CHAPTER 25 CAPITAL INVESTMENT ANALYSIS CLASS DISCUSSION QUESTIONS The principal objections to the use of the average rate of return method are its failing to consider the expected cash flows from the proposals and the timing of these flows The principal limitations of the cash payback method are its failure to consider cash flows occurring after the payback period and its failure to use present value concepts The average rate of return is not based on cash flows, but on operating income Thus, for example, the average rate of return will include the impact of depreciation, but the internal rate of return will not In addition, the internal rate of return approach will use time value of money concepts, while the average rate of return does not The cash payback period ignores the cash flows that occur after the cash payback period, while the net present value method includes all cash flows in the analysis The cash payback period also ignores the time value of money, which is also included in the net present value method A one-year payback will not equal a 100% average rate of return because the payback period is based on cash flows, while the average rate of return is based on income The depreciation on the project will prevent the two methods from reconciling The cash payback period ignores cash flows occurring after the payback period, which will often include large salvage values The majority of the cash flows of a new motion picture are earned within two years of release Thus, the time value of money aspect of the cash flows is less significant for motion pictures than for projects with time extended cash flows This would favor the use of a cash payback period for evaluating the cash flows of the project The $9,750 net present value indicates that the proposal is desirable because the proposal is expected to recover the investment and provide more than the minimum rate of return The net present values indicate that both projects are desirable, but not necessarily equal in desirability The present value index can be used to compare the two projects For example, assume one project required an investment of $10,000 and the other an investment of $100,000 The present value indexes would be calculated as 0.5 and 0.05, respectively, for the two projects That is, a $5,000 net present value on a $10,000 investment would be more desirable than the same net present value on a $100,000 investment 10 The computations for the net present value method are more complex than those for the methods that ignore present value Also, the method assumes that the cash received from the proposal during its useful life will be reinvested at the rate of return used to compute the present value of the proposal This assumption may not always be reasonable 11 The computations for the internal rate of return method are more complex than those for the methods that ignore present value Also, the method assumes that the cash received from the proposal during its useful life will be reinvested at the internal rate of return 12 Allowable deductions for depreciation 13 The life of the proposal with the longer life can be adjusted to a time period that is equal to the life of the proposal with the shorter life 14 The major advantages of leasing are that it avoids the need to use funds to purchase assets and reduces some of the risk of loss if the asset becomes obsolete There may also be some income tax advantages to leasing 15 The speed-up of delivery of products, higher production quality, and greater manufacturing flexibility are examples of qualitative factors that should be considered 16 Monsanto indicated that it recognized that the market was demanding higher product quality that could be achieved only with a 95 large investment in process control technology and automated laboratory equipment The process control technology could reduce the variation in the size of fibers More uniform fibers, in turn, improve the efficiency of the processes used by carpet manufacturers The local area network (LAN) was not a stand-alone investment, but it linked the process control information to operators and management via computer linkages Thus, the LAN was an integral part of the investment portfolio Monsanto indicated the following considerations in making its investment: a After-tax cash flows b Labor savings c Accepting projects that not have a quantifiable payback, such as enablers that allow projects with more visible benefits to be put into place (such as LAN enabling the process control technology to communicate information) d Allowing estimates of increased sales due to higher quality e Considering inventory reductions in the cost of savings f Avoiding reactive investment but considering the organizational vision and long-term strategic direction in the investment decision 96 EXERCISES Ex 25–1 Testing Equipment Centrifuge Estimated average annual income: $10,500 ÷ $12,250 ÷ $2,625 Average investment: ($42,000 + 0) ÷ ($56,000 + 0) ÷ $21,000 Average rate of return: $2,625 ÷ $21,000 $2,450 ÷ $28,000 12.5% $2,450 $28,000 8.75% Ex 25–2 Average Average annual income = rate Average investment of return = = = Average savings* − Annual depreciation − Additional operating costs ( Beginning cost + Residual value) ÷ $26,000 ( $88,000 ÷ ) $8,250 ( $94,000 + $6,000 ) ÷ $6,750 $50,000 = 13.5% * The effect of the savings in wages expense is an increase in income Ex 25–3 Average Average annual income = rate Average investment of return = Annual revenues − Annual product costs * ( Beginning cost + Residual value) ữ2 = ($325 ì 4,500 units) ($295 ì 4,500 units) ($870,000 + $30,000) ữ = $135,000 $450,000 = 30% * The depreciation of the equipment is included in the factory overhead cost per unit Ex 25–4 Year Initial investment Operating cash flows: Annual revenues (8,000 units × $36) Selling expenses (5% × $288,000) Cost to manufacture (8,000 units × $19.55)* Net operating cash flows Total for year Total for years 2–14 (operating cash flow) Residual value Total for last year Years 2–14 Last Year $ 288,000 (14,400) $ 288,000 (14,400) $ 288,000 (14,400) (156,400) $ 117,200 $ (120,800) (156,400) $ 117,200 (156,400) $ 117,200 $ (238,000) $ 117,200 10,000 $ 127,200 *The fixed overhead relates to the depreciation on the equipment [($184,000 – $10,000) ÷ 15 years ÷ 8,000 units = $1.45] Depreciation is not a cash flow and should not be considered in the analysis Ex 25–5 Proposal 1: $250,000 ÷ $50,000 = 5-year cash payback period Proposal 2: 4-year cash payback period, as indicated below Net Cash Flow Year $80,000 Year 70,000 Year 50,000 Year 50,000 $ 150,000 200,000 250,000 Cumulative Net Cash Flows 80,000 Ex 25–6 a The Liquid Soap product line is recommended, based on its shorter cash payback period The cash payback period for both products can be determined using the following schedule: Initial investment: $550,000 Liquid Soap Net Cash Cumulative Net Flow Cash Flows Year Year Year Year Year $150,000 140,000 130,000 130,000 $150,000 290,000 420,000 550,000 Net Cash Flow Cosmetics Cumulative Net Cash Flows $110,000 110,000 110,000 110,000 110,000 $110,000 220,000 330,000 440,000 550,000 Liquid Soap has a 4-year cash payback, and Cosmetics has a 5-year cash payback period b The cash payback periods are different between the two product lines because Liquid Soap earns cash faster than does Cosmetics Even though both products earn the same total net cash flow over the 8-year planning horizon, Liquid Soap returns cash faster in the earlier years The cash payback method emphasizes the initial years’ net cash flows in determining the cash payback period Thus, the project with the greatest net cash flows in the early years of the project life will be favored over the one with less net cash flows in the initial years Ex 25–7 a Year Present Value of $1 at 12% 0.893 0.797 0.712 0.636 Total Amount to be invested Net present value Net Cash Flow Present Value of Net Cash Flow $150,000 120,000 75,000 75,000 $420,000 $ 133,950 95,640 53,400 47,700 $ 330,690 340,000 $ (9,310) b No The ($9,310) net present value indicates that the return on the proposal is less than the minimum desired rate of return of 12% Ex 25–8 a (All amounts are in $millions.) 2006 cash flow: Gross ticket sales Production cost Marketing cost Net cash flow from theatrical release $125 $100 40 $ (15) 2007 home video sales: Total sales Net cash margin Net cash flow $ 90 × 30% $ 27 2008 pay TV 2009 syndication $ 20 Net present value: Year Present Value of $1 at 20% 2006 1.000 2007 0.833 2008 0.694 2009 0.579 Net present value Net Cash Flow $(15) 27 20 Present Value of Net Cash Flow $(15) 22 14 $ 24 b Even though the film lost money at the box office, the project was financially successful as a whole due to additional cash flows from home video sales, pay TV, and network TV syndication Ex 25–9 a Cash inflows: Hours of operation Revenue per hour Revenue per year Cash outflows: Hours of operation Fuel cost per hour Labor cost per hour Total fuel and labor costs per hour Fuel and labor costs per year 1,500 × $98.00 $ 147,000 1,500 $28.00 22.00 × $50.00 Maintenance costs per year Annual net cash flow b Annual net cash flow (at the end of each of five years) Present value of annuity of $1 at 10% for five periods Present value of annual net cash flows Less: Amount to be invested Net present value (75,000) (12,000) $ 60,000 $ 60,000 × 3.791 $ 227,460 235,000 $ (7,540 c No Crowe should not accept the investment because the bulldozer cost exceeds the present value of the cash flows at the minimum desired rate of return of 10% The bulldozer might be an attractive investment if Crowe could get a price reduction, increase the hourly revenue rate, increase the annual hours of use, or extend the useful life of the bulldozer Ex 25–10 Apartment Complex Year Present Value of $1 at 15% 0.870 0.756 0.658 0.572 0.572 Total Amount to be invested Net present value Net Cash Flow $ 220,000 200,000 200,000 180,000 420,000 $ 1,220,000 Present Value of Net Cash Flow $ 191,400 151,200 131,600 102,960 240,240 $ 817,400 (775,000) $ 42,400 Office Building Year Present Value of $1 at 15% 0.870 0.756 0.658 0.572 Total Amount to be invested Net present value Net Cash Flow $ 300,000 300,000 275,000 275,000 $ 1,150,000 Present Value of Net Cash Flow $ 261,000 226,800 180,950 157,300 $ 826,050 (775,000) $ 51,050 The net present value of both projects are positive; thus, both proposals are acceptable However, the net present value of the office building exceeds that of the apartment complex Thus, the office building should be preferred if there is enough investment money for only one of the projects Note to Instructors: Since the investment amount is the same, the net present value can be compared to determine preference That is, the present value index will show the same preference ordering Ex 25–11 Initial investment to develop a restaurant unit Less: Initial franchise fee Net investment Years 1–10 Royalty: Average unit revenue Royalty rate Royalty cash flow Annual lease and other cash flows Total annual cash flows Present value of a $1 annuity for 10 years at 10% (Exhibit 2) Present value of annual cash flows $ 1,993,000 300,000 $ 1,693,000 $1,500,000 × 4.5% $ $ × 6.145 $ 1,490,163 Lease purchase option Present value of $1 for 10 years at 10% (Exhibit 1) Present value of lease purchase option $ × $ Net present value per restaurant unit $ 67,500 175,000 242,500 600,000 0.386 231,600 28,7631 –$1,693,000 + $1,490,163 + $231,600 Thus, the restaurant exceeds IHOP’s minimum rate of return objective Note to Instructors: This problem is developed from the perspective of IHOP, the franchiser The franchisee’s present value calculation would be determined from the present value of the net annual cash inflows from operating the restaurant (including the cost of royalties and lease payments) as compared to the cash outflows for the initial franchise fee and lease purchase option Prob 25–3B Route Expansion Year Present Value of $1 at 15% Net Cash Flow 0.870 $ 420,000 0.756 380,000 0.658 350,000 Total $1,150,000 Amount to be invested Net present value Present Value of Net Cash Flow $365,400 287,280 230,300 $882,980 840,000 $ 42,980 Acquire Railcars Year Present Value of $1 at 15% Net Cash Flow 0.870 $225,000 0.756 200,000 0.658 180,000 Total $605,000 Amount to be invested Net present value Present Value of Net Cash Flow $195,750 151,200 118,440 $465,390 490,000 $ (24,610) New Maintenance Yard Year Present Value of $1 at 15% Net Cash Flow 0.870 $210,000 0.756 200,000 0.658 180,000 Total $590,000 Amount to be invested Net present value Present Value of Net Cash Flow $182,700 151,200 118,440 $452,340 420,000 $ 32,340 Prob 25–3B Concluded Present value index = Total present value of net cash flow Amount to be invested Present value index of route expansion: Present value index of railcars: $882,980 = 1.05* $840,000 $465,390 = 0.95* $490,000 Present value index of maintenance yard: $452,340 = 1.08* $420,000 *Rounded The maintenance yard has the largest present value index Although route expansion has the largest net present value, it returns less present value per dollar invested than does the maintenance yard, as revealed by the present value indexes (1.08 to 1.05) (The present value index for the railcars is less than 1, indicating that it does not meet the minimum rate of return standard.) Prob 25–4B a Generating Unit: Annual net cash flow (at the end of each of four years) Present value of an annuity of $1 at 10% for years (Exhibit 2) Present value of annual net cash flows Less amount to be invested Net present value $ 600,000 × 3.17 $1,902,000 1,822,200 $ 79,800 Distribution Network Expansion: Annual net cash flow (at the end of each of four years) Present value of an annuity of $1 at 10% for years (Exhibit 2) Present value of annual net cash flows Less amount to be invested Net present value $160,000 × 3.17 $507,200 456,800 $ 50,400 b Present value index = Total present value of net cash flow Amount to be invested Present value index of the generating unit: $1,902,000 = 1.04* $1,822,200 Present value index of the distribution network expansion: $507,200 = 1.11* $456,800 *Rounded a Present value factor for an annuity of $1 = Generating unit: Amount to be invested Annual net cash flow $1,822,200 = 3.037 $600,000 Distribution network expansion: $456,800 = 2.855 $160,000 b Internal rate of return: (determined from Exhibit in text) Generating unit: 12% Distribution network expansion: 15% Prob 25–4B Concluded By using the internal rate of return method, all projects are automatically placed on a common basis For example, it was necessary to use the present value index to determine that the distribution network expansion had a greater present value per dollar of investment (greater rate of return) By using the internal rate of return method, it can be easily seen that the distribution network expansion’s rate of return of 15% is greater than the generating unit’s rate of 12% Prob 25–5B Net present value analysis: Project I: Annual net cash flow (at the end of each of six years) Present value of an annuity of $1 at 15% for years (Exhibit 2) Present value of annual net cash flows Less amount to be invested Net present value $ 65,000 × 3.785 $246,025 200,000 $ 46,025 Project II: Annual net cash flow (at the end of each of four years) Present value of an annuity of $1 at 15% for years (Exhibit 2) Present value of annual net cash flows Less amount to be invested Net present value $ 97,500 × 2.855 $278,362.50 200,000.00 $ 78,362.50 Net present value analysis: Year Present Value of $1 at 15% Net Cash Flow Project I Project II 0.870 $ 65,000 $ 97,500 0.756 65,000 97,500 0.658 65,000 97,500 0.572 65,000 97,500 Residual value 0.572 140,000 Total $400,000 $390,000 Amount to be invested Net present value Present Value of Net Cash Flow Project I Project II $ 56,550 49,140 42,770 37,180 80,080 $265,720 200,000 $ 65,720 $ 84,825 73,710 64,155 55,770 $278,460 200,000 $ 78,460* * This amount differs from the net present value calculation in (1) due to rounding error To: Investment Committee Both Projects I and II have a positive net present value This means that both projects meet our minimum expected return of 15% and would be acceptable investments However, if funds are limited and only one of the two projects can be funded, then the two projects must be compared over equal lives Thus, the residual value of Project I at the end of period is used to equalize the two lives The net present value of the two projects over equal lives indicates that Project II has a higher net present value and would be a superior investment Prob 25–6B Proposal A: 4-year cash payback period, as follows: Year Net Cash Flow Cumulative Net Cash Flows $140,000 140,000 140,000 80,000 $140,000 280,000 420,000 500,000 Proposal B: 2-year, 9-month cash payback period, as follows: Year months* Net Cash Flow Cumulative Net Cash Flows $100,000 80,000 45,000 $100,000 180,000 225,000 *The cash flow required for investment payback in Year is $45,000, which is three-fourths ($45,000 ÷ $60,000) of Year 3’s cash flow Thus, months (three-fourths of 12 months) are needed to accumulate an additional $45,000 Proposal C: 3-year cash payback period, as follows: Year Net Cash Flow Cumulative Net Cash Flows $220,000 200,000 180,000 $220,000 420,000 600,000 Proposal D: 3-year, 4-month cash payback period, as follows: Year months* Net Cash Flow Cumulative Net Cash Flows $125,000 95,000 60,000 20,000 $125,000 220,000 280,000 300,000 *The cash flow required for investment payback in Year is $20,000, which is one-third ($20,000 ÷ $60,000) of Year 4’s cash flow Thus, months (one-third of 12 months) are needed to accumulate an additional $20,000 Prob 25–6B Continued Proposal A: 6.4% average rate of return, determined as follows: $16,000 $80,000 ÷ = ( $500,000 + $0) ÷ $250,000 = 6.4% Proposal B: 24% average rate of return, determined as follows: $27,000 $135,000 ÷ = ( $225,000 + $0) ÷ $112,500 = 24% Proposal C: 22% average rate of return, determined as follows: $66,000 $330,000 ÷ = ( $600,000 + $0) ÷ $300,000 = 22% Proposal D: 13.3% average rate of return, determined as follows: $20,000 $100,000 ÷ = = 13.3% $150,000 ($300,000 + $0) ÷ Prob 25–6B Continued Of the four proposed investments, only Proposals B and C meet the company’s requirements, as the following table indicates: Proposal A B C D Cash Payback Period Average Rate of Return yrs yrs., mos yrs yrs., mos Accept for Further Analysis 6.4% 24.0 22.0 13.3 Reject X X X X* *Proposal D is rejected because it fails to meet the maximum payback period requirement, even though it meets the minimum accounting rate of return requirement Proposal B: Year Present Value of $1 at 10% Net Cash Flow Present Value of Net Cash Flow 0.909 $100,000 0.826 80,000 0.751 60,000 0.683 60,000 0.621 60,000 Total $360,000 Amount to be invested Net present value $ 90,900 66,080 45,060 40,980 37,260 $280,280 225,000 $ 55,280 Proposal C: Year Present Value of $1 at 10% Net Cash Flow Present Value of Net Cash Flow 0.909 $220,000 0.826 200,000 0.751 180,000 0.683 180,000 0.621 150,000 Total $930,000 Amount to be invested Net present value $199,980 165,200 135,180 122,940 93,150 $716,450 600,000 $116,450 Prob 25–6B Concluded Present value index = Total present value of net cash flow Amount to be invested Present value index of Proposal B: $280,280 = 1.25* $225,000 Present value index of Proposal C: $716,450 = 1.19* $600,000 *Rounded Based upon the net present value, the proposals should be ranked as follows: Proposal C: $116,450 Proposal B: $55,280 Based upon the present value index (the amount of present value per dollar invested), the proposals should be ranked as follows: Proposal B: 1.25 Proposal C: 1.19 The present value indexes indicate that although Proposal C has the larger net present value, it is not as attractive as Proposal B in terms of the amount of present value per dollar invested Proposal C requires the larger investment Thus, management should use investment resources for Proposal B before investing in Proposal C SPECIAL ACTIVITIES Activity 25–1 The plant manager wants a project to become accepted and places pressure on the analyst to come up with the “right numbers.” I M is right when he states that the net present value analysis has many assumptions and room for interpretation Many use this room for interpretation to work the numbers until they satisfy the minimum return (hurdle) rate In fact, some analysts state that they start with the hurdle rate and work back into the numbers Clearly, this is not what should be expected of Kelly Kelly made an honest effort to discuss the assumptions Kelly’s last statement was an open attempt to begin a conversation around assumptions This is legitimate Notice that I M jumped on that opening and dictated a course of action Instead of discussing assumptions, I M stated what the assumptions are to be and how they are to be reflected in the analysis This is no more than “cooking” the analysis Kelly needs to respond strongly to this attempt by I M to circumvent the process by countering his argument For example, Kelly might point out that it is by no means clear that more storage space translates into more sales In fact, it is probably just the opposite More storage space means that more product waits a long time before being shipped to the customer This means that the customer is guaranteed to receive dated product that may be inferior to product that has been recently produced More warehouse space is counter to a just-in-time orientation Kelly is really trying to prevent the plant manager from going down the wrong path I M needs to work on his systems so that he doesn’t need the warehouse space This very difficult issue revolves around the nature of ethical dilemmas Kelly has brief tenure with the organization She has very little organizational clout and could easily find her career short-circuited by crossing I M It might be tempting for Kelly to slide on this one—after all, who would know? If the project is eventually a failure, it’s unlikely that the decision would come back to haunt Kelly Much time will have passed, and Kelly will likely be in another job in the company The decision to confront I M has immediate repercussions This is the heart of real world ethical dilemmas The dilemma occurs when the ethical decision has grave short-term consequences (I M short-circuits the career) and few seemingly long-term rewards (no one sees the ethical decision), while the unethical decision looks appealing in the short term (I M is my friend) and potentially safe in the long term (who’s going to find out?) The ethical management accountant will recognize these pressures and make the short-term decisions in order to build a strong reputation that can be a very powerful asset later in one’s career The key is to recognize that trading off short-term gain for one’s long-term reputation can be very harmful Thus, enlightened self-interest indicates that the ethical course of action to rebuff I M is rational and correct Activity 25–2 Annual salary Present value of $1 annuity for 10 years at 10% Present value of undergraduate option as of the end of undergraduate degree (beginning of graduate degree) $ 40,000 × 6.145 Annual tuition at the beginning of the graduate year $ (12,000) $ 245,800 Annual salary Present value of $1 annuity for years at 10% Present value salary to end of graduate year Present value of $1 for year at 10% Present value of salary at the beginning of graduate year $ 50,000 × 5.759 $ 287,950 × 0.909 $ 261,747 Present value of graduate option at beginning of graduate year (salary less tuition) $ 249,747 Note: The present values of and must both be determined as of the beginning of the graduate year in order to be compared Thus, the present value of the salary at the end of graduate school must be brought back one period to the beginning of the graduate year, since this salary stream is delayed by one year of schooling The timeline below shows the calculation: ($12,000) 50K $261,747 $249,747 10 50K 50K 50K 50K 50K 50K 50K 50K ($50,000 × 5.759) × 0.909 Present value of graduate option Present value of undergraduate option Net benefit of graduate option $ 249,747 245,800 $ 3,947 Note to Instructors: This solution accounts for the opportunity cost of graduate school in terms of lost earnings during the graduate year To maintain simplicity, the solution does not account for likely growth in earnings over time Activity 25–3 Payback period: $1,250,000 = years $250,000 Net present value: Present value factor for an annuity of $1, 10 periods at 10%: 6.145 Net present value = (6.145 × $250,000) – $1,250,000 = $286,250 Some critical elements that are missing from this analysis are: a The manager is viewing the acquisition of robots as a labor-saving device This is probably a limited way to view the investment Instead, the robots should allow the company to produce the product with higher quality and higher flexibility This should translate into greater sales volume, better pricing, and lower inventories All of these could be brought into the analysis b The cost of the robots does not stop with the initial purchase price and installation costs The robots will require the company to hire engineers and support personnel to keep the machines running, to program the software, and to debug new programs The operators will require new training Thus, extensive training costs will likely be incurred It would not be surprising to see a large portion of the direct labor savings lost by hiring expensive indirect labor support for the technology c There will likely be a start-up or learning curve with this new technology that will cause the benefits to be delayed d The analysis fails to account for taxes Activity 25–4 In all three companies, the executives indicate that financial investment analysis plays a minor role in the selection of projects The reason is that all three companies deal with products that have highly uncertain future cash flows Thus, any attempt at a financial investment analysis could be highly suspect Instead, these managers rely on strategic considerations These considerations include responding to competitors, developing new markets and products for customers, and improving quality The executives indicate that business judgment is more important for these strategic, longer-term decisions than is financial investment analysis This suggests that financial investment analysis is better suited for investments that have more predictable cash flows with possible short duration Activity 25–5 Average rate of return = Estimated average annual income Average investment Project A: $180,000 ÷ ( $360,000 + $0) ÷ = 25% Project B: $187,200 ÷ = 26% ($360,000 + $0) ÷ 2 The timing of net cash flows to be received from a capital investment proposal is important because cash on hand can be invested to earn more cash Therefore, the sooner the cash is received from a project, the better One means of evaluating the effect of the timing of net cash flows on projects is to establish a minimum rate of return and then use the net present value method to determine whether or not the present value from the project exceeds the amount to be invested If the present value equals or exceeds the amount of the investment, the project is desirable For Projects A and B, the net present value method of analysis, based on a rate of return of 12%, is illustrated below Year Present Value of $1 at 12% Net Cash Flow Project A Project B Present Value of Net Cash Flow Project A Project B 0.893 $ 155,000 $ 115,000 $ 138,415 0.797 140,000 130,000 111,580 0.712 130,000 148,000 92,560 0.636 115,000 154,200 73,140 Total $ 540,000 $ 547,200 $ 415,695 Amount to be invested 360,000 Net present value $ 55,695 $ 102,695 103,610 105,376 98,071 $ 409,752 360,000 $ 49,752 As the analysis indicates, the internal rate of return for Projects A and B exceeds 12% Thus, although the average rate of return is higher for Project B, the timing of the receipt of the net cash flows for Project A results in a higher net present value than for Project B Activity 25–6 This activity could be assigned individually or in groups This activity has the student(s) perform a capital investment analysis for a desktop computer, using information available to them on the Internet and from a local business The actual answer depends on the actual numbers determined by the student(s) Have a number of students (or groups) provide their answers to the class and note the variation (or lack thereof) between the various analyses Use this to show that there are often many answers to even simple problems, depending on the assumptions (e.g., what is considered a “mid-range” computer) and underlying data (e.g., rental rate) Below is a sample answer based on our own data and assumptions: Assumed hourly rental rate Semester cost (35 hours × $12) Present value of $420 for six semiannual periods at 5% ($420 × 5.07569) Less assumed price of a mid-range computer Net present value The computer should be purchased $12 per hour $420 $2,132 1,500 $ 632 ... Cash Flow Greenhouse Skid Loader 0.909 $ 25, 000 $ 35,000 0.826 25, 000 30,000 0.751 25, 000 25, 000 0.683 25, 000 20,000 0.621 25, 000 15,000 Total $ 125, 000 $ 125, 000 Amount to be invested Net... Expansion Expansion 0.833 $ 270,000 $ 250 ,000 0.694 250 ,000 250 ,000 0.579 220,000 240,000 0.482 250 ,000 240,000 0.402 260,000 270,000 Total $1 ,250 ,000 $1 ,250 ,000 Amount to be invested ... index of the sewing machine: Present value index of the packing machine: $336, 525 = 1.08 $311,600 $143,584 = 1.13 $126,690 c The present value index indicates that the packing machine would be the