PART 4 - CHAPTER 4

CAPITAL BUDGETING

I. INTRODUCTION

     Capital budgeting is a separate process from developing the regular operating budget for the current time period. It is the process of identifying, evaluating, planning, and financing the major investment projects of an organization. Generally, capital budgeting involves capital assets (the purchase or replacement of equipment), plant expansion, and other major projects that require relatively large amounts of funds and that have a long-range impact on the firm. Capital budgeting is often a formalized process involving standardized forms, review by levels of management and approval by the board of directors.

     A. Strategic Planning Issues

          1. Organizational Objectives: Since capital budgeting decisions are long-term policy decisions, they should satisfy organizational goals and objectives about company growth, market share, social responsibility, and other factors.

          2. Business Analysis: Before the actual capital budgeting process begins, a company should do strategic planning to understand the company's business. Management needs to analyze what business they are in, what direction they want to go in, what their goals are, what they want for the future of the company, etc.

          3. Industry Analysis: Management also needs to analyze the entire industry. Is it growing or declining, what is the competition doing, what is the company's position within the industry? Then the firm will be able to analyze its capital budget within this strategic plan. There is no need to analyze alternatives that are not compatible with the strategic plan.

     B. Qualitative Factors

     Many of the factors involved in capital budgeting are qualitative and thus are difficult to quantify. These include such factors as improved operating efficiency, better product or service quality, more flexibility, and greater on-time delivery. In the battle for scarce resources within the company, non-quantifiable factors such as the persuasiveness of the advocate may be decisive.

     One approach in the attempt to quantify qualitative factors is to analyze the impact of not making the investment, assuming the company's competitors do invest in the new technology. The investment would be compared, not with the status quo, but with the company's reduced market share in the future.

     C. Other Approaches to Capital Budgeting

          1. Intuitive Approach: In practice there are approaches to capital budgeting other than the discounted and non-discounted cash flow models presented in this chapter. One is the intuitive approach, which is non-quantitative and is often used by small business owners. This approach might lead to the same decision as the quantitative models, but the decision maker would not be able to justify the rationale to anyone else. However, no justification is required if the decision maker is the owner.

          2. EPS Approach: Another approach is to analyze the immediate impact on earnings per share. This is an example of America's short-term orientation to long-term decision making.

          3. Justifying Preselected Option: Sometimes, cash flow methods are used to justify an alternative already selected. A previous essay question on the CMA exam discussed the possible ethical problems of this approach. A management accountant was required by her supervisor to revise a capital budget proposal to justify a purchase he wanted to make. When she revised the proposal with much less reasonable assumptions, the purchase still could not be justified, so he told her to start with a positive net present value and work backwards to justify it. The actions in this scenario violate the Management Accountant's Standards of Ethical Conduct.

     D. Risk

     Not all capital budgeting projects will have the same level of risk to the company. Replacing a machine is not the same as entering a new market. Various methods are available to adjust for the levels of risk in different types of projects. The procedures include:

• Establish different discount rates.
  
• Shorten the required payback period.
  
• Reduce the estimated future cash flows.
  
• Perform sensitivity analysis.
  
• Develop probability distributions for the future cash flows.

     E. Tax Effects

     The cash flows used in the cash flow models should be adjusted for the effects of taxes. There are two situations to be aware of.

          1. Depreciation Tax Shield: Depreciation is not a cash flow, but since it is a deductible expense for tax purposes, there is a tax effect to be taken into account. The depreciation tax shield per period is equal to the amount of annual depreciation times the tax rate. The following example demonstrates this effect.

          Example: Assume a new asset was purchased for $50,000. It will be used for 10 years in a project that will yield uniform before-tax cash flows of $15,000. Tax rate is assumed to be 40%. The company uses straight-line depreciation, and no salvage value.

          Computation:

Before Tax Flows	$15,000
Subtract Depreciation	(5,000)
Taxes at 40%	(4,000)
Add Back Depreciation	5,000
After-tax Periodic Cash Flows	$11,000

     Note in this example, that had there not been any depreciation, the taxes would have amounted to $6,000 ($15,000 x 40%), and after-tax cash flows would have been $9,000. The additional $2,000 of after-tax cash flows is generated by the depreciation tax shield computed at 40% on the $5,000 of depreciation.

          2. Asset Disposals: When assets are disposed of, the transaction will usually generate either a gain or a loss. The tax on a gain will reduce cash flows in the year of incurrence. The tax benefit provided by a loss increases cash flows. In each case, to compute the tax effect, multiply the amount of the gain or loss by the tax rate expected to be in effect in the period in question.

          In the cash-flow models presented in this chapter, the potential for tax effects on disposals occur at two different time periods: in the year of investment (usually described as Year 0) when an old asset that is being replaced is sold, and in the disinvesting year (the last period of the new project) when the new asset is sold or disposed of. A gain on disposal of an old asset is usually included in the analysis as an adjustment to the proceeds of the disposal. These proceeds will be reduced by the amount of the tax on the gain. Conversely, the proceeds are increased by the tax benefit generated by any loss experienced.

          These adjusted proceeds may be treated as a cash flow in Year 0, or as a reduction to arrive at a net cost of the new asset (see the example format below). In the year of disposal of the new asset, the proceeds are treated as a separate cash flow. They must be discounted using the present value of one lump sum, x periods in the future. (In other words, they are not included as part of an annuity stream).

Example: Year 0 - Investing Phase: Proceeds of sale of old to arrive at net investment cost.

Cost of New Asset $XXXXX
Less: Proceeds from sale of old ( XXX)
Adjust for tax effect of sale of old
If gain, tax on gain will increase cost X
OR
If loss, tax benefit on loss will decrease cost ( X)
Net investment cost $XXXXX

Last Year - Disinvesting Phase - Additional cash flow when sell new asset in last period.

Proceeds from sale of new asset $ XX
Adjust for tax effect of sale of new
If gain, tax on gain will decrease cash flow ( X)
OR
If loss, tax benefit on loss will increase cash flow X
Additional cash flow last period $XXX

II. THE TIME VALUE OF MONEY

     An amount of money received now is worth more than the same dollar amount of money received in the future. The reason is because interest could be earned on those funds adding to the final amount. Interest tables are a convenience, but the factors can be manually calculated. Also the factors from one table can be converted to the factors from another table. The procedure is demonstrated in the factor conversion section. The CMA exam may give only some of the factors required to solve a problem. The candidate needs to be able to determine which factors are necessary and be able to derive them.

     A. Terminology

          1. Present Value of $1: How large an amount to be invested now at a particular interest rate needs to be in order to be worth X amount at a particular point in the future after n periods. Conversely, how much an amount to be received in the future is worth now.

          2. Future Value of $1: How large an amount invested now will be in n periods. This is also called compound value.

          3. Compounding: Interest is calculated on the principal at the end of the first period. The interest is added to the principal. At the end of the second period, interest is calculated on both the principal and the interest earned during the first period, etc. This is the procedure to convert an amount from its present value to its future value.

          4. Discounting: This is the reverse of the compounding procedure. It is used to determine the original principal amount or to reduce a future amount to its present value.

          5. Period: The compounding or discounting interval - months, quarters or years.

          6. Ordinary Annuity: A series of payments which are paid at the end of each period.

          7. Present Value of an Ordinary Annuity: The amount to be invested now to receive a future series of payments. Conversely, how much a future series of payments is worth now.

          8. Annuity Due: The same as an ordinary annuity except that the payments are made at the beginning of each period.

          9. Future Value of an Annuity: How much a series of investment payments will be worth in the future. Conversely, how much each investment payment needs to be to accumulate a desired amount.

          10. Interpolation: Many tables give only even interest rates. To get interest rates in between the rates given, use straight-line interpolation. For example: to get the factor for 7%, add the factors for 6% and 8%, then divide by 2.

     B. Formulas

FV = PV(1+i) to the nth power
PV = FV /(1+i) to the nth power

Where:
FV = Future Value
PV = Present Value
i = interest rate
n = number of periods

Therefore:
FV = PV x factor from the table
PV = FV -:- factor from the table
Annuity payment amount x factor = PV of annuity
PV of annuity / annuity amount = factor
Look up the factor in the table to get the interest rate.

     C. Factor Conversions

     Since questions on the CMA exam may give several different tables, or only one table that may not be the most appropriate table, a candidate needs to be able to convert the factors given to the ones actually needed to solve the problem.

          1. PV of $1 to PV of an Ordinary Annuity: Add the factors for each period.

          2. PV of an Ordinary Annuity to PV of $1: Determine the incremental increase between the last period and the next to the last period. n - (n - 1)

          3. Ordinary Annuity to Annuity Due: Add 1 to the factor of n - 1. The first payment has a factor of 1, because it is paid now. A payment at the end of a period has the same factor as a payment at the beginning of the next period. For this purpose, December 31 = January 1 (assuming each period is a year in length).

          4. PV to FV and FV to PV: The factors are related thus:

PV factor x FV factor = 1

Therefore:
1 / PV factor = FV factor
and: 1 / FV factor = PV factor

Example: A corporation has agreed to sell some used computer equipment to one of the company's employees for $5,000. They have been discussing alternative financing arrangements for the sale and the present and future values of each alternative. (Present Value of an Ordinary Annuity table was given with the problem. See end of chapter for tables.)

1. The corporation has offered to accept a $1,000 down payment and set up a note receivable that calls for four $1,000 payments at the end of each of the next four years. If they use a 6 percent discount rate, the present value of the note receivable would be:
a. $3,960
b. $3,168
c. $4,212
d. $3,465

2. The employee has agreed to the immediate down payment of $1,000, but would like the note for $4,000 to be payable in full at the end of the fourth year. Because of the increased risk associated with the terms of this note, the company would apply an 8 percent discount rate. The present value of this note would be:
a. $2,940
b. $3,312
c. $3,940
d. $3,675

3. If the employee borrowed the $5,000 at 8 percent interest for four years from his bank and paid the company the full price of the equipment immediately, the company could invest the $5,000 for three years at 7 percent. The future value of this investment (rounded) would be:
a. $6,297
b. $6,127
c. $6,553
d. $6,803

Answers: 1. d.
Method 1: Read the factor from the Present Value of an Ordinary Annuity table given.
Annuity x Factor = PV
1000 x 3.4651 = $3,465.10
Method 2: Conversion from the Present Value of $1 table
Periods 6%
1 .94340
2 .89000
3 .83962
4 .79209
Total factor = 3.46511

2. a.
Method 1: Conversion from Present Value of an Annuity to PV of $1 factor
8% for 4 periods 3.3121
less: 8% for 3 periods 2.5771
- .7350
4000 x .7350 = 2940
Method 2: Formula:
PV = F / (1 + i)nth power
= (1.08)(1.08)(1.08)(1.08) = 1.36
4000 / 1.36 = 2941

3. b.
Method 1: The long method of calculating each year:
yr 1: 5000 x 1.07 = 5350
yr 2: 5350 x 1.07 = 5724.5
yr 3: 5724.5 x 1.07 = 6125.215
Method 2: Formula:
FV = PV (1 + i)n
(1.07)(1.07)(1.07) = 1.225043
5000 x 1.225043 = 6125.215
Method 3: Conversion of the PV of $1 factor from the PV of an annuity table
7% for 3 periods 2.6243
less 7% for 2 periods 1.8080
- .8163
FV = 1 / PV = 1 / .816 = 1.22504
5000 x 1.22504 = 6125.20

Note: None of these methods arrives at exactly the same answer the exam gives as choice b. They used a table rounded to three places and we have a more accurate one with four places. On the exam select the closest answer in a case such as this.

III. DISCOUNTED CASH FLOW METHODS

A. Introduction

These methods involve some means of comparing the net cost of the investment project with the present value of the future cash flows expected to be generated by the project. They are the theoretically correct methods of capital budgeting, because they take into account the time value of money. They also focus on the cash flows involved, not on accrual accounting returns.

B. Interest Rate

1. Which Rate? All present value methods require the discounting of future cash flows at some desired rate of return. Discount rate, hurdle rate, and cost of capital are all terms for the interest rate used to adjust future cash flows to the present.

The discount rate should be based on the rate the shareholder investor could earn on projects of similar risk. This, in effect, is the weighted-average cost of capital. The hurdle rate is sometimes based on the average return on projects. This is not theoretically correct, because this rate could be above or below what the investors could earn elsewhere. In practice, the discount rate is often based on the cost of borrowing current funds, which is actually irrelevant to the rate that should be earned on projects. In CMA questions, the fact pattern usually makes it clear what the desired rate of return is.

2. Adjustment for Risk: Different discount rates may be established for different types of projects to adjust for different levels of risk. Higher risk translates into a higher discount rate. An inflation adjustment is also possible. In practice, the "real rate of interest" is the pure rate of interest plus a risk factor. The "nominal rate of interest" is the real rate plus an inflation factor.

C. Assumptions

1. Timing: Cash flows occur at the beginning or end of a period as specified, not continuously during the period as in real life. In most CMA questions, cash flows are assumed to occur at the end of the period.

2. Certainty: Cash flows are known with certainty - both the amounts and the timing. Probability adjustments could be used in practice, but are not tested on the CMA exam.

3. Reinvestment: In the net present value method, it is assumed that cash flows from the project can be reinvested at the discount (hurdle) rate. This is a conservative approach. In the internal rate of return method, it is assumed that cash inflows can be reinvested at the actual interest rate generated by the project. Since this is often a higher rate than the hurdle rate, this is an optimistic (and aggressive) approach to capital budgeting decision analysis.

4. Relevance: It is assumed that the interest rate used is relevant for the entire life of the project.

D. Cash Flows

The after-tax cash flows must be used. Note that this is different from the income from operations. Some of the following additional considerations may be appropriate depending on the fact pattern of the question.

1. Working Capital Adjustments: If working capital increases at the beginning of a project, it is assumed that some cash has been used to acquire additional inventories, receivables, etc. This is treated as a cash outflow at the inception of the project. There is no tax adjustment for this, because acquisition of such items is not a taxable event. At the end of the project, a decrease in working capital is assumed as the additional working capital is liquidated. This liquidation is assumed to result in a gain, and is reduced by the tax on that gain. The resulting net figure is treated as an additional cash flow in the final year of the project.

In some instances, working capital may decrease at the beginning of the project. In this situation, the liquidation (net of corresponding tax) is treated as a cash flow at the inception of the project, and the corresponding increase in working capital (with no tax effect) is a cash outflow in the final year.

2. Depreciation Issues: When the after-tax cash flows from operations have been given in a fact pattern, the depreciation for financial statement purposes has already been factored in and no additional computations need to be made. However, when different depreciation methods are used for financial accounting purposes as opposed to for tax purposes, the cash from operations must be adjusted for the taxes on the difference between the two depreciation amounts.

Example: Assume an increase in cash from operations of $20,000. Straight-line depreciation of $10,000 has been taken for financial statement purposes, but $6,000 MACRS depreciation was deducted for tax purposes. The tax rate is 40%. Since the taxable income under MACRS would be $4,000 higher (the difference between the two depreciation amounts), an additional $1,600 of taxes ($4,000 x 40%) must be subtracted from the $20,000 cash flows to arrive at cash flows of $18,400. The adjustment would obviously be an addition to the cash from operations if the MACRS depreciation exceeded the financial statement depreciation.

3. Salvage Values: The salvage value of a fully depreciated old asset being disposed of at the inception of a new project is treated as a cash inflow at the inception of the new project, net of related tax. This amount is a reduction of the cost of the new asset in the determination of the net incremental cost of the new project. Where the old asset has not been fully depreciated, the gain or loss on disposal must be computed and the related cash inflow (if a gain) or outflow (if a loss) -- adjusted for taxes paid or tax benefit received -- must be considered in determination of the net cost of the new investment.

The salvage value of a new asset is treated as an additional cash flow in the final year of its life. This figure must also be adjusted for taxes.

Some capital budgeting problems present a comparison between two different options. This is usually retaining and continuing to use an old piece of equipment as opposed to discarding the old and buying a new asset. If there are salvage values for both assets in the final year of the life of the new asset, the difference between these two values (adjusted for tax purposes) is treated as an additional cash flow in the final year of the project.

E. Net Present Value Method (NPV)

The net present value (NPV) method evaluates the net difference between the total discounted cash inflows and outflows. If the NPV is positive, more cash came in than went out. On a simple problem with cash inflows that are the same amount each year, the annuity discount factor can be used. Otherwise, each year's individual cash flow must be discounted separately.

1. Formula:

a. Step One: If the figure has not been given, compute the after-tax cash flows for each period in the life of the new project. Remember to consider all cash flow possibilities identified in Section D above.

b. Step Two: Compute the total present value of the cash flows at the hurdle rate.

c. Step Three: Determine the net cost of the new asset and any other outflows. (Cost less proceeds on sale of old asset adjusted for any tax effects of the sale as identified in Section D above.)

d. Step Four: Subtract the net cost of the new asset from the total present value of the cash flows.

2. Significance of Results:

a. Net Present Value is Zero: In this situation, the total present value of cash flows discounted at the hurdle rate is equal to the net cost of the new asset. This means that the project generates exactly the hurdle rate desired. The project is acceptable.

b. Net Present Value is Positive: Here, the total present value of the cash flows exceeds the net cost of the new asset. This means that the project generates a return higher then the hurdle rate used to discount the flows. This makes the project even more acceptable. Note that the internal rate of return method (the next method discussed) can be used to find out the actual rate being earned.

c. Net Present Value is Negative: The total present value of the cash flows is less than the net cost of the new asset. This means that the project does not generate a return that is at least equal to the hurdle rate desired, and is, therefore, not acceptable.

An example of the computations involved in the net present value method are presented below in a series of questions after a discussion on the internal rate of return method.

F. Internal Rate of Return (IRR)

1. Objective: As was indicated in the discussion of the Net Present Value Method, a positive net present value indicates that a rate of return higher than the hurdle rate is being generated. The object of the internal rate of return is to determine what that interest rate actually is; i.e., what is the discount rate that would make the net present value equal to zero.

2. Computation: If the cash inflows are the same amount each year, the computation is straight-forward. Simply divide the initial net investment by the annual cash inflow to arrive at the discount factor. This factor that can be located on the appropriate period row of a present value of an annuity table to find the interest rate.

If the cash flows are not the same amount each year, the trial and error method must be used. If only one period is different, use the annuity table method as a first approximation, then try close rates. However, the CMA exam has rarely asked for this computation. The emphasis in questions dealing with internal rate of return method is on an understanding of its significance and the reinvestment assumption underlying it (see discussion under Assumptions above).

G. Illustration -- NPV and IRR Methods

Example: Harrison Corporation is considering the replacement of an old machine that is currently being used. The old machine is fully depreciated, but can be used by the corporation through 19x5. If Harrison decides to replace the old machine, Neighbor Company has offered to purchase it for $60,000 on the replacement date. The old machine would have no salvage value in 19x5.

If the replacement occurs, a new machine would be acquired from Roberts Industries on January 2, 19x1. The purchase price of $1,000,000 for the new machine would be paid in cash at the time of replacement. Due to the increased efficiency of the new machine, estimated annual cash savings of $300,000 would be generated through 19x5, the end of its expected useful life. The new machine is not expected to have any salvage value at the end of 19x5.

All operating cash receipts, operating cash expenditures, and applicable tax payments are assumed to occur at the end of the year. Harrison employs the calendar year for reporting purposes. Assume that Harrison Corporation is not subject to income taxes.

Present Value of $1 Received at the End of the Period
Period 9% 12% 15% 18% 21%
1 .92 .89 .87 .85 .83
2 .84 .80 .76 .72 .68
3 .77 .71 .65 .61 .56
4 .71 .64 .57 .51 .47
5 .65 .57 .50 .44 .39

Present Value of an Ordinary Annuity
Period 9% 12% 15% 18% 21%
1 .92 .89 .87 .85 .83
2 1.76 1.69 1.63 1.57 1.51
3 2.53 2.40 2.28 2.18 2.07
4 3.24 3.04 2.85 2.69 2.54
5 3.89 3.61 3.35 3.13 2.93

1. If Harrison requires investments to earn a 12 percent return, the net present value for replacing the old machine with the new machine is:

a. $171,000
b. $136,400
c. $143,000
d. $83,000

2. The internal rate of return, to the nearest percent, to replace the old machine is:

a. 9 percent
b. 15 percent
c. 17 percent
d. 18 percent

Answers:

1. c.
Total discounted annual
cash savings ($300,000 x 3.61) 1,083,000
Less: Net investment cost
Cost of new machine $1,000,000
Less proceeds of sale of old 60,000
- 940,000
Net Present Value 143,000

2. d.
cash paid 1,000,000
cash received - 60,000
net investment 940,000

940,000 = $300,000 x PV factor for 5 periods
(940,000/300000) = 3.13 PV factor for 5 periods
Reading from annuity table, 5 periods row, interest rate column is 18%

Example: Assume the following additional assumptions that apply to questions 3 to 6:

• Harrison requires all investments to earn a 12 percent after tax rate of return.
  
• Harrison is subject to a marginal income tax rate of 40 percent on all income and gains (losses).
  
• The new machine is classified as three-year property for MACRS purposes. The applicable percentages for three year property are as follows:

Recovery Year Applicable Percentage
- 1 25%
- 2 38%
- 3 37%

3. The present value of the after tax cash flow associated with the salvage of the old machine is:

a. $38,640
b. $36,000
c. $32,040
d. $27,960

4. The present value of the annual after tax cash savings that arise from the increased efficiency of the new machine throughout its life (calculated before consideration of any depreciation tax shield) is:

a. $563,400
b. $375,600
c. $433,200
d. $649,800

5. The present value of the depreciation tax shield for 19x2 is:

a. $182,400
b. $121,600
c. $109,440
d. $114,304

6. If the new machine were sold for $80,000 on December 31, 19x5, instead of the estimated salvage value of zero, the present value of the additional after tax cash flow is:

a. $18,240
b. $27,360
c. $45,600
d. $48,000

Answers:
3. b. 60,000 cash received x (1 - .4) = 36,000 received now - no discount
4. d. 300,000 x (1 - .4) = 180,000 (After-tax cash flows)
5 periods at 12% x 3.61
- 649,800

5. b.
1,000,000 x .38 (2nd yr MACRS) = 380,000 (Depreciation)
tax rate x .4
- 152,000 (Depreciation tax shield)
12% at end of 2nd period .8
- 121,600

6. b.
80,000 x (1 - .4) = 48,000 (After-tax proceeds)
12% at end of 5th period x .57
- 27,360

H. Excess Present Value Index

1. Ranking Method: This is also called the profitability index. When more projects meet the hurdle rate than the company has the money to fund, a ranking method is useful to determine how best to use the available resources. It is difficult to determine the relative merits of projects when working from their absolute dollar figures. However, a ranking procedure that relates each project's total present value to its initial net investment cost provides a method where all projects are being judged by the same criterion. This method actually ties the two previous methods (net present value and internal rate of return) together.

2. Computation: The excess present value index is calculated by dividing the total present value of the cash inflows by the initial net investment cost. If the resulting index figure is exactly 1, the hurdle rate is being met. Where the index exceeds 1, the actual rate being generated is higher than the hurdle rate. If the index is less than 1, the project does not meet the hurdle rate. The larger the index, the higher the investment is ranked.

I. Breakeven Time (BET)

The breakeven time of a project is the point where the sum of the cumulative discounted cash inflows from the research and development stage through distribution is equal to that of discounted cash outflows. It provides strategic information particularly useful in situations where a firm is considering bringing a new product to market and where time is an important factor. A danger of its use can be an overemphasis on products that have short new product development times.

IV. NON-DISCOUNTED CASH FLOW METHODS

A. Introduction

Since they ignore the time-value of money, the non-discounted cash flow methods are not considered to be theoretically correct. However, in practice, they are often used because they are easy to understand by non-accounting personnel and simple to calculate.

B. Payback Method

1. Objective: This method measures the length of time required to receive the same amount of cash as the initial investment. It answers the question, "When am I going to get my money back?"

2. Advantages: This method can be useful in situations where liquidity is important. Projects with shorter payback periods are generally preferred over those with longer periods, because assumptions underlying present-value models may not be valid for a long period of time. Also, since it is a cash-flows method, it is not affected by accrual accounting procedures, and it is useful when precisely correct figures are not vital and as a preliminary screening tool.

3. Disadvantages: In addition to the non-recognition of the time value of money, a significant disadvantage is that the method ignores total profitability and all cash flows after the payback period. It would be possible to have a situation where a machine with a shorter payback period also had a shorter useful life compared with another project, thereby reducing the potential for cash flows and profits beyond the narrow focus of the payback period.

4. Calculation: Where the periodic cash flows are uniform, the payback method is calculated by dividing the initial investment by the annual cash inflow to get the number of years to payback. If the cash inflows are not even, the calculation may have to be done on a year by year basis. If so, apply each year's cash flow to the balance of the initial investment to determine the number of years.

Example: A corporation is contemplating the purchase of some specialized machinery. The machinery will cost $250,000 and will be depreciated over its five year life by using the straight line method. Annual inflows of $300,000 and cash operating expenses of $220,000 are anticipated as a result of this new machinery. The corporation is subject to a 40 percent income tax rate. The payback period on this investment (rounded to the nearest tenth) is:

a. 1.4 years
b. 3.2 years
c. 3.7 years
d. 5.2 years

Answer:
Annual inflows $300,000
Cash op exp -220,000
Depr (5 yr SL) - 50,000
Op income 30,000
Tax exp (.40) - 12,000
Net income 18,000
Depr (non cash) + 50,000
After tax cash flow 68,000

Initial Investment / after tax cash flow
= 250,000 / 68,000 = 3.676 = 3.7 years

The reciprocal of the payback calculation can be used to approximate the IRR.

C. Bailout Payback Time

Often, management is interested in knowing the amount of time it would take to recover an investment if the project does not go as planned. Projects which have shorter bailout periods are generally more attractive than those with longer bailout periods, all other factors being equal. This method is helpful in risk-averse decision making situations.

The bailout payback time is the time when the cumulative cash operating savings plus the disposal price of an asset at the end of a particular year are equal to the original investment. Note that these dollars are not discounted.

V. ACCRUAL ACCOUNTING RATE OF RETURN

A. Computation

This method divides the incremental income attributed to the project by either the initial investment or the average investment. As can be seen, it is simply the return on investment ratio (ROI). The incremental income is book income on the accrual basis, not cash flows.

B. Applicability

Accrual basis income includes or excludes items based on GAAP for external reporting, which may not be valid for internal decision making. Furthermore, it uses an average annual incremental figure rather than the explicit cash flows determined in both the discounted and payback methods. Note also that it, like the payback method, ignores the time value of money. However, it does take into account profitability, is easy to understand, and is useful in a situation where a divisional manager is evaluated on a comparable basis (i.e. use of ROI measures).

VI THE FINANCING DECISION

A. Separate Decision

Once an investment project has been selected using capital budgeting techniques, the determination of how best to raise funds to finance that investment is a separate decision in itself. Choices include the use of internal funds, borrowing, the sale of stock, or entering into a leasing arrangement.

B. Analysis Tools

1. Present Value Analysis: The analysis involves the determination of the total present value of the periodic net cash outflows relating to each different financing alternative. All qualitative issues being equal, the alternative that results in the lowest total present value should be the financing plan selected.

2. Appropriate Discount Rate: The interest rate to use when analyzing financing options should not be the hurdle rate used to analyze capital budgeting alternatives. A firm's after-tax incremental cost of borrowing would be an appropriate rate. Where a firm's incremental borrowing rate is given, it should be multiplied by (1 - the tax rate) to arrive at the after-tax rate. For example --a before tax incremental rate of 10% becomes 6% for a firm that has a tax rate of 40%. (10% borrowing rate times [1-.40] = .06)

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