warren sm ch.26 final

CHAPTER 26CAPITAL INVESTMENT ANALYSIS

EYE OPENERS

1. The principal objections to the use of the av-erage rate of return method are its failure 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 residual 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 $7,900 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 0.9 and 0.09, respectively, for the two projects. That is, a $9,000 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 return. This assumption may not always be reasonable.

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. Quicker delivery of products, higher produc-tion quality, and greater manufacturing flexi-bility are examples of qualitative factors that should be considered.

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16. Monsanto indicated that it recognized that the market was demanding higher product quality that could be achieved only with a 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 invest-ment decision.

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PRACTICE EXERCISES

PE 26–1A

Estimated average annual income $12,000 ($36,000/3 years)Average investment $40,000 ($65,000 + $15,000)/2Average rate of return 30% ($12,000/$40,000)

PE 26–1B

Estimate average annual income $27,200 ($136,000/5 years)Average investment $200,000 ($380,000 + $20,000)/2Average rate of return 13.6% ($27,200/$200,000)

PE 26–2A

4.5 years ($37,800/$8,400)

PE 26–2B

6.2 years ($706,800/$114,000)

PE 26–3A

a. ($1,520) [($9,000 × 3.170) – $30,050]

b. 0.95 ($28,530/$30,050)

PE 26–3B

a. $36,610 [($82,000 × 3.605) – $259,000]

b. 1.14 ($295,610/$259,000)

PE 26–4A

6% [($427,779/$87,000) = 4.917, the present value of an annuity factor for six periods at 6%, from Exhibit 2]

PE 26–4B

20% [($56,434/$14,000) = 4.031, the present value of an annuity factor for nine periods at 20%, from Exhibit 2]

PE 26–5A

a.

Present value of $3,000 per year at 20% for 4 years....................... $ 7,767*Present value of $9,000 at 20% at the end of 4 years..................... 4,338 ** Total present value of Project 1........................................................ $12,105Total cost of Project 1........................................................................ 10,000 Net present value of Project 1........................................................... $ 2,105

*[$3,000 × 2.589 (Exhibit 2, 20%, 4 years)]**[$9,000 × 0.482 (Exhibit 1, 20%, 4 years)]

b. Project 2. Project 1’s net present value of $2,105 is less than the net present value of Project 2, $2,500.

PE 26–5B

a.

Present value of $24,000 per year at 12% for 6 years..................... $ 98,664*Present value of $60,000 at 12% at the end of 6 years................... 30,420 ** Total present value of Project A....................................................... $129,084Total cost of Project A....................................................................... 125,000 Net present value of Project A.......................................................... $ 4,084

*[$24,000 × 4.111 (Exhibit 2, 12%, 6 years)]**[$60,000 × 0.507 (Exhibit 1, 12%, 6 years)]

b. Project A. Project A’s net present value of $4,084 is more than the net present value of Project B, $2,400.

EXERCISES

Ex. 26–1

TestingEquipment Vehicle

Estimated average annual income:$13,200/6......................................................................... $2,200$14,000/8......................................................................... $1,750

Average investment:($80,000 + 0)/2................................................................. $40,000($28,000 + 0)/2................................................................. $14,000

Average rate of return:$2,200/$40,000................................................................ 5.5%$1,750/$14,000................................................................ 12.5%

Ex. 26–2

=

=

=

=

= 16%

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

– – –

Ex. 26–3

=

=

=

=

= 40%

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

Ex. 26–4

Year 1 Years 2–9 Last Year

Initial investment............................................. $(156,000)Operating cash flows:

Annual revenues (9,000 units × $42)........ $ 378,000 $ 378,000 $ 378,000Selling expenses (5% × $378,000)............ (18,900) (18,900) (18,900)Cost to manufacture

(9,000 units × $34.00)*.......................... (306,000 ) (306,000 ) (306,000 )Net operating cash flows..................... $ 53,100 $ 53,100 $ 53,100

Total for Year 1................................................. $ (102,900 )Total for Years 2–9 (operating cash flow)..... $ 53,100

Residual value............................................ 12,000 Total for last year............................................. $ 65,100

*The fixed overhead relates to the depreciation on the equipment [($156,000 – $12,000)/10 years/9,000 units = $1.60]. Depreciation is not a cash flow and should not be considered in the analysis.

Ex. 26–5

Location 1: $360,000/$60,000 = 6-year cash payback period.

Location 2: 4-year cash payback period, as indicated below.

Net Cash Cumulative Flow Net Cash Flows

Year 1................................................................ $120,000 $120,000Year 2................................................................ 90,000 210,000Year 3................................................................ 75,000 285,000Year 4................................................................ 75,000 360,000

Ex. 26–6

a. The Liquid Soap product line is recommended, based on its shorter cash pay-back period. The cash payback period for both products can be determined us-ing the following schedule:

Initial investment: $500,000

Liquid Soap Body Lotion Net Cash Cumulative Net Net Cash Cumulative Net

Flow Cash Flows Flow Cash Flows

Year 1 $190,000 $190,000 $100,000 $100,000Year 2 180,000 370,000 100,000 200,000Year 3 130,000 500,000 100,000 300,000Year 4 100,000 400,000Year 5 100,000 500,000

Liquid Soap has a three-year cash payback period, and Body Lotion has a five-year cash payback.

b. The cash payback periods are different between the two product lines because Liquid Soap earns cash faster than does Body Lotion. Even though both prod-ucts earn the same total net cash flow over the eight-year planning horizon, Liq-uid Soap returns cash faster in the earlier years. The cash payback method em-phasizes the initial years’ net cash flows in determining the cash payback pe-riod. 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. 26–7

a.

Present Value Net Cash Present Value ofYear of $1 at 15% Flow Net Cash Flow

1 0.870 $ 64,000 $ 55,6802 0.756 49,000 37,0443 0.658 37,000 24,3464 0.572 25,000 14,300

Total................................................. $175,000 $ 131,370Amount to be invested.................. 104,000 Net present value........................... $ 27,370

b. Yes. The $27,370 net present value indicates that the return on the proposal is greater than the minimum desired rate of return of 15%.

Ex. 26–8

a.

2010 2011 2012 2013 2014

Revenues............. $ 60,000 $ 60,000 $ 60,000 $ 60,000 $ 60,000Driver salary......... (43,000) (45,000) (47,000) (49,000) (51,000)Insurance............. (4,000) (4,000) (4,000) (4,000) (4,000)Residual value..... _______ 5,000 Annual net cash

flow.................. $ 13,000 $ 11,000 $ 9,000 $ 7,000 $ 10,000

b.

Net Cash Flow Present Value of Present Value ofYear [from part (a)] $1 at 12% Net Cash Flow

2010 $13,000 0.893 $11,6092011 11,000 0.797 8,7672012 9,000 0.712 6,4082013 7,000 0.636 4,4522014 10,000 0.567 5,670 Total present value of cash flows...................................... $36,906Investment in delivery truck............................................... 38,000 Net present value of delivery truck.................................... $ (1,094 )

c. The total present value of cash flows from the delivery truck investment is less than the total purchase price of the truck. That is, the net present value is nega-tive. Thus, this analysis does not support investment in the truck.

Ex. 26–9

a.

(in millions)

Annual revenues.................................................................................. $44Total expenses..................................................................................... $25Less noncash depreciation expense................................................. 5 Annual cash expenses........................................................................ 20 Annual net cash flow........................................................................... $24

*Annual depreciation expense, $150 million/30 years = $5 million per year

b.

(in millions,except present

value factor)

Annual net cash flow........................................................................... $ 24Present value of an annuity of $1 at 14% for 30 periods................. × 7 .0027 *Present value of hotel project cash flows......................................... $ 168Less hotel construction costs............................................................ 150 Net present value of hotel project...................................................... $ 18

*From Appendix A in the text.

c. The present value of the hotel’s operating cash flows exceeds the construction costs by $18 million. That is, the net present value is positive. Therefore, con-struction of the new hotel can be supported by this analysis.

Ex. 26–10

a. Cash inflows:

Hours of operation...................................... 1,500Revenue per hour........................................ × $130.00 Revenue per year......................................... $ 195,000

Cash outflows:

Hours of operation...................................... 1,500Fuel cost per hour....................................... $42.00Labor cost per hour.................................... 32.00 Total fuel and labor costs per hour........... × $74.00 Fuel and labor costs per year..................... (111,000)

Maintenance costs per year....................... (15,000 )Annual net cash flow................................... $ 69,000

b. Annual net cash flow (at the end of each of five years)................... $ 69,000Present value of annuity of $1 at 10% for five periods.................... × 3.791 Present value of annual net cash flows............................................. $ 261,579Less amount to be invested............................................................... 245,000 Net present value................................................................................. $ (16,579 )

c. Yes. E&T should accept the investment because the bulldozer cost is less than the present value of the cash flows at the minimum desired rate of return of 10%.

Ex. 26–11

a. Revenues (3,600 × 300 days × $450)............................................. $ 486,000,000Less: Variable expenses (3,600 × 300 days × $90).................... (97,200,000)

Fixed expenses (other than depreciation)....................... (100,000,000 )Annual net cash flow...................................................................... $ 288,800,000

b. Present value of annual net cash flows ($288,800,000 × 5.650). $1,631,720,000Present value of residual value ($120,000,000 × 0.322).............. 38,640,000 Total present value......................................................................... $1,670,360,000Initial investment............................................................................ 750,000,000 Net present value............................................................................ $ 920,360,000

Ex. 26–12

Present Value Index =

Present value index of Location A: = 1.07

Present value index of Location B: = 0.96

Ex. 26–13

a. Annual net cash flow—

Sewing Machine: $97,920 = 1,700 hours × 120 incremental baseballs × $0.48

Annual net cash flow—

Packing Machine:$41,600 = 1,600 × $26 labor cost saved per hour

Sewing Machine:

Annual net cash flow (at the end of each of 8 years)....................... $ 97,920Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)..... × 4.487 Present value of annual net cash flows............................................. $439,367Less amount to be invested............................................................... 384,600 Net present value................................................................................. $ 54,767

Packing Machine:

Annual net cash flow (at the end of each of 8 years)....................... $ 41,600Present value of an annuity of $1 at 15% for 8 years (Exhibit 2)..... × 4.487 Present value of annual net cash flows............................................. $186,659Less amount to be invested............................................................... 157,900 Net present value................................................................................. $ 28,759

b. Present Value Index =

Present value index of the sewing machine: = 1.14

Present value index of the packing machine: = 1.18

c. The present value index indicates that the packing machine would be the pre-ferred investment, assuming that all other qualitative considerations are equal. Note that the net present value of the sewing machine is greater than the pack-ing machine’s. However, the sewing machine requires over double the invest-ment that the packing machine does ($384,600 vs. $157,900), for less than dou-ble extra net present value ($54,767 vs. $28,759). Thus, the present value index indicates the packing machine is favored.

Ex. 26–14

a. Average rate of return on investment: = 30%

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

$61,500 – ($246,000/10 years) = $36,900

b. Cash payback period: = 4 years

c. Present value of annual net cash flows ($61,500 × 6.145*).............. $377,918Amount to be invested........................................................................ 246,000 Net present value................................................................................. $ 131,918

*Present value of an annuity of $1 at 10% for 10 periods from Exhibit 2.

Ex. 26–15

a. Payback period: = 4 years

b. Net present value:

Present value factor for an annuity of $1, 10 periods at 10%: 6.145

Net present value = (6.145 × $600,000) – $2,400,000 = $1,287,000

c. Some critical elements that are missing from this analysis are:

The manager is viewing the acquisition of automated assembly equipment as a labor-saving device. This is probably a limited way to view the investment. Instead, the equipment should allow the company to assemble 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.

The cost of the automated assembly equipment does not stop with the initial purchase price and installation costs. The equipment will require the com-pany to hire engineers and support personnel to keep the machines running, to program the software, and to debug new programs. The operators will re-quire 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.

There will likely be a start-up or learning curve with this new technology that will cause the benefits to be delayed.

The analysis fails to account for taxes.

Ex. 26–16

a.=

=

= 3.326

b. 20% Row 6 in Exhibit 2. The column associated with the factor 3.326 is 20%.

Ex. 26–17

=

=

= 4.192

4.192 is the present value of an annuity factor for 10 years at 20% from Exhibit 2; thus, the internal rate of return on the cash flows for 10 years is 20%.

Ex. 26–18

a. Delivery Truck

Cash received from additional delivery (48,200 bags × $0.42)........ $20,244Cash used for operating expenses (18,000 miles × $0.60).............. 10,800 Net cash flow for delivery truck.......................................................... $ 9,444

=

=

= 4.160

Internal Rate of Return = 15% (from text Exhibit 2 for 7 periods)

Bagging Machine

Direct labor savings (3.0 hrs./day × $18/hr. × 250 days/yr.)............. $13,500

=

=

= 4.868

Internal Rate of Return = 10% (from text Exhibit 2 for 7 periods)

b. To: Management

Re: Investment Recommendation

An internal rate of return analysis was performed for the delivery truck and bag-ging machine investments. The internal rate of return for the bagging machine is 10%, while the delivery truck is 15% (detailed analysis available). The bagging machine fails to exceed our minimum rate of return requirement of 13%. In addi -tion, there do not appear to be any qualitative considerations that would favor the bagging machine. Therefore, the recommendation is to invest in the delivery truck.

Present Value Factor for anAnnuity of $1 for 7 Periods

Present Value Factor for anAnnuity of $1 for 7 Periods

Ex. 26–19

a. Present value of annual net cash flows ($22,000 × 4.487*).............. $ 98,714Amount to be invested........................................................................ 109,296 Net present value................................................................................. $ (10,582 )

*Present value of an annuity of $1 at 15% for 8 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 =

=

= 4.968

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

Ex. 26–20

With an expected useful life of five years, the cash payback period could not be greater than five 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 20% average rate of return and useful life are correct, the cash payback period must be less than five years. Alternatively, if both the 20% average rate of return and 5.5 years for the cash payback period are correct, the machinery must have a useful life of more than five years.

Ex. 26–21

Apartment Complex


1 0.870 $ 225,000 $ 195,7502 0.756 200,000 151,2003 0.658 200,000 131,6004 0.572 140,000 80,0804 (residual value) 0.572 325,000 185,900 Total................................................. $1,090,000 $ 744,530Amount to be invested.................. (720,000 )Net present value........................... $ 24,530

Office Building


1 0.870 $ 290,000 $ 252,3002 0.756 290,000 219,2403 0.658 230,000 151,3404 0.572 220,000 125,840

Total................................................. $1,030,000 $ 748,720Amount to be invested.................. (720,000 )Net present value........................... $ 28,720

The net present value of both projects is positive; thus, both proposals are accept-able. However, the net present value of the office building exceeds that of the apart-ment complex. Thus, the office building should be preferred if there is enough in-vestment 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. 26–22

a.

Blending Equipment

Equal annual cash flows for Years 1–5............................... $12,000Present value of a $1 annuity at 10% for five periods....... × 3.791 Present value of operating cash flows............................... $45,492Residual value at end of fifth year....................................... $ 8,000Present value of $1 at 10% for five periods........................ × 0.621 Present value of residual value........................................... 4,968 Total present value of cash flows....................................... $50,460Amount to be invested......................................................... (40,000 )Net present value.................................................................. $ 10,460

Computer System

Equal annual cash flows for Years 1–5............................... $15,500Present value of a $1 annuity at 10% for five periods....... × 3.791 Present value of cash flows................................................. $58,761Amount to be invested......................................................... (45,000 )Net present value.................................................................. $ 13,761

b.

Present value index of blending equipment: = 1.26

Present value index of computer system: = 1.31

Both the net present value calculations in part (a) and the present value index calcu-lations in part (b) suggest that the computer system should be selected between the two options if there is sufficient capital for only one project investment.

PROBLEMS

Prob. 26–1A

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

= = 17.5%

b. Net present value analysis:

Present Value of Net Cash Flow Net Cash Flow

Present Value of Tracking TrackingYear $1 at 15% Warehouse Technology Warehouse Technology

1 0.870 $138,000 $185,000 $120,060 $160,9502 0.756 138,000 165,000 104,328 124,7403 0.658 138,000 130,000 90,804 85,5404 0.572 138,000 110,000 78,936 62,9205 0.497 138,000 100,000 68,586 49,700

Total................................. $690,000 $690,000 $462,714 $483,850

Amount to be invested............................................. 480,000 480,000

Net present value...................................................... $ (17,286 ) $ 3,850

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

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

b. The tracking technology net present value exceeds the selected rate estab-lished for discounted cash flows (15%), while the warehouse does not. Thus, considering only quantitative factors, the tracking technology investment should be selected.

Prob. 26–2A

1. a. Cash payback period for both products: 2 years (the year in which accumu-lated net cash flows equal $270,000), shown as follows:

Home & Garden Music Beat Net Cash Cumulative Net Cash Cumulative

Year Flow Net Cash Flow Year Flow Net Cash Flow

1 $150,000 $150,000 1 $125,000 $125,0002 120,000 270,000 2 145,000 270,000


Present Value ofPresent Net Cash Flow Net Cash Flow Value of Home & Music Home & Music

Year $1 at 10% Garden Beat Garden Beat

1 0.909 $150,000 $125,000 $136,350 $113,6252 0.826 120,000 145,000 99,120 119,7703 0.751 105,000 100,000 78,855 75,1004 0.683 84,000 70,000 57,372 47,8105 0.621 41,000 60,000 25,461 37,260

Total............................. $500,000 $500,000 $397,158 $393,565


Net present value...................................................... $ 127,158 $ 123,565

2. The report can take many forms and should include, as a minimum, the follow-ing 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 & Gar-den magazine offers a higher net present value.

d. Both products provide a positive net present value. This means both prod-ucts would be acceptable, since they exceed the minimum rate of return.

Prob. 26–3A

1.

Branch Office Expansion


1 0.870 $350,000 $304,5002 0.756 325,000 245,7003 0.658 300,000 197,400

Total........................................................... $975,000 $747,600Amount to be invested................................................................... 700,000 Net present value............................................................................ $ 47,600

Computer System Upgrade


1 0.870 $250,000 $217,5002 0.756 225,000 170,1003 0.658 200,000 131,600

Total........................................................... $675,000 $519,200Amount to be invested................................................................... 475,000 Net present value............................................................................ $ 44,200

Install Internet Bill-Pay


1 0.870 $160,000 $139,2002 0.756 110,000 83,1603 0.658 80,000 52,640

Total........................................................... $350,000 $275,000Amount to be invested................................................................... 280,000 Net present value............................................................................ $ (5,000 )

Prob. 26–3A Concluded

2. Present Value Index =

Present value index of branch office: = 1.07*

Present value index of computer system: = 1.09*

Present value index of Internet bill-pay: = 0.98*

*Rounded

3. The computer system upgrade has the largest present value index. Although the branch office expansion has the largest net present value, it returns less present value per dollar invested than does the computer system upgrade, as revealed by the present value indexes (1.09 to 1.07). (The present value index for the Internet bill-pay is less than 1, indicating that it does not meet the minimum rate of return standard.)

Prob. 26–4A

1. a. Radio Station:

Annual net cash flow (at the end of each of 4 years)................. $ 350,000

Present value of an annuity of $1 at 10% for 4 years (Exhibit 2) ×3.170

Present value of annual net cash flows....................................... $1,109,500

Less amount to be invested.......................................................... 999,250

Net present value............................................................................ $ 110,250

TV Station:

Annual net cash flow (at the end of each of 4 years)................. $ 700,000

Present value of an annuity of $1 at 10% for 4 years (Exhibit 2) × 3.170

Present value of annual net cash flows....................................... $2,219,000

Less amount to be invested.......................................................... 2,125,900

Net present value............................................................................ $ 93,100


Present value index of the radio station: = 1.11*

Present value index of the TV station: = 1.04*

*Rounded

2. a. Present Value Factor for an Annuity of $1 =

Radio Station: = 2.855

TV Station: = 3.037

b. Internal rate of return (determined from Exhibit 2 for 4 years in text)

Radio Station: 15%

TV Station: 12%


3. By using the internal rate of return method, all proposals are placed on a com-mon basis. For example, the net present value analyses in part (1a) indicated that the net present value was greater for the TV station. However, it was neces-sary 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 internal rate of 15% is greater than the TV station’s internal rate of 12%.

Prob. 26–5A

1. Net present value analysis:

Site A:

Annual net cash flow (at the end of each of 6 years)....................... $225,000Present value of an annuity of $1 at 20% for 6 years (Exhibit 2)..... × 3.326 Present value of annual net cash flows............................................. $748,350Less amount to be invested............................................................... 565,000 Net present value................................................................................. $ 183,350

Site B:

Annual net cash flow (at the end of each of 4 years)....................... $280,000Present value of an annuity of $1 at 20% for 4 years (Exhibit 2)..... × 2.589 Present value of annual net cash flows............................................. $724,920Less amount to be invested............................................................... 565,000 Net present value................................................................................. $159,920


Present Value ofPresent Value of Net Cash Flow Net Cash Flow

Year $1 at 20% Site A Site B Site A Site B

1 0.833 $ 225,000 $ 280,000 $187,425 $233,2402 0.694 225,000 280,000 156,150 194,3203 0.579 225,000 280,000 130,275 162,1204 0.482 225,000 280,000 108,450 134,9604 (residual value) 0.482 290,000 0 139,780 0

Total.............................................. $1,190,000 $1,120,000 $722,080 $724,640Amount to be invested........................................................ 565,000 565,000 Net present value................................................................. $157,080* $159,640*

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

3. To: Investment Committee

Both Sites A and B have a positive net present value. This means that both projects meet our minimum expected return of 20% and would be acceptable in-vestments. 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 indicates that Site B has a higher net present value and would be a superior investment.

Prob. 26–6A

1. Proposal A: 3-year and 6 months cash payback period, as follows:

Net Cash CumulativeYear Flow Net Cash Flows

1 $125,000 $125,0002 125,000 250,0003 125,000 375,0006 months* 50,000 425,000

*The net cash flow required is $50,000 out of $100,000 in Year 4 or 1/2. Thus, 1/2 of 12 months is 6 months.

Proposal B: 2-year and 3 months cash payback period, as follows:


1 $280,000 $280,0002 280,000 560,0003 months* 50,000 610,000


Proposal C: 2-year and 9 months cash payback period, as follows:


1 $100,000 $100,0002 100,000 200,0009 months* 75,000 275,000

*The net cash flow required is $75,000 out of $100,000 in Year 3, or 75%. Thus, 75% of 12 months is 9 months.

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


1 $60,000 $ 60,0002 60,000 120,0003 60,000 180,0003 months* 10,000 190,000


Prob. 26–6A Continued

2. Proposal A: 9.4% average rate of return, determined as follows:

= = 9.4% (rounded)

Proposal B: 26.2% average rate of return, determined as follows:

= = 26.2% (rounded)

Proposal C: 31.3% average rate of return, determined as follows:

= = 31.3% (rounded)

Proposal D: 14.7% average rate of return, determined as follows:

= = 14.7%

Prob. 26–6A Continued

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

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

A 3 yrs., 6 mos. 9.4% XB 2 yrs., 3 mos. 26.2 XC 2 yrs., 9 mos. 31.3 XD 3 yrs., 3 mos. 14.7 X*

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

4.

Proposal B


1 0.893 $ 280,000 $250,0402 0.797 280,000 223,1603 0.712 200,000 142,4004 0.636 150,000 95,4005 0.567 100,000 56,700

Total................................................................. $1,010,000 $767,700Amount to be invested................................................................... 610,000 Net present value............................................................................ $ 157,700

Proposal C


1 0.893 $100,000 $ 89,3002 0.797 100,000 79,7003 0.712 100,000 71,2004 0.636 100,000 63,6005 0.567 90,000 51,030

Total................................................................. $490,000 $354,830Amount to be invested................................................................... 275,000 Net present value............................................................................ $ 79,830



Present value index of Proposal B: = 1.26*

Present value index of Proposal C: = 1.29*

*Rounded

6. Based on the net present value, the proposals should be ranked as follows:

Proposal B: $157,700

Proposal C: $79,830

7. Based on the present value index (the amount of present value per dollar in-vested), the proposals should be ranked as follows:

Proposal C: 1.29

Proposal B: 1.26

8. The present value indexes indicate that although Proposal B has the larger net present value, it is not as attractive as Proposal C in terms of the amount of present value per dollar invested. Proposal B requires the larger investment. Thus, management should use investment resources for Proposal C before in-vesting in Proposal B.

Prob. 26–1B

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

= = 60%


Present Present Value ofValue of Net Cash Flow Net Cash Flow

Year $1 at 12% Greenhouse Skid Loader Greenhouse Skid Loader

1 0.893 $ 45,000 $ 65,000 $ 40,185 $ 58,0452 0.797 45,000 50,000 35,865 39,8503 0.712 45,000 42,000 32,040 29,9044 0.636 45,000 35,000 28,620 22,2605 0.567 45,000 33,000 25,515 18,711

Total.............................. $225,000 $225,000 $162,225 $168,770



2. The report to the capital investment committee can take many forms. The report 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 discounted cash flows, the skid loader offers a larger net present value. The skid loader has a larger net present value because larger cash flows occur 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. 26–2B

1. a. Cash payback period for both projects: 3 years (the year in which accumu-lated net cash flows equal $480,000), shown as follows:

Plant Expansion Retail Store Net Cash Cumulative Net Cash Cumulative

Year Flow Net Cash Flow Year Flow Net Cash Flow

1 $170,000 $170,000 1 $200,000 $200,0002 170,000 340,000 2 160,000 360,0003 140,000 480,000 3 120,000 480,000


Present Value of Net Cash Flow Net Cash Flow

Present Value of Plant Retail Store Plant Retail StoreYear $1 at 15% Expansion Expansion Expansion Expansion

1 0.870 $170,000 $200,000 $147,900 $174,0002 0.756 170,000 160,000 128,520 120,9603 0.658 140,000 120,000 92,120 78,9604 0.572 110,000 120,000 62,920 68,6405 0.497 120,000 110,000 59,640 54,670

Total.............................. $710,000 $710,000 $491,100 $497,230



2. The report can take many forms and should include, as a minimum, the follow-ing 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 retail store 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 return.

Prob. 26–3B

1.

New Maintenance Yard


1 0.833 $ 7,400,000 $ 6,164,2002 0.694 6,000,000 4,164,0003 0.579 5,500,000 3,184,500

Total................................................ $18,900,000 $13,512,700Amount to be invested........................................................ 14,000,000 Net present value................................................................ $ (487,300 )

Acquire Railcars


1 0.833 $32,000,000 $26,656,0002 0.694 24,500,000 17,003,0003 0.579 15,800,000 9,148,200

Total................................................ $72,300,000 $52,807,200Amount to be invested........................................................ 45,000,000 Net present value................................................................ $ 7,807,200

Route Expansion


1 0.833 $18,500,000 $15,410,5002 0.694 14,500,000 10,063,0003 0.579 10,800,000 6,253,200

Total................................................ $43,800,000 $31,726,700Amount to be invested........................................................ 25,000,000 Net present value................................................................ $ 6,726,700

Prob. 26–3B Concluded


Present value index of new maintenance yard: = 0.97*

Present value index of railcars: = 1.17*

Present value index of route expansion: = 1.27*

*Rounded

3. The route expansion has the largest present value index. Although acquire rail-cars has the largest net present value, it returns less present value per dollar in-vested than does the route expansion, as revealed by the present value indexes (1.27 to 1.17). (The present value index for the maintenance yard is less than 1, indicating that it does not meet the minimum rate of return standard.)

Prob. 26–4B

1. a. Generating Unit:

Annual net cash flow (at the end of each of 4 years)................. $ 580,000Present value of an annuity of $1 at 6% for 4 years (Exhibit 2). × 3.465 Present value of annual net cash flows....................................... $2,009,700Less amount to be invested.......................................................... 1,761,460 Net present value............................................................................ $ 248,240

Distribution Network Expansion:

Annual net cash flow (at the end of each of 4 years)................. $210,000Present value of an annuity of $1 at 6% for 4 years (Exhibit 2). × 3.465 Present value of annual net cash flows....................................... $727,650Less amount to be invested.......................................................... 665,700 Net present value............................................................................ $ 61,950


Present value index of the generating unit: = 1.14*

Present value index of the distribution network expansion: = 1.09*

*Rounded

2. a. Present Value Factor for an Annuity of $1 =

Generating unit: = 3.037

Distribution network expansion: = 3.170

b. Internal rate of return (determined from Exhibit 2 for 4 years in text)

Generating unit: 12%

Distribution network expansion: 10%

3. By using the internal rate of return method, all projects are placed on a common basis. For example, it was necessary to use the present value index to deter-mine that the generating unit had a greater present value per dollar of invest-ment (greater rate of return). By using the internal rate of return method, it can be easily seen that the generating unit’s rate of return of 12% is greater than the distribution network expansion’s rate of 10%.

Prob. 26–5B


Project I:

Annual net cash flow (at the end of each of 6 years).................... $ 90,000Present value of an annuity of $1 at 12% for 6 years (Exhibit 2). . × 4.111 Present value of annual net cash flows.......................................... $369,990Less amount to be invested............................................................. 300,000 Net present value.............................................................................. $ 69,990

Project II:

Annual net cash flow (at the end of each of 4 years).................... $125,000Present value of an annuity of $1 at 12% for 4 years (Exhibit 2). . × 3.037 Present value of annual net cash flows.......................................... $379,625Less amount to be invested............................................................. 300,000 Net present value.............................................................................. $ 79,625


Present Value ofPresent Value of Net Cash Flow Net Cash Flow

Year $1 at 12% Project I Project II Project I Project II

1 0.893 $ 90,000 $125,000 $ 80,370 $111,6252 0.797 90,000 125,000 71,730 99,6253 0.712 90,000 125,000 64,080 89,0004 0.636 90,000 125,000 57,240 79,5004 (residual value) 0.636 175,000 0 111,300 0 Total........................................... $535,000 $500,000 $384,720 $379,750Amount to be invested................................................... 300,000 300,000 Net present value........................................................... $ 84,720 * $ 79,750 *

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

3. 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 12% and would be acceptable in-vestments. 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 indicates that Project I has a higher net present value and would be a superior investment.

Prob. 26–6B

1. Proposal A: 3-year, 3-month cash payback period, as follows:


1 $170,000 $170,0002 130,000 300,0003 100,000 400,0003 months* 20,000 420,000

*The cash flow required is $20,000 out of $80,000 in Year 4. Thus, 25% of 12 months is 3 months.

Proposal B: 2-year, 10-month cash payback period, as follows:


1 $300,000 $300,0002 300,000 600,000

10 months* 250,000 850,000

*The cash flow required for investment payback in Year 3 is $250,000, which is five-sixths ($250,000/$300,000) of Year 3’s cash flow. Thus, 10 months (five-sixths of 12 months) are needed to accumulate an additional $250,000.

Proposal C: 4-year cash payback period, as follows:


1 $70,000 $ 70,0002 70,000 140,0003 70,000 210,0004 40,000 250,000

Proposal D: 2-year, 6-month cash payback period, as follows:


1 $90,000 $ 90,0002 60,000 150,0006 months* 30,000 180,000

*The cash flow required for investment payback in Year 3 is $30,000, which is one-half ($30,000/$60,000) of Year 3’s cash flow. Thus, 6 months (one-half of 12 months) are needed to accumulate an additional $30,000.

Prob. 26–6B Continued

2. Proposal A: 13.3% average rate of return, determined as follows:

= = 13.3%

Proposal B: 28.2% average rate of return, determined as follows:

= = 28.2%

Proposal C: 6.4% average rate of return, determined as follows:

= = 6.4%

Proposal D: 28.9% average rate of return, determined as follows:

= = 28.9%

Prob. 26–6B Continued

3. Of the four proposed investments, only Proposals A and C meet the company’s requirements, as the following table indicates:

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

A 3 yrs., 3 mos. 13.3% X*B 2 yrs., 10 mos. 28.2 XC 4 yrs. 6.4 XD 2 yrs., 6 mos. 28.9 X

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

4.

Proposal B


1 0.870 $ 300,000 $261,0002 0.756 300,000 226,8003 0.658 300,000 197,4004 0.572 300,000 171,6005 0.497 250,000 124,250

Total................................................................. $1,450,000 $981,050Amount to be invested................................................................... 850,000 Net present value............................................................................ $ 131,050

Proposal D


1 0.870 $ 90,000 $ 78,3002 0.756 60,000 45,3603 0.658 60,000 39,4804 0.572 50,000 28,6005 0.497 50,000 24,850

Total................................................................. $310,000 $216,590Amount to be invested................................................................... 180,000 Net present value............................................................................ $ 36,590

Prob. 26–6B Concluded


Present value index of Proposal B: = 1.15*

Present value index of Proposal D: = 1.20*

*Rounded.

6. Based on the net present value, the proposals should be ranked as follows:

Proposal B: $131,050

Proposal D: $36,590

7. Based on the present value index (the amount of present value per dollar in-vested), the proposals should be ranked as follows:

Proposal D: 1.20

Proposal B: 1.15

8. The present value indexes indicate that although Proposal B has the larger net present value, it is not as attractive as Proposal D in terms of the amount of present value per dollar invested. Proposal B requires the larger investment. Thus, management should use investment resources for Proposal D before in-vesting in Proposal B.

SPECIAL ACTIVITIES

Activity 26–1

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 Dawn.

Dawn made an honest effort to discuss the assumptions. Dawn’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. Dawn needs to respond strongly to this attempt by I. M. to circumvent the process by countering his argument. For example, Dawn might point out that it is by no means clear that more storage space translates into more sales. In fact, it is proba-bly 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 guaran-teed 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. Dawn 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. Dawn 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 Dawn 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 Dawn. Much time will have passed, and Dawn will likely be in another job in the company. The decision to con-front I. M. has immediate repercussions. This is the heart of real world ethical dilem-mas. The dilemma occurs when the ethical decision has grave short-term conse-quences (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 difficult 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 26–2

1. Annual salary.............................................................................. $ 46,000Present 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)................................................................................... $ 282,670

2. Annual tuition at the beginning of the graduate year............. $ (10,000 )

Annual salary.............................................................................. $ 57,000Present value of $1 annuity for 9 years at 10%....................... × 5.759 Present value salary to end of graduate year.......................... $ 328,263Present value of $1 for 1 year at 10%....................................... × 0.909 Present value of salary at the beginning of graduate year.... $ 298,391

Present value of graduate option at beginning of graduateyear (salary less tuition)....................................................... $ 288,391

Note: The present values of parts (1) and (2) 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.

0 1 2 3 4 5 6 7 8 9 10

($10,000) 57K 57K 57K 57K 57K 57K 57K 57K 57K

$298,391 ($57,000 5.759) 0.909

$288,391

3. Present value of graduate option............................................. $ 288,391Present value of undergraduate option................................... 282,670 Net benefit of graduate option.................................................. $ 5,721

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 26–3

a. Since all the net 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 decline. 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 local 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 re-duce 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 lo -cal 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 de-cline. 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. 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 increase, increasing the internal rate of return.

Activity 26–4

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 at-tempt at a financial investment analysis could be highly suspect. Instead, these managers rely on strategic considerations. These considerations include respond-ing to competitors, developing new markets and products for customers, and im-proving 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 26–5

a. (All amounts are in millions.)

2011 cash flow:

Gross ticket sales........................................................... $235Production cost.............................................................. (195)Marketing cost................................................................ (50 )

Net cash flow from theatrical release................................ $ (10 )

2012 Home video sales....................................................... $ 362013 Pay TV.......................................................................... 432014 Syndication................................................................. 12

Net present value:


2011 0.833 $(10) $ (8)2012 0.694 36 252013 0.579 43 252014 0.482 12 6 Net present value................................................................. $ 48

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.

Activity 26–6

This activity could be assigned individually or in groups. This activity has the stu-dent(s) perform a capital investment analysis for a desktop computer, using infor-mation available to them on the Internet and from a local business. The actual an-swer 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............................................................ $8 per hourSemester cost (40 hours × $8)........................................................ $320

Present value of $320 for 6 semiannual periods at 5%($320 × 5.07569)..................................................................... $1,624

Less assumed price of a mid-range computer............................. 1,200 Net present value............................................................................. $ 424

The computer should be purchased.