10
Cash CHAPTER Flows and Other Topics in Capital Budgeting
CHAPTER ORIENTATION
Capital budgeting involves the decision-making process with respect to the investment in fixed assets; specifically, it involves measuring the free cash flows or incremental cash flows associated with investment proposals and evaluating the attractiveness of these cash flows relative to the project's costs. This chapter focuses on the estimation of those cash flows based on various decision criteria, and how to deal with capital rationing and mutually exclusive projects.
CHAPTER OUTLINE
I. What criteria should we use in the evaluation of alternative investment proposals? A. B. Use free cash flows rather than accounting profits because free cash flows allow us to correctly analyze the time element of the flows. Examine free cash flows on an after-tax basis because they are the flows available to shareholders. C. D. Include only the incremental cash flows resulting from the investment decision. Ignore all other flows.
In deciding which free cash flows are relevant we want to: 1. 2. Use free cash flows rather than accounting profits as our measurement tool. Think incrementally, looking at the company with and without the new project. Only incremental after tax cash flows, or free cash flows, are relevant. Beware of cash flows diverted from existing products, again, looking at the firm as a whole with the new product versus without the new product.
3.
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4. 5. 6. 7. 8. 9. II.
Bring in working capital needs. Take account of the fact that a new project may involve the additional investment in working capital. Consider incremental expenses. Do not include stock costs as incremental cash flows. Account for opportunity costs. Decide if overhead costs are truly incremental cash flows. Ignore interest payments and financing flows.
Measuring free cash flows. We are interested in measuring the incremental after-tax cash flows, or free cash flows, resulting from the investment proposal. In general, there will be three major sources of cash flows: initial outlays, differential cash flows over the project's life, and terminal cash flows. A. Initial outlays include whatever cash flows are necessary to get the project in running order, for example: 1. 2. The installed cost of the asset In the case of a replacement proposal, the selling price of the old machine minus (or plus) any tax gain (or tax loss) offsetting the initial outlay Any expense items (for example, training) necessary for the operation of the proposal Any other non-expense cash outlays required, such as increased working-capital needs
3. 4. B.
Differential cash flows over the project's life include the incremental after-tax flows over the life of the project, for example: 1. 2. 3. 4. 5. 6. 7. 8. Added revenue (less added selling expenses) for the proposal Any labor and/or material savings incurred Increases in overhead incurred Changes in taxes. Change in net working capital. Change in capital spending. Make sure calculations reflect the fact that while depreciation is an expense, it does not involve any cash flows. A word of warning not to include financing charges (such as interest or preferred stock dividends), for they are implicitly taken care of in the discounting process.
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C.
Terminal cash flows include any incremental cash flows that result at the termination of the project, for example: 1. 2. The project's salvage value plus (or minus) any taxable gains or losses associated with the project Any terminal cash flow needed, perhaps disposal of obsolete equipment
3. Recovery of any non-expense cash outlays associated with the project, such as recovery of increased working-capital needs associated with the proposal. III. Measuring the cash flows using the pro forma method A. A projects free cash flows = projects change in operating cash flows B change in net working capital change in capital spending
If we rewrite this, inserting the calculations for the projects change in operating cash flows (OCF), we get: A projects free cash flows = Change in earnings before interest and taxes + change in taxes change in depreciation change in net working capital change in capital spending
C.
In addition to using the pro forma method for calculating operating cash flows, there are three other approaches that are also commonly used. A summary of all the different approaches follows, OCF Calculation: The Pro Forma Approach: Operating Cash Flows = Change in Earnings Before Interest and Taxes Change in Taxes + Change in Depreciation
D.
E.
Alternative OCF Calculation 1: Add Back Approach Operating Cash Flows = Net income + Depreciation
E.
Alternative OCF Calculation 2: Definitional Approach Operating Cash Flows = Change in revenues - Change in cash expenses Change in Taxes
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F.
Alternative OCF Calculation 3: Depreciation Tax Shield Approach Operating Cash Flows = (Revenues cash expenses) X (1 tax rate) + (change in depreciation X tax rate) Youll notice that interest payments are no where to be found, thats because we ignore them when were calculating operating cash flows. Youll also notice that we end up with the same answer regardless of how we work the problem.
IV.
Mutually exclusive projects: Although the IRR and the present-value methods will, in general, give consistent accept-reject decisions, they may not rank projects identically. This becomes important in the case of mutually exclusive projects. A. A project is mutually exclusive if acceptance of it precludes the acceptance of one or more projects. Then, in this case, the project's relative ranking becomes important. Ranking conflicts come as a result of the different assumptions on the reinvestment rate on funds released from the proposals. Thus, when conflicting ranking of mutually exclusive projects results from the different reinvestment assumptions, the decision boils down to which assumption is best. In general, the net present value method is considered to be theoretically superior.
B. C.
D. V.
Capital rationing is the situation in which a budget ceiling or constraint is placed upon the amount of funds that can be invested during a time period. Theoretically, a firm should never reject a project that yields more than the required rate of return. Although there are circumstances that may create complicated situations in general, an investment policy limited by capital rationing is less than optimal.
VI.
Options in Capital Budgeting. Options in capital budgeting deal with the opportunity to modify the project. Three of the most common types of options that can add value to a capital budgeting project are: (1) the option to delay a project until the future cash flows are more favorable this option is common when the firm has exclusive rights, perhaps a patent, to a product or technology, (2) the option to expand a project, perhaps in size or even to new products that would not have otherwise been feasible, and (3) the option to abandon a project if the future cash flows fall short of expectations.
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ANSWERS TO END-OF-CHAPTER QUESTIONS
10-1. We focus on cash flows rather than accounting profits because these are the flows that the firm receives and can reinvest. Only by examining cash flows are we able to correctly analyze the timing of the benefit or cost. Also, we are only interested in these cash flows on an after tax basis as only those flows are available to the shareholder. In addition, it is only the incremental cash flows that interest us, because, looking at the project from the point of the company as a whole, the incremental cash flows are the marginal benefits from the project and, as such, are the increased value to the firm from accepting the project. 10-2. Although depreciation is not a cash flow item, it does affect the level of the differential cash flows over the project's life because of its effect on taxes. Depreciation is an expense item and, the more depreciation incurred, the larger are expenses. Thus, accounting profits become lower and, in turn, so do taxes, which are a cash flow item. 10-3. If a project requires an increased investment in working capital, the amount of this investment should be considered as part of the initial outlay associated with the project's acceptance. Since this investment in working capital is never "consumed," an offsetting inflow of the same size as the working capital's initial outlay will occur at the termination of the project corresponding to the recapture of this working capital. In effect, only the time value of money associated with the working capital investment is lost. 10-4. When evaluating a capital budgeting proposal, sunk costs are ignored. We are interested in only the incremental after-tax cash flows to the company as a whole. Regardless of the decision made on the investment at hand, the sunk costs will have already occurred, which means these are not incremental cash flows. Hence, they are irrelevant. 10-5. Mutually exclusive projects involve two or more projects where the acceptance of one project will necessarily mean the rejection of the other project. This usually occurs when the set of projects perform essentially the same task. Relating this to our discounted cash flow criteria, it means that not all projects with positive NPV's, profitability indexes greater than 1.0 and IRRs greater than the required rate of return will be accepted. Moreover, since our discounted cash flow criteria do not always yield the same ranking of projects, one criterion may indicate that the mutually exclusive project A should be accepted, while another criterion may indicate that the mutually exclusive project B should be accepted. 10-6. There are three principal reasons for imposing a capital rationing constraint. First, the management may feel that market conditions are temporarily adverse. In the early- and mid-seventies, this reason was fairly common, because interest rates were at an all-time high and stock prices were at a depressed level. The second reason is a manpower shortage, that is, a shortage of qualified managers to direct new projects. The final reason involves intangible considerations. For example, the management may simply fear debt, and so avoid interest payments at any cost. Or the common 254
stock issuance may be limited in order to allow the current owners to maintain strict voting control over the company or to maintain a stable dividend policy. Whether or not this is a rational move depends upon the extent of the rationing. If it is minor and noncontinuing, then the firm's share price will probably not suffer to any great extent. However, it should be emphasized that capital rationing and rejection of projects with positive net present values is contrary to the firm's goal of maximization of shareholders wealth. 10-7. When two mutually exclusive projects of unequal size are compared, the firm should select the project with the largest net present value, when there is no capital rationing. If there is capital rationing, then the firm should select the set of projects with the highest net present value. The firm needs to consider alternative uses of funds if the project with the lowest net present value is chosen. 10-8. The time disparity problem and the conflicting rankings that accompany it result from the differing reinvestment assumptions made by the net present value and internal rate of return decision criteria. The net present value criterion assumes that cash flows over the life of the project can be reinvested at the required rate of return; the internal rate of return implicitly assumes that the cash flows over the life of the project can be reinvested at the internal rate of return. 10.9. The problem of incomparability of projects with different lives is not directly a result of the projects having different lives but of the fact that future profitable investment proposals are being affected by the decision currently being made. Again the key is: "Does the investment decision being made today affect future profitable investment proposals?" If so, the projects are not comparable. While the most theoretically proper approach is to make assumptions as to investment opportunities in the future, this method is probably too difficult to be of any value in most cases. Thus, the most common method used to deal with this problem is the creation of a replacement chain to equalize life spans. In effect, the reinvestment opportunities in the future are assumed to be similar to the current ones. Another approach is to calculate the equivalent annual annuity of each project.
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
Solutions to Problem Set A
10-1A. (a) Tax payments associated with the sale for $35,000 Recapture of depreciation = ($35,000-$15,000) (0.34) = $6,800 (b) Tax payments associated with sale for $25,000 Recapture of depreciation = ($25,000-$15,000) (0.34) = $3,400
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(c) (d) 10-2A.
No taxes, because the machine would have been sold for its book value. Tax savings from sale below book value: Tax savings = ($15,000-$12,000) (0.34) = $1,020
New Sales Less: Sales taken from existing product lines
$25,000,000 - 5,000,000 $20,000,000
10-3A. Change in net working capital equals the increase in accounts receivable and inventory less the increase in accounts payable = $18,000 + $15,000 - $24,000 = $9,000. The change in taxes will be EBIT X marginal tax rate = $475,000 X .34 = $161,500. A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = + $475,000 $161,500 $100,000 $9,000 $0 = $404,500 10-4A. Change in net working capital equals the increase in accounts receivable and inventory less the increase in accounts payable = $8,000 + $15,000 - $16,000 = $7,000. The change in taxes will be EBIT X marginal tax rate = $900,000 X .34 = $306,000. A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $900,000 - $306,000 + $300,000 - $7,000 - $0 = $887,000
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10-5A. Given this, the firms net profit after tax can be calculated as: Revenue - Cash expenses - Depreciation = EBIT - Taxes (34%) = Net income $2,000,000 800,000 200,000 $1,000,000 340,000 $ 660,000
OCF Calculation: Pro Forma Approach Operating Cash Flows = Change in Earnings Before Interest and Taxes - Change in Taxes + Change in Depreciation = $1,000,000 - $340,000 + $200,000 = $860,000 Alternative OCF Calculation 1: Add Back Approach Operating Cash Flows = Net income + Depreciation = $660,000 + $200,000 = $860,000 Alternative OCF Calculation 2: Definitional Approach Operating Cash Flows = Change in revenues - Change in cash expenses Change in Taxes = $2,000,000 - $800,000 -$340,000 = $860,000 Alternative OCF Calculation 3: Depreciation Tax Shield Approach Operating Cash Flows = (Revenues cash expenses) X (1 tax rate) + (change in depreciation X tax rate) = ($2,000,000 - $800,000) X (1-.34) + ($200,000 X.34) = $860,000 Youll notice that interest payments are nowhere to be found, thats because we ignore them when were calculating operating cash flows. Youll also notice that we end up with the same answer regardless of how we work the problem. 10-6A. Given this, the firms net profit after tax can be calculated as: Revenue - Cash expenses - Depreciation = EBIT - Taxes (34%) = Net income $3,000,000 900,000 400,000 $1,700,000 578,000 $1,122,000
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As you can see, regardless of which method you use to calculate operating cash flows, you get the same answer: OCF Calculation: Pro Forma Approach Operating Cash Flows = Change in Earnings Before Interest and Taxes - Change in Taxes + Change in Depreciation = $1,700,000 - $578,000 + $400,000 = $1,522,000 Alternative OCF Calculation 1: Add Back Approach Operating Cash Flows = Net income + Depreciation = $1,122,000 + $400,000 = $1,522,000 Alternative OCF Calculation 2: Definitional Approach Operating Cash Flows = Change in revenues - Change in cash expenses Change in Taxes = $3,000,000 - $900,000 -$578,000 = $1,522,000 Alternative OCF Calculation 3: Depreciation Tax Shield Approach Operating Cash Flows = (Revenues cash expenses) X (1 tax rate) + (change in depreciation X tax rate) = ($3,000,000 - $900,000)X(1-.34) + ($400,000 X.34) = $1,522,000 Youll notice that interest payments are no where to be found, thats because we ignore them when were calculating operating cash flows. Youll also notice that we end up with the same answer regardless of how we work the problem. 10-7A. (a) Initial Outlay Outflows: Purchase price Increased Inventory Net Initial Outlay (b) Differential annual cash flows (years 1-9) First, given this, the firms net profit after tax can be calculated as: Revenue - Cash expenses - Depreciation* = EBIT - Taxes (34%) = Net income $1,000,000 560,000 100,000 $340,000 115,600 $224,400 $1,000,000 50,000 $1,050,000
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A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $340,000 - $115,600 + $100,000* - $0 - $0 = $324,400 *Annual Depreciation on the new machine is calculated by taking the purchase price ($1,000,000) and adding in costs necessary to get the new machine in operating order (in this case $0) and dividing by the expected life. (c) Terminal Cash flow (year 10) Inflows: Free Cash flow in year 10 Recapture of working capital (inventory) Total terminal cash flow (d) NPV $324,400 50,000 $374,400
= $324,400 (PVIFA10%,9 yr.) + $374,400 (PVIF10%, 10 yr.) - $1,050,000 = $324,400 (5.759) + $374,400 (.386) - $1,050,000 = $1,868,220 + $144,518 - $1,050,000 = $962,738
10-8A. (a) Initial Outlay Outflows: Purchase price Increased Inventory Net Initial Outlay (b) Differential annual cash flows (years 1-4) First, given this, the firms net profit after tax can be calculated as: Revenue - Cash expenses - Depreciation* = EBIT - Taxes (34%) $5,000,000 3,500,000 1,000,000 $ 500,000 170,000 $5,000,000 1,000,000 $6,000,000
259
= Net income
$ 330,000
260
A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $500,000 - $170,000 + $1,000,000* - $0 - $0 = $1,330,000 *Annual Depreciation on the new machine is calculated by taking the purchase price ($5,000,000) and adding in costs necessary to get the new machine in operating order ($0) and dividing by the expected life. (c) Terminal Cash flow (year 5) Inflows: Free Cash flow in year 5 Recapture of working capital (inventory) Total terminal cash flow (d) NPV $1,330,000 1,000,000 $2,330,000
= $1,330,000 (PVIFA10%,4 yr.) + $2,330,000 (PVIF10%, 5 yr.) - $6,000,000 = $1,330,000 (3.170) + $2,330,000 (.621) - $6,000,000 = $4,216,100 + $1,446,930 - $6,000,000 = -$336,970
Since the NPV is negative, this project should be rejected. 10-9A. (a) Initial Outlay Outflows: Purchase price Installation Fee Increased Working Capital Inventory Net Initial Outlay $100,000 5,000 5,000 $110,000
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(b)
Differential annual free cash flows (years 1-9) A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $35,000 - $11,900 + $10,500* - $0 - $0 = $33,600
* Annual Depreciation on the new machine is calculated by taking the purchase price ($100,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life. (c) Terminal Free Cash flow (year 10) Inflows: Free Cash flow in year 10 Recapture of working capital (inventory) Total terminal cash flow (d) NPV $33,600 5,000 $ 38,600
= $33,600 (PVIFA15%,9 yr.) + $38,600 (PVIF15%, 10 yr.) - $110,000 = $33,600 (4.772) + $38,600 (.247) - $110,000 = $160,339.20 + $9,534.20 - $110,000 = $59,873.40
Yes, the NPV > 0. 10-10A.(a) Initial Outlay Outflows: Purchase price Installation Fee Training Session Fee Increased Inventory Net Initial Outlay
$ 500,000 5,000 25,000 30,000 $560,000
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(b)
Differential annual free cash flows (years 1-9) A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $150,000 - $51,000 + $50,500* - $0 - $0 = $149,500
*Annual Depreciation on the new machine is calculated by taking the purchase price ($500,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life. (c) Terminal Free Cash flow (year 10) Inflows: Free Cash flow in year 10 Recapture of working capital (inventory) Total terminal cash flow (d) NPV $149,500 30,000 $ 179,500
= $149,500 (PVIFA15%,9 yr.) + $179,500 (PVIF15%, 10 yr.) - $560,000 = $149,500 (4.772) + $179,500 (.247) - $560,000 = $713,414 + $44,336.50 - $560,000 = $197,750.50
Yes, the NPV > 0. 10-11A.(a) Initial Outlay Outflows: Purchase price Installation Fee Training Session Fee Increased Inventory Net Initial Outlay $ 200,000 5,000 5,000 20,000 $230,000
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(b)
Differential annual cash flows (years 1-9) A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $50,000 - $17,000 + $20,500* - $0 - $0 = $53,500
*Annual Depreciation on the new machine is calculated by taking the purchase price ($200,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life. (c) Terminal Cash flow (year 10) Inflows: Free Cash flow in year 10 Recapture of working capital (inventory) Total terminal cash flow (d) NPV $53,500 20,000 $ 73,500
= $53,500 (PVIFA10%,9 yr.) + $73,500 (PVIF10%, 10 yr.) - $230,000
= $53,500 (5.759) + $73,500 (.386) - $230,000 = $308,106.50 + $28,371 - $230,000 = $106,477.50 Yes, the NPV > 0.
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10-12A
Section I. Calculate the change in EBIT, Taxes, and Depreciation (this becomes an input in the calculation of Operating Cash Flow in Section II). Year 0 1 2 3 4 5 Units Sold 70,000 120,000 120,000 80,000 70,000 Sale Price $300 $300 $300 $300 $250 Sales Revenue Less: Variable Costs Less: Fixed Costs Equals: EBDIT Less: Depreciation Equals: EBIT Taxes (@34%) $21,000,000 9,800,000 $700,000 $10,500,000 $3,000,000 $7,500,000 $2,550,000 $36,000,000 16,800,000 $700,000 $18,500,000 $3,000,000 $15,500,000 $5,270,000 $36,000,000 16,800,000 $700,000 $18,500,000 $3,000,000 $15,500,000 $5,270,000 $24,000,000 11,200,000 $700,000 $12,100,000 $3,000,000 $9,100,000 $3,094,000 $17,500,000 9,800,000 $700,000 $7,000,000 $3,000,000 $4,000,000 $1,360,000
Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV). Operating Cash Flow: EBIT $7,500,000 $15,500,000 $15,500,000 Minus: Taxes $2,550,000 $5,270,000 $5,270,000 Plus: Depreciation $3,000,000 $3,000,000 $3,000,000 Equals: Operating Cash Flow $7,950,000 $13,230,000 $13,230,000
$9,100,000 $3,094,000 $3,000,000 $9,006,000
$4,000,000 $1,360,000 $3,000,000 $5,640,000
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Section III. Calculate the Net Working Capital (this becomes an input in the calculation of Free Cash Flows in Section IV) Change in Net Working Capital: Revenue: $21,000,000 $36,000,000 $36,000,000 $24,000,000 Initial Working Capital Requirement $200,000 Net Working Capital Needs: $2,100,000 $3,600,000 $3,600,000 $2,400,000 Liquidation of Working Capital Change in Working Capital: $200,000 $1,900,000 $1,500,000 $0 ($1,200,000) Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in Capital Spending). Free Cash Flow: Operating Cash Flow $7,950,000 $13,230,000 $13,230,000 $9,006,000 Minus: Change in Net Working Capital $200,000 $1,900,000 $1,500,000 $0 ($1,200,000) Minus: Change in Capital Spending $15,000,000 $0 $0 $0 $0 Free Cash Flow: ($15,200,000) $6,050,000 $11,730,000 $13,230,000 $10,206,000 NPV $17,461,989 PI 2.15 IRR 45%
$17,500,000 $1,750,000 $1,750,000 ($2,400,000)
$5,640,000 ($2,400,000) $0 $8,040,000
Should accept project
10-13A
Section I. Calculate the change in EBIT, Taxes, and Depreciation (this becomes an input in the calculation of Operating Cash Flow in Section II). Year 0 1 2 3 4 5 Units Sold 80,000 100,000 120,000 70,000 70,000 Sale Price $250 $250 $250 $250 $250 Sales Revenue Less: Variable Costs Less: Fixed Costs Equals: EBDIT Less: Depreciation Equals: EBIT Taxes (@34%) $20,000,000 10,400,000 $300,000 $9,300,000 $1,400,000 $7,900,000 $2,686,000 $25,000,000 13,000,000 $300,000 $11,700,000 $1,400,000 $10,300,000 $3,502,000 $30,000,000 15,600,000 $300,000 $14,100,000 $1,400,000 $12,700,000 $4,318,000 $17,500,000 9,100,000 $300,000 $8,100,000 $1,400,000 $6,700,000 $2,278,000 $14,000,000 9,100,000 $300,000 $4,600,000 $1,400,000 $3,200,000 $1,088,000
Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV). Operating Cash Flow: EBIT $7,900,000 $10,300,000 $12,700,000 Minus: Taxes $2,686,000 $3,502,000 $4,318,000 Plus: Depreciation $1,400,000 $1,400,000 $1,400,000 Equals: Operating Cash Flow $6,614,000 $8,198,000 $9,782,000
$6,700,000 $2,278,000 $1,400,000 $5,822,000
$3,200,000 $1,088,000 $1,400,000 $3,512,000
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Section III. Calculate the Net Working Capital (this becomes an input in the calculation of Free Cash Flows in Section IV) Change in Net Working Capital: Revenue: $20,000,000 $25,000,000 $30,000,000 $17,500,000 Initial Working Capital Requirement $100,000 Net Working Capital Needs: $2,000,000 $2,500,000 $3,000,000 $1,750,000 Liquidation of Working Capital Change in Working Capital: $100,000 $1,900,000 $500,000 $500,000 ($1,250,000) Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in Capital Spending). Free Cash Flow: Operating Cash Flow $6,614,000 $8,198,000 $9,782,000 $5,822,000 Minus: Change in Net Working $100,000 $1,900,000 $500,000 $500,000 ($1,250,000) Capital Minus: Change in Capital Spending $7,000,000 $0 $0 $0 $0 Free Cash Flow: ($7,100,000) $4,714,000 $7,698,000 $9,282,000 $7,072,000 NPV $15,582,572.99 PI 3.19 IRR 85%
$14,000,000 $1,400,000 $1,400,000 ($1,750,000)
$3,512,000 ($1,750,000) $0 $5,262,000
Should accept project.
10-14A.(a)
NPVA =
$700
(1 + 0.10)1
= =
- $500
$636.30 - $500 $136.30 $6,000
NPVB
= = =
(1 + 0.10)1
$454 $636.30 $500.00 1.2726 $5,454 $5,000 1.0908
- $5,000
$5,454 - $5,000
(b)
PIA
= =
PIB
= =
(c)
$500 0.714 Thus, IRRA $5,000 0.833
= = = = =
$700 [PVIFIRR%,1 yr] PVIFIRR%,1 yr 40% $6,000 [PVIFIRR%,1 yr] [PVIFIRR%,1 yr]
Thus, IRRB= 20% (d) If there is no capital rationing, project B should be accepted because it has a larger net present value. If there is a capital constraint, the problem then focuses on what can be done with the additional $4,500 freed up if project A is chosen. If Dorner Farms can earn more on project A, plus the project financed with the additional $4,500, it than can on project B, then project A and the marginal project should be accepted. Payback A = 3.2 years Payback B = 4.5 years B assumes even cash flow throughout year 5. NPVA = = = =
t =1
10-15A.(a)
(b)
5
$15,625 (1 + 0.10) t
- $50,000
$15,625 (3.791) - $50,000 $59,234 - $50,000 $9,234 267
NPVB
= = = =
$1,000,000 - $50,000 (1 + 0.10) 5 $100,000 (0.621) - $50,000 $62,100 - $50,000 $12,100 $15,625 [PVIFAIRR %,5 yrs] A PVIFAIRR%,5 yrs 17% $100,000 [PVIFIRR %,5 yrs] B
(c)
$50,000 3.2 Thus, IRRA $50,000
= = = =
.50
= Thus, IRRB
PVIFIRR %,5 yrs B = 15%
(d)
The conflicting rankings are caused by the differing reinvestment assumptions made by the NPV and IRR decision criteria. The NPV criterion assumes that cash flows over the life of the project can be reinvested at the required rate of return or cost of capital, while the IRR criterion implicitly assumes that the cash flows over the life of the project can be reinvested at the internal rate of return. Project B should be taken because it has the largest NPV. The NPV criterion is preferred because it makes the most acceptable assumption for the wealth maximizing firm. Payback A Payback B = = = = = = NPVB = = = = 1.589 years 3.019 years
t =1 3
(e)
10-16A. (a)
(b)
NPVA
$12,590 (1 + 0.15) t
- $20,000
$12,590 (2.283) - $20,000 $28,743 - $20,000 $8,743
9
t =1
$6,625 - $20,000 (1 + 0.15) t
$6,625 (4.772) - $20,000 $31,615 - $20,000 $11,615
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(c)
$20,000 Thus, IRRA $20,000 Thus, IRRB
= = = =
$12,590 [PVIFAIRR %,3 yrs] A 40% $6,625 [PVIFAIRR %,9 yrs] B 30%
(d)
These projects are not comparable because future profitable investment proposals are affected by the decision currently being made. If project A is taken, at its termination the firm could replace the machine and receive additional benefits while acceptance of project B would exclude this possibility. Using 3 replacement chains, project A's cash flows would become: Year 0 1 2 3 4 5 6 7 8 9 Cash flow -$20,000 12,590 12,590 - 7,410 12,590 12,590 - 7,410 12,590 12,590 12,590
t
(e)
NPVA
= = = =
t =1
9
$12,590 (1 + 0.15)
- $20,000 -
$20,000 (1 + 0.15)
3
$20,000 (1 + 0.15)6
$12,590(4.772) - $20,000 - $20,000 (0.658) - $20,000 (0.432) $60,079 - $20,000 - $13,160 - $8,640 $18,279
The replacement chain analysis indicated that project A should be selected as the replacement chain associated with it has a larger NPV than project B. Project A's EAA: Step 1: Calculate the project's NPV (from part b): NPVA = $8,743 Step 2: Calculate the EAA: EAAA = NPV / PVIFA15%, 3 yr. = = Project B's EAA: Step 1: Calculate the project's NPV (from part b): $8,743 / 2.283 $3,830
269
NPVB EAAB
=
$11,615
Step 2: Calculate the EAA: = = = 10-17A.(a) Project A's EAA: Step1: Calculate the project's NPV: NPVA = = = = EAAA = = = Project B's EAA: Step 1: Calculate the project's NPV: NPVB = = = = EAAB = = = (b) NPV ,A NPV ,B = = = = $36,000 (PVIFA10%, 3 yr.) - $50,000 $36,000 (2.487) - $50,000 $89,532 - $50,000 $39,532 NPV / PVIFA10%, 3 yr. $39,532 / 2.487 $15,895 $9,729 / .10 $97,290 $15,895 / .10 $158,950 $20,000 (PVIFA10%, 7 yr.) - $50,000 $20,000 (4.868) - $50,000 $97,360 - $50,000 $47,360 NPV / PVIFA10%, 7 yr. $47,360 / 4.868 $9,729 NPV / PVIFA15%, 9 yr. $11,615 / 4.772 $2,434
Project A should be selected because it has a higher EAA.
Step 2: Calculate the EAA:
Step 2: Calculate the EAA:
Project B should be selected because it has a higher EAA.
270
10-18A.(a) Project A B C D E F G Cost $4,000,000 3,000,000 5,000,000 6,000,000 4,000,000 6,000,000 4,000,000 Profitability Index 1.18 1.08 1.33 1.31 1.19 1.20 1.18 Present Value of Future Cash Flows $4,720,000 3,240,000 6,650,000 7,860,000 4,760,000 7,200,000 4,720,000 NPV $ 720,000 240,000 1,650,000 1,860,000 760,000 1,200,000 720,000
COMBINATIONS WITH TOTAL COSTS BELOW $12,000,000 Projects A&B A&C A&D A&E A&F A&G B&C B&D B&E B&F B&G C&D C&E C&F C&G D&E D&F D&G E&F E&G F&G A&B&C A&B&G A&B&E A&E&G B&C&E B&C&G Costs $ 7,000,000 9,000,000 10,000,000 8,000,000 10,000,000 8,000,000 8,000,000 9,000,000 7,000,000 9,000,000 7,000,000 11,000,000 9,000,000 11,000,000 9,000,000 10,000,000 12,000,000 10,000,000 10,000,000 8,000,000 10,000,000 12,000,000 11,000,000 11,000,000 12,000,000 12,000,000 12,000,000 NPV $ 960,000 2,370,000 2,580,000 1,480,000 1,920,000 1,440,000 1,890,000 2,100,000 1,000,000 1,440,000 960,000 3,510,000 2,410,000 2,850,000 2,370,000 2,620,000 3,060,000 2,580,000 1,960,000 1,480,000 1,920,000 2,610,000 1,680,000 1,720,000 2,200,000 2,650,000 2,610,000
Thus projects C&D should be selected under strict capital rationing as they provide the combination of projects with the highest net present value. (b) Because capital rationing forces the rejection of profitable projects it is not an optimal strategy. 271
SOLUTION TO INTEGRATIVE PROBLEMS
1. We focus on free cash flows rather than accounting profits because these are the flows that the firm receives and can reinvest. Only by examining cash flows are we able to correctly analyze the timing of the benefit or cost. Also, we are only interested in these cash flows on an after tax basis as only those flows are available to the shareholder. In addition, it is only the incremental cash flows that interest us, because, looking at the project from the point of the company as a whole, the incremental cash flows are the marginal benefits from the project and, as such, are the increased value to the firm from accepting the project. Although depreciation is not a cash flow item, it does affect the level of the differential cash flows over the project's life because of its effect on taxes. Depreciation is an expense item and, the more depreciation incurred, the larger are expenses. Thus, accounting profits become lower and in turn, so do taxes which are a cash flow item. When evaluating a capital budgeting proposal, sunk costs are ignored. We are interested in only the incremental after-tax cash flows, or free cash flows, to the company as a whole. Regardless of the decision made on the investment at hand, the sunk costs will have already occurred, which means these are not incremental cash flows. Hence, they are irrelevant.
2.
3.
272
Solution to Integrative Problem, parts 4, 5, & 6.
Section I. Calculate the change in EBIT, Taxes, and Depreciation (this become an input in the calculation of Operating Cash Flow in Section II). Year 0 1 2 3 4 Units Sold 70,000 120,000 140,000 80,000 Sale Price $300 $300 $300 $300 Sales Revenue Less: Variable Costs Less: Fixed Costs Equals: EBDIT Less: Depreciation Equals: EBIT Taxes (@34%) $21,000,000 12,600,000 $200,000 $8,200,000 $1,600,000 $6,600,000 $2,244,000 $36,000,000 21,600,000 $200,000 $14,200,000 $1,600,000 $12,600,000 $4,284,000 $42,000,000 25,200,000 $200,000 $16,600,000 $1,600,000 $15,000,000 $5,100,000 $24,000,000 14,400,000 $200,000 $9,400,000 $1,600,000 $7,800,000 $2,652,000 5 60,000 $260 $15,600,000 10,800,000 $200,000 $4,600,000 $1,600,000 $3,000,000 $1,020,000
Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV). Operating Cash Flow: EBIT $6,600,000 $12,600,000 $15,000,000 Minus: Taxes $2,244,000 $4,284,000 $5,100,000 Plus: Depreciation $1,600,000 $1,600,000 $1,600,000 Equals: Operating Cash Flow $5,956,000 $9,916,000 $11,500,000 Section III. Calculate the Net Working Capital (This becomes an input in the calculation of Free Cash Flows in Section IV). Change In Net Working Capital: Revenue: $21,000,000 $36,000,000 $42,000,000 Initial Working Capital Requirement $100,000 Net Working Capital Needs: $2,100,000 $3,600,000 $4,200,000 Liquidation of Working Capital Change in Working Capital: $100,000 $2,000,000 $1,500,000 $600,000
$7,800,000 $2,652,000 $1,600,000 $6,748,000
$3,000,000 $1,020,000 $1,600,000 $3,580,000
272
$24,000,000 $2,400,000 ($1,800,000)
$15,600,000 $1,560,000 $1,560,000 ($2,400,000)
Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in Capital Spending). Free Cash Flow: Operating Cash Flow $5,956,000 $9,916,000 $11,500,000 $6748,000 Minus: Change in Net Working Capital $100,000 $2,000,000 $1,500,000 $600,000 ($1,800,000) Minus: Change in Capital Spending $8,000,000 0 $0 0 0 Free Cash Flow: ($8,100,000) $3,956,000 $8,416,000 $10,900,000 $8,548,000 NPV = IRR =
$3,580,000 ($2,400,000) 0 $5,980,000
$16,731,095.66 77%
7.
Cash flow diagram $3,956,000 $8,416,000 $10,900,000 $8,548,000 $5,980,000
($8,100,000) 8. 9. 10. NPV IRR = $16,731,095.66 = 77%
Yes. This project should be accepted because the NPV 0. and the IRR required rate of return. a. NPVA = = = NPVB = = = b. PIA = = PIB = = c. $195,000 0.8125 $240,000 (1 + 0.10)1 - $195,000
11.
$218,182 - $195,000 $23,182 $1,650,000 (1 + 0.10)1 - $1,200,000
$1,500,000 - $1,200,000 $300,000 $218,182 $195,000 1.1189 $1,500,000 $1,200,000 1.25 = $240,000 [PVIFIRR %,1 yr] A = PVIFIRR %,1 yr A
274
Thus, IRRA = 23% $1,200,000 = $1,650,000 [PVIFIRR %,1 yr] B 0.7273 = [PVIFIRR %,1 yr] B
Thus, IRRB = 37.5% d. If there is no capital rationing, project B should be accepted because it has a larger net present value. If there is a capital constraint, the problem then focuses on what can be done with the additional $1,005,000 freed up if project A is chosen. If Caledonia can earn more on project A, plus the project financed with the additional $1,005,000, than it can on project B, then project A and the marginal project should be accepted. Payback A = 3.125 years Payback B = 4.5 years B assumes even cash flow throughout year 5. NPVA =
5
12.
a.
b.
$32,000 (1 + 0.11) t
t =1
- $100,000
= $32,000 (3.696) - $100,000 = $118,272 - $100,000 = $18,272 NPVB = $200,000 (1 + 0.11)5 - $100,000
= $200,000 (0.593) - $100,000 = $118,600 - $100,000 = $18,600 c. $100,000 3.125 = $32,000 [PVIFAIRR %,5 yrs] A = PVIFAIRR %,5 yrs A = $200,000 [PVIFIRR %,5 yrs] B = PVIFIRR %,5 yrs B
Thus, IRRA = 18.03% $100,000 .50
Thus IRRB is just under 15% (14.87%).
275
d.
The conflicting rankings are caused by the differing reinvestment assumptions made by the NPV and IRR decision criteria. The NPV criterion assume that cash flows over the life of the project can be reinvested at the required rate of return or cost of capital, while the IRR criterion implicitly assumes that the cash flows over the life of the project can be reinvested at the internal rate of return. Project B should be taken because it has the largest NPV. The NPV criterion is preferred because it makes the most acceptable assumption for the wealth maximizing firm. Payback A = 1.5385 years Payback B = 3.0769 years NPVA =
3
e.
13.
a.
b.
$65,000 (1 + 0.14) t
t =1
- $100,000
= $65,000 (2.322) - $100,000 = $150,930 - $100,000 = $50,930 NPVB =
9
$32,500 (1 + 0.14) t
t =1
- $100,000
= $32,500 (4.946) - $100,000 = $160,745 - $100,000 = $60,745 c. $100,000 = $65,000 [PVIFAIRR %,3 yrs] A
Thus, IRRA = over 40% (42.57%) $100,000 = $32,500 [PVIFAIRR %,9 yrs] B
Thus, IRRB = 29% d. These projects are not comparable because future profitable investment proposals are affected by the decision currently being made. If project A is taken, at its termination the firm could replace the machine and receive additional benefits while acceptance of project B would exclude this possibility.
276
e.
Using 3 replacement chains, project A's cash flows would become: Year 0 1 2 3 4 5 6 7 8 9 NPVA =
9
Cash flow -$100,000 65,000 65,000 -35,000 65,000 65,000 - 35,000 65,000 65,000 65,000 $65,000 (1 + 0.14)
t
t =1
- $100,000 -
$100,000 (1 + 0.14)
3
$100,000 (1 + 0.14)6
= $65,000(4.946) - $100,000 - $100,000 (0.675) - $100,000 (0.456) = $321,490 - $100,000 - $67,500 - $45,600 = $108,390 The replacement chain analysis indicated that project A should be selected as the replacement chain associated with it has a larger NPV than project B. Project A's EAA: Step 1: Calculate the project's NPV (from part b): NPVA = $50,930
Step 2: Calculate the EAA: EAAA = NPV / PVIFA14%, 3 yr. = $50,930/ 2.322 = $21,934 Project B's EAA: Step 1: Calculate the project's NPV (from part b): NPVB EAAB = $60,745
Step 2: Calculate the EAA: = NPV / PVIFA14%, 9 yr. = $60,745 / 4.946 = $12,282 Project A should be selected because it has a higher EAA. 277
Solutions to Problem Set B
10-1B. (a) Tax payments associated with the sale for $45,000: Recapture of depreciation = ($45,000-$20,000) (0.34) = $8,500 (b) Tax payments associated with sale for $40,000: Recapture of depreciation = ($40,000-$20,000) (0.34) = $6,800 (c) (d) No taxes, because the machine would have been sold for its book value. Tax savings from sale below book value: Tax savings = ($20,000-$17,000) (0.34) = $1,020 10-2B. New Sales Less: Sales taken from existing product lines 10-3B. Change in net working capital equals the increase in accounts receivable and inventory less the increase in accounts payable = $34,000 + $80,000 - $50,000 = $64,000. The change in taxes will be EBIT X marginal tax rate = $775,000 X .34 = $263,500. A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $775,000 - $263,500 + $200,000 - $64,000 - $0 = $647,500 $100,000,000 - 40,000,000 $60,000,000
278
10-4B. Change in net working capital equals the decrease in accounts receivable, the increase in inventory less the increase in accounts payable = -$10,000 + $15,000 - $36,000 = $31,000. The change in taxes will be EBIT X marginal tax rate = $300,000 X .34 = $102,000. A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $300,000 - $102,000 + $50,000 - ($31,000) - $0 = $279,000 10-5B. (a) Initial Outlay Purchase price Installation Fee Increased Working Capital Inventory Net Initial Outlay (b) Differential annual free cash flows (years 1-9) A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $70,000 - $23,800 + $26,000* - $0 - $0 = $72,200 *Annual Depreciation on the new machine is calculated by taking the purchase price ($250,000) and adding in costs necessary to get the new machine in operating order 279 $ 250,000 10,000 15,000 $275,000 Outflows:
(the installation fee of $10,000) and dividing by the expected life. (c) Terminal Free Cash flow (year 10) Inflows: Differential free cash flow in year 10 Recapture of working capital (inventory) Total terminal cash flow (d) NPV $72,200 15,000 $87,200
= $72,200 (PVIFA15%,9 yr.) + $87,200 (PVIF15%, 10 yr.) - $275,000 = $72,200 (4.772) + $87,200 (.247) - $275,000 = $344,538.40 + $21,538.40 - $275,000 = $91,076.80
Yes, the NPV > 0. 10-6B. (a) Initial Outlay Outflows: Purchase price Installation Fee Training Session Fee Increased Inventory Net Initial Outlay (b) Differential annual free cash flows (years 1-9) Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $400,000 - $136,000 + $105,000* - $0 - $0 = $369,000 *Annual Depreciation on the new machine is calculated by taking the purchase price ($1,000,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $50,000) and dividing by the expected life. A projects free cash flows = $ 1,000,000 50,000 100,000 150,000 $ 1,300,000
280
(c)
Terminal Free Cash flow (year 10) Inflows: Differential flow in year 10 Recapture of working capital (inventory) Total terminal cash flow $369,000 150,000 $519,000
(d)
NPV
= $369,000 (PVIFA12%,9 yr.) + $519,000 (PVIF12%, 10 yr.) - $1,300,000 = $369,000 (5.328) + $519,000 (.322) - $1,300,000 = $1,966,032 + $167,118 - $1,300,000 = $833,150
Yes, the NPV > 0. 10-7B. (a) Initial Outlay Purchase price Installation Fee Training Session Fee Increased Inventory Net Initial Outlay (b) Differential annual free cash flows (years 1-9) A projects free cash flows = Change in earnings before interest and taxes - change in taxes + change in depreciation - change in net working capital - change in capital spending = $25,000 - $8,500 + $10,500* - $0 - $0 = $27,000 *Annual Depreciation on the new machine is calculated by taking the purchase price ($100,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life. $ 100,000 5,000 5,000 25,000 $ 135,000 Outflows:
281
(c)
Terminal Free Cash flow (year 10) Inflows: Differential flow in year 10 Recapture of working capital (inventory) Total terminal cash flow $27,000 25,000 $52,000
(d)
NPV
= $27,000 (PVIFA12%,9 yr.) + $52,000 (PVIF12%, 10 yr.) = $27,000 (5.328) + $52,000 (.322) - $135,000 = $143,856 + $16,744 - $135,000 = $25,600
- $135,000
Yes, the NPV > 0.
282
10-8B
Section I. Calculate the change in EBIT, Taxes, and Depreciation (this becomes an input in the calculation of Operating Cash Flow in Section II). Year 0 1 2 3 4 5 Units Sold 1,000,000 1,800,000 1,800,000 1,200,000 700,000 Sale Price $800 $800 $800 $800 $600 Sales Revenue Less: Variable Costs Less: Fixed Costs Equals: EBDIT Less: Depreciation Equals: EBIT Taxes (@34%) $800,000,000 400,000,000 $10,000,000 $390,000,000 $40,000,000 $350,000,000 $119,000,000 $1,440,000,000 720,000,000 $10,000,000 $710,000,000 $40,000,000 $670,000,000 $227,800,000 $1,440,000,000 720,000,000 $10,000,000 $710,000,000 $40,000,000 $670,000,000 $227,800,000 $960,000,000 480,000,000 $10,000,000 $470,000,000 $40,000,000 $430,000,000 $146,200,000 $420,000,000 280,000,000 $10,000,000 $130,000,000 $40,000,000 $90,000,000 $30,600,000
Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV). Operating Cash Flow: EBIT $350,000,000 $670,000,000 $670,000,000 Minus: Taxes $119,000,000 $227,800,000 $227,800,000 Plus: Depreciation $40,000,000 $40,000,000 $40,000,000 Equals: Operating Cash Flow $271,000,000 $482,200,000 $482,200,000
$430,000,000 $146,200,000 $40,000,000 $323,800,000
$90,000,000 $30,600,000 $40,000,000 $99,400,000
282
Section III. Calculate the Net Working Capital (this becomes an input in the calculation of Free Cash Flows in Section IV) Change in Net Working Capital: Revenue: $800,000,000 $1,440,000,000 $1,440,000,000 $960,000,000 Initial Working Capital Requirement $2,000,000 Net Working Capital Needs: $80,000,000 $144,000,000 $144,000,000 $96,000,000 Liquidation of Working Capital Change in Working Capital: $2,000,000 $78,000,000 $64,000,000 $0 ($48,000,000) Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in Capital Spending). Free Cash Flow: Operating Cash Flow $271,000,000 $482,200,000 $482,200,000 $323,800,000 Minus: Change in Net Working Capital $2,000,000 $78,000,000 $64,000,000 $0 ($48,000,000) Minus: Change in Capital Spending $200,000,000 $0 $0 $0 $0 Free Cash Flow: ($202,000,000) $193,000,000 $418,200,000 $482,200,000 $371,800,000 NPV $908,825,886.69 PI 5.5 IRR 140%
$420,000,000 $42,000,000 $42,000,000 ($96,000,000)
$99,400,000 ($96,000,000) $0 $195,400,000
Accept project
10-9B
Section I. Calculate the change in EBIT, Taxes, and Depreciation (this becomes an input in the calculation of Operating Cash Flow in Section II). Year 0 1 2 3 4 Units Sold 70,000 100,000 140,000 70,000 Sale Price $280 $280 $280 $280 Sales Revenue Less: Variable Costs Less: Fixed Costs Equals: EBDIT Less: Depreciation Equals: EBIT Taxes (@34%) $19,600,000 9,800,000 $300,000 $9,500,000 $2,000,000 $7,500,000 $2,550,000 $28,000,000 14,000,000 $300,000 $13,700,000 $2,000,000 $111,700,000 $3,978,600 $39,200,000 19,600,000 $300,000 $19,300,000 $2,000,000 $17,300,000 $5,882,000 $19,600,000 9,800,000 $300,000 $9,500,000 $2,000,000 $7,500,000 $2,550,000 5 60,000 $180
$10,800,000 8,400,000 $300,000 $2,100,000 $2,000,000 $100,000 $34,000
Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV). Operating Cash Flow: EBIT $7,500,000 $11,700,000 $17,300,000 Minus: Taxes $2,550,600 $3,978,600 $5,882,000 Plus: Depreciation $2,000,000 $2,000,000 $2,000,000 Equals: Operating Cash Flow $6,950,400 $9,722,400 $13,418,000
$7,500,000 $3,107,600 $2,000,000 $6,950,000
$100,000 $34,000 $2,000,000 $2,066,000
283
Section III. Calculate the Net Working Capital (this becomes an input in the calculation of Free Cash Flows in Section IV) Change in Net Working Capital: Revenue: $19,600,000 $28,000,000 $39,200,000 $19,600,000 Initial Working Capital Requirement $100,000 Net Working Capital Needs: $1,960,000 $2,800,000 $3,920,000 $1,960,000 Liquidation of Working Capital Change in Working Capital: $100,000 $1,860,000 $840,800 $1,120,000 ($1,960,000) Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in Capital Spending). Free Cash Flow: Operating Cash Flow $6,950,000 $9,722,400 $13,418,000 $6,950,400 Minus: Change in Net Working Capital $100,000 $1,860,000 $840,000 $1,120,000 ($1,960,000) Minus: Change in Capital Spending $10,000,000 $0 $0 $0 $0 Free Cash Flow: ($10,100,000) $5,090,400 $8,882,400 $12,298,400 $8,910,400 NPV $16,232,618 PI 2.6 IRR 68.6%
$10,800,000 $1,080,000 $1,080,000 ($1,960,000)
$2,066,000 ($1,960,000) $0 $4,026,000
Accept project
285
10-10B. (a) NPVA = $800 (1 + 0.10)1 - $650
= $727.20 - $650 = $77.20 NPVB = $5,500 (1 + 0.10)1 - $4,000
= $5,000 - $4,000 = $1,000 (b) PIA = $727.20 $650.00
= 1.1188 PIB = $5,000 $4,000
= 1.25 (c) $650 0.8125 Thus, IRRA $4,000 0.7273 Thus, IRRB (d) = $800 [PVIFIRR %,1 yr] A = PVIFIRR %,1 yr A
= 23% = $5,500 [PVIFIRR %,1 yr] B = [PVIFIRR %,1 yr] B = 37.5%
If there is no capital rationing, project B should be accepted because it has a larger net present value. If there is a capital constraint, the problem then focuses on what can be done with the additional $3,350 freed up if project A is chosen. If Unk's Farms can earn more on project A, plus the project financed with the additional $3,350, than it can on project B, then project A and the marginal project should be accepted.
286
10-11B. (a)
Payback A = 3.125 years Payback B = 4.5 years B assumes even cash flow throughout year 5.
(b)
NPVA
=
t =1
5
$16,000 (1 + 0.11) t
- $50,000
= $16,000 (3.696) - $50,000 = $59,136 - $50,000 = $9,136 NPVB = $100,000 (1 + 0.11)5 - $50,000
= $100,000 (0.593) - $50,000 = $59,300 - $50,000 = $9,300 (c) $50,000 3.125 = $16,000 [PVIFAIRR %,5 yrs] A = PVIFAIRR %,5 yrs A
Thus, IRRA = 18% $50,000 .50 = $100,000 [PVIFIRR %,5 yrs] B = PVIFIRR %,5 yrs B
Thus IRRB is just under 15%. (d) The conflicting rankings are caused by the differing reinvestment assumptions made by the NPV and IRR decision criteria. The NPV criterion assume that cash flows over the life of the project can be reinvested at the required rate of return or cost of capital, while the IRR criterion implicitly assumes that the cash flows over the life of the project can be reinvested at the internal rate of return. Project B should be taken because it has the largest NPV. The NPV criterion is preferred because it makes the most acceptable assumption for the wealth maximizing firm.
(e)
287
10-12B. (a) Payback A = 1.5385 years Payback B = 3.0769 years NPVA =
3
(b)
$13,000 (1 + 0.14) t
t =1
- $20,000
= $13,000 (2.322) - $20,000 = $30,186 - $20,000 = $10,186 NPVB =
9
$6,500 (1 + 0.14) t
t =1
- $20,000
= $6,500 (4.946) - $20,000 = $32,149 - $20,000 = $12,149 (c) $20,000 = $13,000 [PVIFAIRR %,3 yrs] A
Thus, IRRA = over 40% (42.57%) $20,000 = $6,500 [PVIFAIRR %,9 yrs] B
Thus, IRRB = 29.3% (d) These projects are not comparable because future profitable investment proposals are affected by the decision currently being made. If project A is taken, at its termination the firm could replace the machine and receive additional benefits while acceptance of project B would exclude this possibility. Using 3 replacement chains, project A's cash flows would become: Year 0 1 2 3 4 5 6 7 8 9 Cash flow -$20,000 13,000 13,000 - 7,000 13,000 13,000 - 7,000 13,000 13,000 13,000
(e)
288
NPVA
=
t =1
9
$13,000 (1 + 0.14)
t
- $20,000 -
$20,000 (1 + 0.14)
3
$20,000 (1 + 0.14)6
= $13,000(4.946) - $20,000 - $20,000 (0.675) - $20,000 (0.456) = $64,298 - $20,000 - $13,500 - $9,120 = $21,678 The replacement chain analysis indicated that project A should be selected as the replacement chain associated with it has a larger NPV than project B. Project A's EAA: Step 1: Calculate the project's NPV (from part b): NPVA Step 2: = $10,186
Calculate the EAA: EAAA = NPV / PVIFA14%, 3 yr. = $10,186 / 2.322 = $4,387
Project B's EAA: Step 1: Calculate the project's NPV (from part b): NPVB = $12,149
Step 2: Calculate the EAA: EAAB = NPV / PVIFA14%, 9 yr. = $12,149 / 4.946 = $2,456 Project A should be selected because it has a higher EAA.
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10-13B. (a) Project A's EAA: Step 1: Calculate the project's NPV: NPVA = $20,000 (PVIFA10%, 7 yr.) - $40,000 = $20,000 (4.868) - $40,000 = $97,360 - $40,000 = $57,360 Step 2: Calculate the EAA: EAAA = NPV / PVIFA10%, 7 yr. = $57,360 / 4.868 = $11,783 Project B's EAA: Step 1: Calculate the project's NPV: NPVB = $25,000 (PVIFA10%, 5 yr.) - $40,000 = $25,000 (3.791) - $40,000 = $94,775 - $40,000 = $54,775 Step 2: Calculate the EAA: EAAB = NPV / PVIFA10%, 5 yr. = $54,775 / 3.791 = $14,449 Project B should be selected because it has a higher EAA. (b) NPV ,A = $11,783 / .10 = $117,830 NPV ,B = $14,449 / .10 = $144,490
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10-14B. (a) Project A B C D E F G Cost $4,000,000 3,000,000 5,000,000 6,000,000 4,000,000 6,000,000 4,000,000 Profitability Index 1.18 1.08 1.33 1.31 1.19 1.20 1.18 Present Value of Future Cash Flows $4,720,000 3,240,000 6,650,000 7,860,000 4,760,000 7,200,000 4,720,000 NPV $ 720,000 240,000 1,650,000 1,860,000 760,000 1,200,000 720,000
COMBINATIONS WITH TOTAL COSTS BELOW $12,000,000 Projects A&B A&C A&D A&E A&F A&G B&C B&D B&E B&F B&G C&D C&E C&F C&G D&E D&F D&G E&F E&G F&G A&B&C A&B&E A&B&G A&E&G B&C&E B&C&G Costs $ 7,000,000 9,000,000 10,000,000 8,000,000 10,000,000 8,000,000 8,000,000 9,000,000 7,000,000 9,000,000 7,000,000 11,000,000 9,000,000 11,000,000 9,000,000 10,000,000 12,000,000 10,000,000 10,000,000 8,000,000 10,000,000 12,000,000 11,000,000 11,000,000 12,000,000 12,000,000 12,000,000 NPV $ 960,000 2,370,000 2,580,000 1,480,000 1,920,000 1,440,000 1,890,000 2,100,000 1,000,000 1,440,000 960,000 3,510,000 2,410,000 2,850,000 2,370,000 2,620,000 3,060,000 2,580,000 1,960,000 1,480,000 1,920,000 2,610,000 1,720,000 1,680,000 2,200,000 2,650,000 2,610,000
Thus projects C&D should be selected under strict capital rationing as they provide the combination of projects with the highest net present value. (b) Because capital rationing forces the rejection of profitable projects it is not an optimal strategy. 291