CH25

CHAPTER 25CAPITAL INVESTMENT ANALYSIS

CLASS DISCUSSION QUESTIONS

1. The principal objections to the use of the av-erage rate of return method are its failing to consider the expected cash flows from the proposals and the timing of these flows.

2. 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.

3. 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.

4. The cash payback period ignores the cash flows that occur after the cash payback pe-riod, while the net present value method in-cludes 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.

5. A one-year payback will not equal a 100% average rate of return because the payback period is based on cash flows, while the av-erage rate of return is based on income. The depreciation on the project will prevent the two methods from reconciling.

6. The cash payback period ignores cash flows occurring after the payback period, which will often include large salvage values.

7. The majority of the cash flows of a new mo-tion picture are earned within two years of release. Thus, the time value of money as-pect 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.

8. The $9,750 net present value indicates that the proposal is desirable because the pro-posal is expected to recover the investment and provide more than the minimum rate of return.

9. 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 com-pute the present value of the proposal. This assumption may not always be reasonable.

11. The computations for the internal rate of re-turn method are more complex than those for the methods that ignore present value. Also, the method assumes that the cash re-ceived from the proposal during its useful life will be reinvested at the internal rate of re-turn.

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 manufactur-ing flexibility are examples of qualitative fac-tors 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

351351

large investment in process control technol-ogy and automated laboratory equipment. The process control technology could re-duce the variation in the size of fibers. More uniform fibers, in turn, improve the efficiency of the processes used by carpet manufac-turers. 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 in-vestment portfolio. Monsanto indicated the following considerations in making its invest-ment:a. After-tax cash flows.b. Labor savings.

c. Accepting projects that do not have a quantifiable payback, such as enablers that allow projects with more visible ben-efits 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 consid-ering the organizational vision and long-term strategic direction in the investment decision.

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EXERCISES

Ex. 25–1

TestingEquipment Centrifuge

Estimated average annual income:$10,500 ÷ 4...................................................................... $2,625$12,250 ÷ 5...................................................................... $2,450

Average investment:($42,000 + 0) ÷ 2.............................................................. $21,000($56,000 + 0) ÷ 2.............................................................. $28,000

Average rate of return:$2,625 ÷ $21,000............................................................. 12.5%$2,450 ÷ $28,000............................................................. 8.75%

Ex. 25–2

Averagerate

of return = Average annual incom e

Average investm ent

= Average savings* Annual depreciation Additional operating costs

Beginning cost + Residual value ÷ 2

=

=

= 13.5%* The effect of the savings in wages expense is an increase in income.

Ex. 25–3

Averagerate

of return= Average annual incom e

Average investm ent

= Annual revenues Annual product costs *

Beginning cost + Residual value ÷ 2

=

=

= 30%

* The depreciation of the equipment is included in the factory overhead cost per unit.

Ex. 25–4

Year 1 Years 2–14 Last YearInitial investment............................................. $ (238,000 )Operating cash flows:

Annual revenues (8,000 units × $36)........ $ 288,000 $ 288,000 $ 288,000Selling expenses (5% × $288,000)............ (14,400) (14,400) (14,400)Cost to manufacture

(8,000 units × $19.55)*.......................... (156,400 ) (156,400 ) (156,400 )Net operating cash flows..................... $ 117,200 $ 117,200 $ 117,200

Total for year 1................................................. $ (120,800 )Total for years 2–14 (operating cash flow). . . $ 117,200

Residual value............................................ 10,000 Total for last year............................................. $ 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 Cumulative Flow Net Cash Flows

Year 1................................................................ $80,000 $ 80,000Year 2................................................................ 70,000 150,000Year 3................................................................ 50,000 200,000Year 4................................................................ 50,000 250,000

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 deter-mined using the following schedule:

Initial investment: $550,000

Liquid Soap Cosmetics Net Cash Cumulative Net Net Cash Cumulative Net

Flow Cash Flows Flow Cash Flows

Year 1 $150,000 $150,000 $110,000 $110,000Year 2 140,000 290,000 110,000 220,000Year 3 130,000 420,000 110,000 330,000Year 4 130,000 550,000 110,000 440,000Year 5 110,000 550,000Liquid 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 be-cause 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.Present Value Net Cash Present Value of

Year of $1 at 12% Flow Net Cash Flow

1 0.893 $150,000 $ 133,9502 0.797 120,000 95,6403 0.712 75,000 53,4004 0.636 75,000 47,700

Total................................................. $420,000 $ 330,690Amount to be invested.................. 340,000 Net present value........................... $ (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..................................................... $125Production cost......................................................... $100Marketing cost........................................................... 40

Net cash flow from theatrical release........................... $ (15 )2007 home video sales:

Total sales................................................................. $ 90Net cash margin........................................................ 30%

Net cash flow.................................................................. $ 27

2008 pay TV..................................................................... $ 202009 syndication............................................................ 5

Net present value:Present Value Net Cash Present Value of


2006 1.000 $(15) $(15)2007 0.833 27 222008 0.694 20 142009 0.579 5 3 Net present value........................... $ 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...................................... 1,500Revenue per hour........................................ × $98.00 Revenue per year......................................... $ 147,000Cash outflows:Hours of operation...................................... 1,500Fuel cost per hour....................................... $28.00Labor cost per hour.................................... 22.00 Total fuel and labor costs per hour........... × $50.00 Fuel and labor costs per year..................... (75,000)Maintenance costs per year....................... (12,000 )Annual net cash flow................................... $ 60,000

b. Annual net cash flow (at the end of each of five years)................... $ 60,000Present value of annuity of $1 at 10% for five periods.................... × 3.791 Present value of annual net cash flows............................................. $ 227,460Less: Amount to be invested.............................................................. 235,000 Net present value................................................................................. $ (7,540 )

c. No. Crowe should not accept the investment because the bulldozer cost ex-ceeds the present value of the cash flows at the minimum desired rate of re-turn 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 ComplexPresent Value Net Cash Present Value of


1 0.870 $ 220,000 $ 191,4002 0.756 200,000 151,2003 0.658 200,000 131,6004 0.572 180,000 102,9604 0.572 420,000 240,240

Total................................................. $ 1,220,000 $ 817,400Amount to be invested.................. (775,000 )Net present value........................... $ 42,400

Office BuildingPresent Value Net Cash Present Value of


1 0.870 $ 300,000 $ 261,0002 0.756 300,000 226,8003 0.658 275,000 180,9504 0.572 275,000 157,300

Total................................................. $ 1,150,000 $ 826,050Amount to be invested.................. (775,000 )Net present value........................... $ 51,050

The net present value of both projects are positive; thus, both proposals are ac-ceptable. 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.............. $ 1,993,000Less: Initial franchise fee................................................. 300,000 Net investment.................................................................. $ 1,693,000

Years 1–10Royalty:

Average unit revenue................................................ $1,500,000Royalty rate................................................................ × 4.5%

Royalty cash flow.............................................................. $ 67,500Annual lease and other cash flows................................. 175,000 Total annual cash flows................................................... $ 242,500Present value of a $1 annuity for 10 years at 10%

(Exhibit 2).................................................................... × 6.145 Present value of annual cash flows................................ $ 1,490,163

Lease purchase option..................................................... $ 600,000Present value of $1 for 10 years at 10% (Exhibit 1)....... × 0.386 Present value of lease purchase option......................... $ 231,600

Net present value per restaurant unit............................. $ 28,763 1

1 –$1,693,000 + $1,490,163 + $231,600. Thus, the restaurant exceeds IHOP’s mini -mum 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.

Ex. 25–12

a. Revenues (3,000 × 80% × 300 days × $310)................................. $ 223,200,000Less: Variable expenses (3,000 × 80% × 300 days × $75)......... 54,000,000

Fixed expenses (other than depreciation)....................... 78,000,000 Annual net cash flow...................................................................... $ 91,200,000

b. Present value of annual net cash flows ($91,200,000 × 5.65)..... $ 515,280,000Present value of salvage value ($85,000,000 × 0.322)................. 27,370,000 Total present value......................................................................... $ 542,650,000Initial investment............................................................................ 510,000,000 Net present value............................................................................ $ 32,650,000

c. Annual cash flow assuming $320 revenue per cruise day:Revenues (3,000 × 80% × 300 days × $320)................................. $ 230,400,000Less: Variable expenses (3,000 × 80% × 300 days × $75)......... 54,000,000

Fixed expenses (other than depreciation)....................... 78,000,000 Annual net cash flow...................................................................... $ 98,400,000 Net present value calculation at 15% minimum rate of return:Present value of annual net cash flows ($98,400,000 × 5.019)... $ 493,869,600Present value of salvage value ($85,000,000 × 0.247)................. 20,995,000 Total present value......................................................................... $ 514,864,600Initial investment............................................................................ 510,000,000 Net present value............................................................................ $ 4,864,600 The net present value is positive. Thus, the increase in price is sufficient to earn a 15% rate of return.

Ex. 25–13

Present value index = Total present value of net cash flowAmount to be invested

Present value index of Proposal A: = 0.96

Present value index of Proposal B: = 1.07

Ex. 25–14

a. Annual net cash flow—Sewing Machine: $75,000 = 2,000 hours × 50 baseballs × $0.75

Annual net cash flow—Packing Machine: $32,000 = 1,600 × $20 labor cost saved per hour

Sewing Machine:Annual net cash flow (at the end of each of eight years)................ $ 75,000Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)..... × 4.487 Present value of annual net cash flows............................................. $336,525Less amount to be invested............................................................... 311,600 Net present value................................................................................. $ 24,925 Packing Machine:Annual net cash flow (at the end of each of eight years)................ $ 32,000Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)..... × 4.487 Present value of annual net cash flows............................................. $143,584Less amount to be invested............................................................... 126,690 Net present value................................................................................. $ 16,894

b. Present value index = Total present value of net cash flowAmount to be invested

Present value index of the sewing machine: = 1.08

Present value index of the packing machine: = 1.13

c. The present value index indicates that the packing machine would be the preferred investment, assuming that all other qualitative considerations are equal. Note that the net present value of the sewing machine is greater than the packing machine’s. However, the sewing machine requires a greater in-vestment than the packing machine, for very little extra net present value. Thus, the present value index indicates the packing machine is favored.

Ex. 25–15

a. Average rate of return on investment: = 20%

* The annual earnings are equal to the cash flow less the annual depreciation expense, shown as follows:

$93,760 – ($468,800 ÷ 10 years) = $46,880

b. Cash payback period: = 5 years

c. Present value of annual net cash flows ($93,760 × 5.65*)................ $529,744Amount to be invested........................................................................ 468,800 Net present value................................................................................. $ 60,944 *Present value of an annuity of $1 at 12% for 10 periods from chapter table.

Ex. 25–16

a. Present value factor for anannuity of $1 for 8 periods =

Amount to be investedAnnual net cash flow

=

= 4.968

b. 12%

Ex. 25–17

Equal annual savings per year: = $83,333,333

Present value of an annuity factor: = 2.283

Go to row three in Exhibit 2. In row three, the column associated with the factor 2.283 is 15%. Thus, the internal rate of return under these assumptions is 15%.

Ex. 25–18

a. Delivery Truck

Cash received from additional delivery (40,000 bags × $0.35)........ $14,000Cash used for operating expenses (16,000 miles × $0.32).............. 5,120 Net cash flow for delivery truck.......................................................... $ 8,880 Present value factor for anannuity of $1 for 6 periods = Amount to be invested

Annual net cash flow

=

= 4.111

Internal Rate of Return = 12% (from text Exhibit 2)

Bagging Machine

Direct labor savings (2.0 hrs./day × $14/hr. × 260 days/yr.)............. $7,280

Present value factor for anannuity of $1 for 6 periods = Amount to be invested

Annual net cash flow

=

= 3.785

Internal Rate of Return = 15% (from text Exhibit 2)

Ex. 25–18 Concluded

b. To: ManagementRe: Investment RecommendationAn internal rate of return analysis was performed for the delivery truck and bagging machine investments. The internal rate of return for the bagging ma-chine is 15%, while the delivery truck is 12% (detailed analysis available). In addition, there do not appear to be any qualitative considerations that would favor the delivery truck. Therefore, the recommendation is to invest in the bagging machine. If additional funds become available, however, the delivery truck would be an acceptable investment because the internal rate of return of 12% exceeds the company’s minimum rate of return of 11%.

Ex. 25–19

a. Present value of annual net cash flows ($18,500 × 4.16*)................ $76,960Amount to be invested........................................................................ 84,434 Net present value................................................................................. $(7,474 )*Present value of an annuity of $1 at 15% for 7 periods from text Exhibit 2.

b. The rate of return is less than 15% because there is a negative net present value.

c. Present value factor for an annuity of $1 = Amount to be investedAnnual net cash flow

=

= 4.564

Internal rate of return = 12% (from text Exhibit 2)

Ex. 25–20

With an expected useful life of 4 years, the cash payback period could not be greater than 4 years. This would indicate that the cost of the initial investment would not be recovered during the useful life of the asset. However, there would be no average rate of return in such a case because a net loss would result. If the 25% average rate of return and useful life are correct, the cash payback period must be less than 4 years. Alternatively, if both the 25% average rate of return and 4.5 years for the cash payback period are correct, the machinery must have a useful life of more than 4 years.

Ex. 25–21

a. Since all the cash flows are incurred in the local economy under this as-sumption, it is likely that the internal rate of return of the new plant will de-cline. This is because the cash profits earned on the plant will be less in U.S. dollars as a result of the devaluation. For example, if the product sold for a profit of 10 units of local currency, it would need to double to 20 units of lo-cal currency in order to generate the same U.S. dollars of profit. This could be done with a large price increase. However, such a price increase would probably significantly reduce demand. If the price stayed the same, then the number of U.S. dollars earned in profit would be halved.

b. If the plant produced for export only, then the expenses would be incurred in local currency, while the revenues would be earned in U.S. dollars. This could work in favor of the project because the expenses in U.S. dollar terms would decline. For example, if the local wages were 16 units of local currency per hour, then after the devaluation, these 16 units would cost half as much in U.S. dollar terms (from $4 to $2). Since the product is sold in the United States, the currency exchange rate would have no impact on revenues. The net result is that the cash flows in U.S. dollar terms would potentially in -crease, increasing the internal rate of return.

PROBLEMS

Prob. 25–1A

1. a. Average annual rate of return for both projects:

= = 16%

b. Net present value analysis:

Present Value of Net Cash Flow Net Cash Flow

Present Value of Tracking TrackingYear $1 at 12% Warehouse Technology Warehouse Technology

1 0.893 $154,000 $135,000 $137,522 $120,5552 0.797 154,000 145,000 122,738 115,5653 0.712 154,000 155,000 109,648 110,3604 0.636 154,000 165,000 97,944 104,9405 0.567 154,000 170,000 87,318 96,390

Total................................. $770,000 $770,000 $555,170 $547,810Amount to be invested............................................. 550,000 550,000 Net present value...................................................... $ 5,170 $ (2,190 )

2. The report to the capital investment committee can take many forms. The re-port should, as a minimum, present the following points:a. Both projects offer the same average annual rate of return.b. The warehouse net present value exceeds the selected rate established

for discounted cash flows (12%), while the tracking technology does not. Thus, considering only quantitative factors, the warehouse investment should be selected.

Prob. 25–2A

1. a. Cash payback period for both products: 2 years (the year in which accu-mulated net cash flows equal $420,000).

b. Net present value analysis:

Present Value ofPresent Net Cash Flow Net Cash Flow Value of Home & Today’s Home & Today’s

Year $1 at 15% Garden Teen Garden Teen

1 0.870 $220,000 $150,000 $191,400 $130,5002 0.756 200,000 270,000 151,200 204,1203 0.658 180,000 190,000 118,440 125,0204 0.572 40,000 30,000 22,880 17,1605 0.497 30,000 30,000 14,910 14,910

Total............................. $670,000 $670,000 $498,830 $491,710Amount to be invested............................................. 420,000 420,000 Net present value...................................................... $ 78,830 $ 71,710

2. The report can take many forms and should include, as a minimum, the fol-lowing points:a. Both products offer the same total net cash flow.b. Both products offer the same cash payback period.c. Because of the timing of the receipt of the net cash flows, the Home &

Garden magazine offers a higher net present value.d. Both products provide a positive net present value. This means both

products would be acceptable, since they exceed the minimum rate of re-turn.

Prob. 25–3A

1.Branch Office Expansion

Present Value Net Cash Present Value ofYear of $1 at 20% Flow Net Cash Flow

1 0.833 $260,000 $216,5802 0.694 240,000 166,5603 0.579 220,000 127,380

Total........................................................... $720,000 $510,520Amount to be invested................................................................... 520,000 Net present value............................................................................ $ (9,480 )

Computer System UpgradePresent Value Net Cash Present Value of


1 0.833 $200,000 $166,6002 0.694 195,000 135,3303 0.579 185,000 107,115

Total........................................................... $580,000 $409,045Amount to be invested................................................................... 380,000 Net present value............................................................................ $ 29,045

Install Internet Bill-PayPresent Value Net Cash Present Value of


1 0.833 $325,000 $270,7252 0.694 310,000 215,1403 0.579 305,000 176,595

Total........................................................... $940,000 $662,460Amount to be invested................................................................... 625,000 Net present value............................................................................ $ 37,460

Prob. 25–3A Concluded

2. Present value index = Total present value of net cash flowAmount to be invested

Present value index of branch office: = 0.98*

Present value index of computer system: = 1.08*

Present value index of Internet bill-pay: = 1.06*

*Rounded.

3. The computer system upgrade has the largest present value index. Although the Internet bill-pay has the largest net present value, it returns less present value per dollar invested than does the computer system upgrade, as re-vealed by the present value indexes (1.08 to 1.06). (The present value index for the branch office expansion is less than 1, indicating that it does not meet the minimum rate of return standard.)

Prob. 25–4A

1. a. Radio Station:Annual net cash flow (at the end of each of four years)............ $ 180,000Present value of an annuity of $1 at 12% for 4 years (Exhibit 2) ×3.037 Present value of annual net cash flows....................................... $ 546,660Less amount to be invested.......................................................... 466,020 Net present value............................................................................ $ 80,640

TV Station:Annual net cash flow (at the end of each of four years)............ $ 480,000Present value of an annuity of $1 at 12% for 4 years (Exhibit 2) ×3.037 Present value of annual net cash flows....................................... $ 1,457,760Less amount to be invested.......................................................... 1,370,400 Net present value............................................................................ $ 87,360


Present value index of the radio station: = 1.17*

Present value index of the TV station: = 1.06*

*Rounded.

2. a. Present value factor for an annuity of $1 = Amount to be investedAnnual net cash flow

Radio Station: = 2.589

TV Station: = 2.855

b. Internal rate of return: (determined from Exhibit 2 in text)Radio Station: 20%TV Station: 15%


3. By using the internal rate of return method, all proposals are automatically placed on a common basis. For example, the net present value analyses in (1a) indicated that the net present value was greater for the TV station. How-ever, it was necessary to use the present value index to determine that the radio station 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 radio station’s rate of 20% is greater than the TV station’s rate of 15%.

Prob. 25–5A

1. Net present value analysis:Site A:Annual net cash flow (at the end of each of six years).................... $140,000Present value of an annuity of $1 at 15% for 6 years (Exhibit 2)..... × 3.785 Present value of annual net cash flows............................................. $529,900Less amount to be invested............................................................... 465,000 Net present value................................................................................. $ 64,900 Site B:Annual net cash flow (at the end of each of four years).................. $210,000Present value of an annuity of $1 at 15% for 4 years (Exhibit 2)..... × 2.855 Present value of annual net cash flows............................................. $599,550Less amount to be invested............................................................... 465,000 Net present value................................................................................. $134,550

2. Net present value analysis:

Present Value ofPresent Value of Net Cash Flow Net Cash Flow

Year $1 at 15% Site A Site B Site A Site B

1 0.870 $140,000 $210,000 $121,800 $182,7002 0.756 140,000 210,000 105,840 158,7603 0.658 140,000 210,000 92,120 138,1804 0.572 140,000 210,000 80,080 120,120

Residual value........ 0.572 300,000 0 171,600 0 Total.............................................. $860,000 $840,000 $571,440 $599,760Amount to be invested........................................................ 465,000 465,000 Net present value................................................................. $106,440 $134,760**This amount differs from the net present value calculation in (1) due to rounding error.

3. To: Investment CommitteeBoth Sites A and B 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 Site A at the end of period 4 is used to equalize the two lives. The net present value of the two projects over equal lives indi-cates that Site B has a higher net present value and would be a superior in-vestment.

Prob. 25–6A

1. Proposal A: 3-year and 4 months cash payback period, as follows:

Net Cash CumulativeYear Flow Net Cash Flows

1 $220,000 $220,0002 220,000 440,0003 220,000 660,0004 months* 60,000 720,000

* The net cash flow for year 4 is $180,000. Hence, the net cash flow per month is $15,000 ($180,000 ÷ 12). Thus, 4 months are needed to accumulate an addi-tional $60,000 (4 × $15,000).

Proposal B: 2-year cash payback period, as follows:


1 $40,000 $ 40,0002 84,000 124,000

Proposal C: 3-year and 9 months cash payback period, as follows:


1 $80,000 $ 80,0002 80,000 160,0003 80,000 240,0009 months* 60,000 300,000

*The net cash flow required is $60,000 out of $80,000 in year 4, or 75%. Thus, 75% of 12 mos. is 9 mos.

Proposal D: 3-year cash payback period, as follows:


1 $80,000 $ 80,0002 80,000 160,0003 65,000 225,000

Prob. 25–6A Continued

2. Proposal A: 16.7% average rate of return, determined as follows:

= = 16.7% (rounded)

Proposal B: 29% average rate of return, determined as follows:

= = 29.0% (rounded)

Proposal C: 9.3% average rate of return, determined as follows:

= = 9.3% (rounded)

Proposal D: 23.1% average rate of return, determined as follows:

= = 23.1% (rounded)

Prob. 25–6A Continued

3. Of the four proposed investments, only Proposals B and D meet the com-pany’s requirements, as the following table indicates:

Cash Payback Average Rate Accept forProposal Period of Return Further Analysis Reject

A 3 yrs., 4 mos. 16.7% X*B 2 yrs. 29.0 XC 3 yrs., 9 mos. 9.3 XD 3 yrs. 23.1 X

* Proposal A is rejected because it fails to meet the maximum payback period requirement, even though it meets the minimum accounting rate of return re-quirement.

4.Proposal B:


1 0.909 $ 40,000 $ 36,3602 0.826 84,000 69,3843 0.751 40,000 30,0404 0.683 30,000 20,4905 0.621 20,000 12,420

Total................................................................. $214,000 $168,694Amount to be invested................................................................... 124,000 Net present value............................................................................ $ 44,694

Proposal D:Present Value Net Cash Present Value of


1 0.909 $ 80,000 $ 72,7202 0.826 80,000 66,0803 0.751 65,000 48,8154 0.683 65,000 44,3955 0.621 65,000 40,365




Present value index of Proposal B: = 1.36*

Present value index of Proposal D: = 1.21*

*Rounded.

6. Based upon the net present value, the proposals should be ranked as fol-lows:Proposal D: $47,375Proposal B: $44,694

7. Based upon the present value index (the amount of present value per dollar invested), the proposals should be ranked as follows:Proposal B: 1.36Proposal D: 1.21

8. The present value indexes indicate that although Proposal D 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 D requires the larger invest -ment. Thus, management should use investment resources for Proposal B before investing in Proposal D.

Prob. 25–1B

1. a. Average annual rate of return for both projects:

= = 22.5%

b. Net present value analysis:Present Value of

Present Value of Net Cash Flow Net Cash Flow Year $1 at 10% Greenhouse Skid Loader Greenhouse Skid Loader

1 0.909 $ 25,000 $ 35,000 $22,725 $31,8152 0.826 25,000 30,000 20,650 24,7803 0.751 25,000 25,000 18,775 18,7754 0.683 25,000 20,000 17,075 13,6605 0.621 25,000 15,000 15,525 9,315

Total.............................. $125,000 $125,000 $94,750 $98,345Amount to be invested............................................. 80,000 80,000 Net present value...................................................... $ 14,750 $ 18,345

2. The report to the capital investment committee can take many forms. The re-port should, as a minimum, present the following points:

a. Both projects offer the same average annual rate of return.

b. Although both projects exceed the selected rate established for dis-counted cash flows, the skid loader offers a larger net present value. The skid loader has a larger net present value because larger cash flows oc-cur earlier in time for the skid loader compared to the greenhouse. Thus, if only one of the two projects can be accepted, the skid loader would be the more attractive.

Prob. 25–2B

1. a. Cash payback period for both projects: 3 years (the year in which accu-mulated net cash flows equal $740,000).

b. Net present value analysis:Present Value of

Net Cash Flow Net Cash Flow Present Value of Plant Retail Store Plant Retail Store

Year $1 at 20% Expansion Expansion Expansion Expansion

1 0.833 $ 270,000 $ 250,000 $224,910 $208,2502 0.694 250,000 250,000 173,500 173,5003 0.579 220,000 240,000 127,380 138,9604 0.482 250,000 240,000 120,500 115,6805 0.402 260,000 270,000 104,520 108,540

Total.............................. $1,250,000 $1,250,000 $750,810 $744,930Amount to be invested............................................. 740,000 740,000 Net present value...................................................... $ 10,810 $ 4,930

2. The report can take many forms and should include, as a minimum, the fol-lowing points:a. Both projects offer the same total net cash flow.b. Both projects offer the same cash payback period.c. Because of the timing of the receipt of the net cash flows, the plant ex-

pansion offers a higher net present value.d. Both projects provide a positive net present value. This means both

projects would be acceptable, since they exceed the minimum rate of re-turn.

Prob. 25–3B

1.Route Expansion


1 0.870 $ 420,000 $365,4002 0.756 380,000 287,2803 0.658 350,000 230,300

Total................................................ $1,150,000 $882,980Amount to be invested........................................................ 840,000 Net present value................................................................ $ 42,980

Acquire RailcarsPresent Value Net Cash Present Value of


1 0.870 $225,000 $195,7502 0.756 200,000 151,2003 0.658 180,000 118,440

Total................................................ $605,000 $465,390Amount to be invested........................................................ 490,000 Net present value................................................................ $ (24,610 )

New Maintenance YardPresent Value Net Cash Present Value of


1 0.870 $210,000 $182,7002 0.756 200,000 151,2003 0.658 180,000 118,440

Total................................................ $590,000 $452,340Amount to be invested........................................................ 420,000 Net present value................................................................ $ 32,340

Prob. 25–3B Concluded


Present value index of route expansion: = 1.05*

Present value index of railcars: = 0.95*

Present value index of maintenance yard: = 1.08*

*Rounded.

3. 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

1. a. Generating Unit:Annual net cash flow (at the end of each of four years).................. $ 600,000Present value of an annuity of $1 at 10% for 4 years (Exhibit 2).. . . × 3.17 Present value of annual net cash flows............................................. $1,902,000Less amount to be invested............................................................... 1,822,200 Net present value................................................................................. $ 79,800 Distribution Network Expansion:Annual net cash flow (at the end of each of four years).................. $160,000Present value of an annuity of $1 at 10% for 4 years (Exhibit 2).. . . × 3.17 Present value of annual net cash flows............................................. $507,200Less amount to be invested............................................................... 456,800 Net present value................................................................................. $ 50,400


Present value index of the generating unit: = 1.04*

Present value index of the distribution network expansion:

= 1.11*

*Rounded.

2. a. Present value factor for an annuity of $1 = Amount to be investedAnnual net cash flow

Generating unit: = 3.037

Distribution network expansion: = 2.855

b. Internal rate of return: (determined from Exhibit 2 in text)Generating unit: 12%Distribution network expansion: 15%


3. 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 us-ing the internal rate of return method, it can be easily seen that the distribu-tion network expansion’s rate of return of 15% is greater than the generating unit’s rate of 12%.

Prob. 25–5B

1. Net present value analysis:

Project I:Annual net cash flow (at the end of each of six years)................. $ 65,000Present value of an annuity of $1 at 15% for 6 years (Exhibit 2). . × 3.785 Present value of annual net cash flows.......................................... $246,025Less amount to be invested............................................................. 200,000 Net present value.............................................................................. $ 46,025 Project II:Annual net cash flow (at the end of each of four years)............... $ 97,500Present value of an annuity of $1 at 15% for 4 years (Exhibit 2). . × 2.855 Present value of annual net cash flows.......................................... $278,362.50Less amount to be invested............................................................. 200,000.00 Net present value.............................................................................. $ 78,362.50

2. Net present value analysis:Present Value of

Present Value of Net Cash Flow Net Cash FlowYear $1 at 15% Project I Project II Project I Project II

1 0.870 $ 65,000 $ 97,500 $ 56,550 $ 84,8252 0.756 65,000 97,500 49,140 73,7103 0.658 65,000 97,500 42,770 64,1554 0.572 65,000 97,500 37,180 55,770

Residual value..... 0.572 140,000 0 80,080 0 Total........................................... $400,000 $390,000 $265,720 $278,460Amount to be invested................................................... 200,000 200,000 Net present value........................................................... $ 65,720 $ 78,460 *

* This amount differs from the net present value calculation in (1) due to rounding error.

3. To: Investment CommitteeBoth 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 4 is used to equalize the two lives. The net present value of the two projects over equal lives indi-cates that Project II has a higher net present value and would be a superior investment.

Prob. 25–6B

1. Proposal A: 4-year cash payback period, as follows:


1 $140,000 $140,0002 140,000 280,0003 140,000 420,0004 80,000 500,000

Proposal B: 2-year, 9-month cash payback period, as follows:


1 $100,000 $100,0002 80,000 180,0009 months* 45,000 225,000

*The cash flow required for investment payback in Year 3 is $45,000, which is three-fourths ($45,000 ÷ $60,000) of Year 3’s cash flow. Thus, 9 months (three-fourths of 12 months) are needed to accumulate an additional $45,000.

Proposal C: 3-year cash payback period, as follows:


1 $220,000 $220,0002 200,000 420,0003 180,000 600,000

Proposal D: 3-year, 4-month cash payback period, as follows:


1 $125,000 $125,0002 95,000 220,0003 60,000 280,0004 months* 20,000 300,000

*The cash flow required for investment payback in Year 4 is $20,000, which is one-third ($20,000 ÷ $60,000) of Year 4’s cash flow. Thus, 4 months (one-third of 12 months) are needed to accumulate an additional $20,000.

Prob. 25–6B Continued

2. Proposal A: 6.4% average rate of return, determined as follows:

= = 6.4%

Proposal B: 24% average rate of return, determined as follows:

= = 24%

Proposal C: 22% average rate of return, determined as follows:

= = 22%

Proposal D: 13.3% average rate of return, determined as follows:

= = 13.3%

Prob. 25–6B Continued

3. Of the four proposed investments, only Proposals B and C meet the com-pany’s requirements, as the following table indicates:

Cash Payback Average Rate Accept forProposal Period of Return Further Analysis Reject

A 4 yrs. 6.4% XB 2 yrs., 9 mos. 24.0 XC 3 yrs. 22.0 XD 3 yrs., 4 mos. 13.3 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.

4.

Proposal B:Present Value Net Cash Present Value of


1 0.909 $100,000 $ 90,9002 0.826 80,000 66,0803 0.751 60,000 45,0604 0.683 60,000 40,9805 0.621 60,000 37,260


Proposal C:Present Value Net Cash Present Value of


1 0.909 $220,000 $199,9802 0.826 200,000 165,2003 0.751 180,000 135,1804 0.683 180,000 122,9405 0.621 150,000 93,150

Total................................................................. $930,000 $716,450Amount to be invested................................................................... 600,000 Net present value............................................................................ $116,450



Present value index of Proposal B: = 1.25*

Present value index of Proposal C: = 1.19*

*Rounded.

6. Based upon the net present value, the proposals should be ranked as fol-lows:Proposal C: $116,450Proposal B: $55,280

7. Based upon the present value index (the amount of present value per dollar invested), the proposals should be ranked as follows:Proposal B: 1.25Proposal C: 1.19

8. 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 invest -ment. 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 interpreta-tion. 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 legiti-mate. 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 circum-vent 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 prod-uct 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 eventu-ally 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 com-pany. The decision to confront I. M. has immediate repercussions. This is the heart of real world ethical dilemmas. The dilemma occurs when the ethical deci-sion 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 unethi -cal 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 ac-countant will recognize these pressures and make the short-term decisions in or-der 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

1. Annual salary.............................................................................. $ 40,000Present value of $1 annuity for 10 years at 10%..................... × 6.145 Present value of undergraduate option as of the end

of undergraduate degree (beginning of graduatedegree)................................................................................... $ 245,800

2. Annual tuition at the beginning of the graduate year............. $ (12,000 )Annual salary.............................................................................. $ 50,000Present value of $1 annuity for 9 years at 10%....................... × 5.759 Present value salary to end of graduate year.......................... $ 287,950Present value of $1 for 1 year at 10%....................................... × 0.909 Present value of salary at the beginning of graduate year.... $ 261,747 Present value of graduate option at beginning of graduate

year (salary less tuition)....................................................... $ 249,747

Note: The present values of 1. and 2. must both be determined as of the be-ginning 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:

1 2 3 4 5 6 7 8 9 10

($12,000) 50K 50K 50K 50K 50K 50K 50K 50K 50K

$261,747 ($50,000 5.759) 0.909$249,747

3. Present value of graduate option............................................. $ 249,747Present value of undergraduate option................................... 245,800 Net benefit of graduate option.................................................. $ 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

1. Payback period: = 5 years

2. Net present value:Present value factor for an annuity of $1, 10 periods at 10%: 6.145Net present value = (6.145 × $250,000) – $1,250,000 = $286,250

3. Some critical elements that are missing from this analysis are:a. The manager is viewing the acquisition of robots as a labor-saving de-

vice. 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 vol-ume, 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 in-stallation 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 hir-ing 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 compa -nies 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 re-sponding 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 in -vestments that have more predictable cash flows with possible short duration.

Activity 25–5

1. Average rate of return = Estimated average annual incomeAverage investment

Project A: = 25%

Project B: = 26%

2. The timing of net cash flows to be received from a capital investment pro-posal 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 ex-ceeds 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 il -lustrated below.

Present Value ofPresent Value of Net Cash Flow Net Cash Flow

Year $1 at 12% Project A Project B Project A Project B

1 0.893 $ 155,000 $ 115,000 $ 138,415 $ 102,6952 0.797 140,000 130,000 111,580 103,6103 0.712 130,000 148,000 92,560 105,3764 0.636 115,000 154,200 73,140 98,071

Total...................................... $ 540,000 $ 547,200 $ 415,695 $ 409,752Amount to be invested..................................................... 360,000 360,000 Net present value.............................................................. $ 55,695 $ 49,752

As the analysis indicates, the internal rate of return for Projects A and B ex-ceeds 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 ac-tual 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 as-sumptions (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 as -sumptions:Assumed hourly rental rate............................................................ $12 per hourSemester cost (35 hours × $12)...................................................... $420Present value of $420 for six semiannual periods at 5%

($420 × 5.07569)..................................................................... $2,132Less assumed price of a mid-range computer............................. 1,500 Net present value............................................................................. $ 632 The computer should be purchased.

Documents

CH25