and the present value of the cash outflows is called a project's net present value If the net present value of a project is negative, the project is rejected The discount rate in the net prsent value method is usually based on a minimum required rate of return such as a company's cost of capital The internal rate of return is the rate of return that equates the present value of the cash inflows and the present value of the cash outflows, resulting in a zero net present value If the internal rate of return is less than a company's minimum required rate of return, the project is rejected After rejecting projects whose net present values are negative or whose internal rates of return are less than the minimum required rate of return, more projects may remain than can be supported with available funds -the remaining projects can be ranked using either the project profitability index or internal rate of return The project profitability index is computed by dividing the net present value of the project by the required intiial investment Some companies prefer to use either the payback method or the simple rate of return to evaluate investment proposals The payback period is the number of periods that are required to fully recover the initial investment in a project The simple rate of return is determined by dividing a project's accounting net operating income by the initital investment in the project
Capital Budgeting Decisions
Managers often consider decisions that involve an investment today in the hope of realizing future profits -all of these investments require spending now with the expectation of additional future net cash flows The term capital budgeting is used to describe how managers plan signfiicant investments in projects that have long-term implications such as the purchase of new equipment or the introduction of new products Most companies have many more potential projects than can actually be funded Hence, managers must carefully select those projects that promise the greatest future return -how well managesr make these capital budgeting decisions is a critical factor in the long-run financial health of the organization
Typical Cash Inflows
Most projects also have at least three types of cash inflows First, a project will normally increase revenues or reduce costs Either way, the amount involved should be treated as a cash inflow for capital budgeting purposes -notice that from a cash flow standpoint, a reduction in costs is equivalent to an increase in revenues Second, cash inflows are also frequently realized from selling equipment for its salvage value when a project ends, although the company may actually have to pay to dispose of some low-value or hazardous items Third, any working capital that was tied up in the project can be released for use elsewhere at the end of the project and should be treated as a cash inflow at that time Working capital is released when a company sells off its inventory or collects its accounts receivable
Typical Cash Outflows
Most projects have at least three types of cash outflows First, they often require an immediate cash outflow in the form of an initial investment in equipment, other assets, and installation costs Any salvage value realized from the sale of old equipment can be recognized as a reduction in the initial investment or as a cash inflow Second, some projects require a company to expand its working capital Working capital is current assets (ex. cash, accounts receivable, and inventory) less current liabilities When a company takes on a new project, the balances in the current asset accounts often increase Third, many projects require periodic outlays for repairs and maintenance and additional operating costs
An Extended Example of the Net Present Value Method
Out of pocket costs are actual cash outlays for salaries, advertising, and other operating expenses
Least-Cost Decisions
Some decisions do not involve any revenues -in situations uch as these, where no revenues are inolved, the most desirable alternative is the one with the least total cost from a present value persepective. hence, these are known as least-cost decisions When done correctly, the total-cost and incremental-cost approahces arrive at the same answer
Real Options
The analysis in this chapter has assumed that an investment cannot be postponsed and that once started, nothign can be done to alter the course of the project In reality, investments can often be postponed Postponement is a particuarly attractive option when the net present value of a project is modest using current estimates of future cash flows and the future cash flows involve a great deal of uncertainty that may be resolved over time -similarly, once an investment is made, management can often exploit changes in the business environment and take actions that enhance future cash flows In the case of an investment in automated equipment, management may initially buy only the basic model without costly add-ons, but keep the option open to add more capacity and capability later The ability to delay the start of a project, to expand it if conditions are favorable, to cut losses if they are unfavorable, and to otherwise modify plans as business conditions change adds value to many investments these advantages can be quantified using whati s called real options analysis, but the techniques are beyond the scope of this book
The Cost of Capital as a Screening Tool
The cost of capital is often used to screen out undesirable investment projects -this screening is accomplished in different ways, depending on whether the company is using the internal rate of retrun method or the net present value method When the internal rate of return method is used, the cost of capital is used as the hurdle rate that a project must clear for acceptance If the internal rate of return of a project is not high enough to clear the cost of capital hurdle, then the project is ordinarily rejected When the net present value method is used, the cost of capital is the discount rate used to compute the net present value of a proposed project -any project yielding a negative net present value is rejected unless other factors are signficant enough to warrant its acceptance
Discounted Cash Flows- The Internal Rate of Return Method
The internal rate of return is the rate of return of an investment project over its useful life The internal rate of return is computed by finding the discount rate that equates the present value of a project's cash outflows with the present value of its cash inflows In other words, the internal rate of retrun is the discount rate that results in a net present value of zero
The Total-Cost Approach
The most flexible method for comparing competing projects First, all cash inflows and all cash outflows are included in the solution under each alternative -no effort has been made to isolate these cash flows that are relevant to the decision and those that are not relevant -the inclusion of all cash flows associated with each alternative gives the approach its name- the total-cost approach Second, notice that a net present value is computed for each alternative. This is a distinct advantage of the total-cost approach because an unlimited number of alternatives can be compared side by side to determine the best option
Other Approaches to Capital Budgeting Decisions
The net present value and internal rate of return methods are widely used as decision-making tools however, some managers also use the payback method and simple rate of return method to make capital budgeting decisions
Recovery of the Initial Investment
The net present value method automatically provides for return of the original investment Whenever the net present value of a project is positive, the project will recover the original cost of the investment plus sufficient excess cash inflows to compensate the organization for typing up funds in the project
Comparison of the Net Present Value and Internal Rate of Return Methods
The net present value method has several important advantages over the internal rate of return method First, the net present value method is often simpler to use than the internal rate of return method The internal rate of return method may require hunting for the discount rate that results in a net present value of zero -this can be a very laborious trial-and-error process, although it can be automated using a computer second, the internal rate of return method makes a questionable assumption -both methods assume that cash flows generated by a project durings its useful life are immediately reinvested elsewhere. However, the two methods make different assumption concerning the rate of return that is used on those cash flows The net present value mehtod assumes the rate of return is the discount rate, whereas the internal rate of retrun method assumes the rate of retrun earned on cash flows is the internal rate of return on the project -specifically, if the internal rate of return of the project is high, this assumption may not be realistic - it is generally more realistic to assume that cash inflows can be reinvested at a rate of return equal to the discount rate (particuarly if the discount rate is the company's cost of capital or an opportunity rate of return) In short, when the net present value method and the internal rate of return method do not agree concerning the attractiveness of a project, it is best to go with the net present value method -of the two methods, it makes the more realistic assumption about the rate of return that can be earned on cash flows from the project
Net Present Value Method
The net present value of one project cannot be directly compared to the net present value of another project unless the initial investments are equal Project profitability index= Net present value of the project/Investment required When using the project profitability index to rank competing investments projects, the preference rule is: The higher the project profability index, the more deisrable the project, The project profitability index is an application of the techniques for utilizing constrained resources discussed in an earlier chapter -in this case, the constrained resource is the limited funds available for investment, and the project profitability index is similar to the contribution margin per unit of the constrained resource A few details should be clarified with respect to the computation of the project profitability index The "investment required" refers to any cash outflows that occur at the beginning of the project, reduced by any salvage value recovered from teh sale of old equipment -the "investment required" also investment in working capital that the project may need
Evaluation of the Payback Method
The payback method is not a true measure of the profitability of an investment -rather, it simply tells a manager how many years are required to recover the orginal investment -unfortunately, a shorter payback period does not always mean that one investment is not more desirable than another The payback method ignores all cash flows that occur after the payback period A further criticsm of the payback method is that it does not consider the time value of money - a cash inflow to be recieved several years in the future is wieghed the same as a cash inflow received right now Under certain conditions, the payback method can be very useful - it can help identify which investment proposals are in the "ballpark" -it can be used as a screening tool to help answer the question, "Should i consider this proposal further" If a proposal doesn't provide a payback with some specified period, then there may be no need to consider it further. In addition, the payback period is oten important to new companies that are "cash poor" When a company is cash poor, a project with a short payback period but a low rate of return might be preferred over another project with a high rate of return but a long payback period -the reason is that the company may simply need a faster return of its cash investment The payback method is sometimes used in industries where products become obselete very rapidly -because products may last only a year or two, the payback period on investments must be very short
An Extended Example of Payback
The payback period is computed by dividing the investment in a project by the project's annual net cash inflows If new equipment is replacing old equipment, then any salvage value to be received when disposing of the old equipment should be deducted from the cost of the new equipment, and only the incremental investment should be used in the payback computation In addition, any depreciation deducted in arriving at the project's net operating income must be added back to obtain the project's expected annual net cash inflow Depreciation is not a cash outlay; thus, it must be added back to adjust net operating income to a cash basis Second, the payback computation deducts the salvage value of the old machines from the cost of the new equipment so that only the incremental investment is used in computing the payback period
Compound Interest Definition
The process of paying interest on interest in an investment
Discount Rate
The rate of return that is used to find the present value of a future cash flow
Criticisms of the Simple Rate of Return
The simple rate of return method ignores the time value of money It considers a dollar received from 10 years from now to be as valuable as a dollar received today The simple rate of return method can be misleading if the alternatives have different cash flow patterns Many projects do not have constant incremental revenues and expenses over their useful lives -as a result, the simple rate of return will fluctuate from year to year, with the possibility that a project may appaer to be desirable in some years and undesirable in others In contrast, the net present value method provides a single number that summarizes all of the cash flows over the entire useful life of the project
Salvage Value and Other Cash Flows
The technique just demonstrated works if a project's cash flows are identical every year -but what if they are not? (for example, what if a project will have some salvage value at the end of its life in addition to the annual cash inflows -under these circumstances, a trial-and-error process may be used to find the rate of return that will result in a zero net present value The trial-and-error-process can be carried out by hand; however, computer software programs such as spreadsheets can preform the necessary computations in seconds Erratic or uneven cash flows shold not prevent an analyst from determining a project's internal rate of return
Present Value
The value now of an amount that will be received in some future period
The Internal Rate of Return Method
To compute the internal rate of return of the new mower, we must find the discount rate that will result in a zero net present value -how do we do this? the simplest and most direct approah when the net cash inflow is the same every year is to divide the investment in the project yb the expected annual net cash inflow Factor of the internal rate of return= Investment required/Annual net cash inflow
Using the Internal Rate of Return
To evaluate a project, the internal rate of return is compared to the company's minimum required rate of return, which is usually the company's cost of capital If the internal rate of return is equal to or greater than the required rate of return, then the project is acceptable If the internal rate of return is less than the required rate of return, then the project is rejected
Discounted Cash Flows- The Net Present Value Method
Two approaches to making capital budgeting decisiosn use discounted cash flows One is the net present value method, and the other is the internal rate of return method
Simplifying Assumptions
Two simplifying assumptions are usually made in net present value analysis The first assumption is that all cashflows other than the initial investment occur at the end of periods - this is somewhat unrealistic in that cash flows typically occur throughout a period rather than just at its end. The purpose of this assumption is to simplify computations. -the second assumption is that all cash flows generated by an investment project are immediate reinvested at a rate of return equal to the discount rate -unless these conditions are met, the net present value computed for the project will not be accurate
The Net Present Value Method Illustrated
Under the net present value method, the present value of a project's cash outflows The difference between the present value of these cash flows, called the net present value, determines whether or not the project is an acceptable investment Whenever the net present value is zero or greater, an investment project is acceptable Whenever the net present value is negative (the present value of the cash outflows exceeds the present value of the cash inflows), an investment project is not acceptable If the net present value is positive, then the project is acceptable because its return is greater than the required rate of return If the net present value is zero, then the project is acceptable because its return is equal to the required rate of return If the net present value is negative, then the project is not acceptable because its return is less than the required rate of return
Income Taxes in Capital Budgeting Decisions
We ignored income taxes in this chapter for two reasons -First, many organizations do not pay income taxes. Not for profit organizations are exempt from income taxes -Second, capital budgeting is complex and is best absorbed in small doses The US income tax code is enormously complex -to keep the subject within reasonable bounds, we have made many simplifying assumptions about the tax code -(1) taxable income equals net income as computed for financial reports (2)the tax rate is a flat percentage of taxable income -
Preference Decisions- The Ranking of Investment Projects
When considering investment opportunities, managers must make two types of decisions: screening decisions and preference decisions Screening decisions, which come first, pertain to whether or not a proposed investment is acceptable Preference decisions come after screening decisions and attempt to answer the following question: How do the remaining investment proposals, all of which have been screened and provdie an acceptable rate of return, rank in terms of preference? -which one(s) would be best for the company to accept Sometimes preference decisions are called rationing decisions, or ranking decisions Limited investment funds must be rationed among many competing alternatives -hence, the alternatives must be ranked -either teh internal rate of return method or the net present value method can be used in making prefrence decisions -however, as discussed earlier, if the two methods are in conflict it is best to use the net present value method, which is more reliable
The Incremental-Cost Approach
When only two alternatives are being considered, the incremental-cost approach offers a simpler and more direct route to a decision In the incremental-cost approach, only those costs and revenues that differ between the two alternatives are included in the analysis
Payback and Uneven Cash Flows
When the cash flows associated with an investment project change from year to year, the simple payback formula that we outlined earleir cannot be used necessary to track the unrecovered investment year by year
Internal Rate of Return Method
When using the internal rate of return method to rank competing investment projects, the preference rule is: The higher the internal rate of return, the more desirable the project Internal rate of return is widely used to rank projects
Example of Income Taxes and Capital Budgeting
When we take the net present value of after-tax cash flows, we use the after-tax cost of capital as the discount rate
The Payback Method
focuses on the payback period the payback period is the length of time that it takes for a project to recover its initial cost from the net cash inflows that it generates This period is sometimes referred to as "the time that it takes for an investment to pay for itself" The basic premise of the payback method is that the more quickly the cost of an investment can be recovered, the more desirable is the investment The payback period is expressed in years. When the annual net cash inflow is the same every year, the following formula can be used to compute the payback period: Payback period=Investment Required Annualnet cash inflow
The Simple Rate of Return Method
the simple rate of retrun method is another capital budgeting technique that does not involve discounting cash flows The simple rate of return is also known as the accounting rate of return or the unadjusted rate of return Unlike the other capital budgeting methods that we have discussed, the simple rate of return method focuses on accounting net operating income rather than cash flows To obtain the simple rate of return, the annual incremental net operating income generated by a project is divided by the initial investment in the project Simple rate of return=Annual incremental net operating income/Initial investment First, depreciation charges that result from making the investment should be deducted when determining the annual incremental net operating income Second, the initial investment should be reduced by any salvage value realized from the sale of old equipment To apply the formula for the simple rate of return, we must first determine the annual incremental net operating income from the project
Uncertain Cash Flows
thus far, we have assumed that all future cash flows are known with certainty -future csh flows are often uncertain or difficult to estimate -a number of techniques are available for handling this coplication -some of these techniques are quite techincal (involving computer simulations or advanced mathematical skills) and are beyond the scope of this book we can provide some very useful information to managers without getting too technical
