EXERCISES. Testing Equipment Vehicle Estimated average annual income: $24,300/6... $4,050 $15,000/8... $1,875

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1 Ex (FIN MAN); Ex (MAN) EXERCISES Testing Equipment Vehicle Estimated average annual income: $24,300/6... $4,050 $15,000/8... $1,875 Average investment: ($90, )/2... $45,000 ($25, )/2... $12,500 Average rate of return: $4,050/$45, % $1,875/$12, % Ex (FIN MAN); Ex (MAN) Average Rate of Return Average Annual Income Average Investment Average Savings* AnnualDepreciation Beginning Cost + Residual Value / 2 $ 30,000 [($90,000 $10,000)/10 years] $4,500 ($90,000 + $10,000)/2 $17,500 $50,000 35% Additional Operating Costs *The effect of the savings in wages expense is an increase in income. 460

2 Ex (FIN MAN); Ex (MAN) Average Rate of Return Average Annual Income Average Investment Annual Revenues Annual Product Costs * Beginning Cost + Residual Value / 2 $ 370 2,100 units $250 2,100 units $920,000 + $88,000 / 2 $252,000 $504,000 50% *The depreciation of the equipment is included in the factory overhead cost per unit. Ex (FIN MAN); Ex (MAN) Year 1 Years 2 9 Last Year Initial investment... $(177,000) Operating cash flows: Annual revenues (10,000 units $58)... $ 580,000 $ 580,000 $ 580,000 Selling expenses (5% $580,000)... (29,000) (29,000) (29,000) Cost to manufacture (10,000 units $47.20)*... (472,000) (472,000) (472,000) Net operating cash flows... $ 79,000 $ 79,000 $ 79,000 Total for Year 1... $ (98,000) Total for Years 2 9 (operating cash flow)... $ 79,000 Residual value... Total for last year... 13,000 $ 92,000 *The fixed overhead relates to the depreciation on the equipment. Depreciation is not a cash flow and should not be considered in the analysis. 461

3 Ex (FIN MAN); Ex (MAN) Location 1: $320,000/$64,000 5-year cash payback period. Location 2: 4-year cash payback period, as indicated below. Net Cash Cumulative Flow Net Cash Flows Year 1... $110,000 $110,000 Year , ,000 Year , ,000 Year , ,000 Ex (FIN MAN); Ex (MAN) a. The Body Lotion product line is recommended, based of its shorter cash payback period. The cash payback period for both products can be determined using the following schedule: Initial investment: $660,000 Liquid Soap Body Lotion Net Cash Cumulative Net Net Cash Cumulative Net Flow Cash Flows Flow Cash Flows Year 1 $110,000 $110,000 $210,000 $210,000 Year 2 110, , , ,000 Year 3 110, , , ,000 Year 4 110, , , ,000 Year 5 110, ,000 Year 6 110, ,000 Body Lotion has a four-year cash payback period, and Liquid Soap has a sixyear cash payback. b. The cash payback periods are different between the two product lines because Body Lotion earns cash faster than does Liquid Soap. Even though both products earn the same total net cash flow over the eight-year planning horizon, Body Lotion 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. 462

4 Ex (FIN MAN); Ex (MAN) a. Present Value Net Cash Present Value of Year of $1 at 15% Flow Net Cash Flow $ 65,000 $ 56, ,000 42, ,000 27, ,000 14,300 Total... $188,000 $140,822 Amount to be invested... Net present value ,000 $ 14,822 b. Yes. The $14,822 net present value indicates that the return on the proposal is greater than the minimum desired rate of return of 15%. Ex (FIN MAN); Ex (MAN) a Revenues... $ 62,000 $ 62,000 $ 62,000 $ 62,000 $ 62,000 Driver salary... (45,000) (47,000) (49,000) (51,000) (53,000) Insurance... (3,000) (3,000) (3,000) (3,000) (3,000) Residual value... 12,000 Annual net cash flow... $ 14,000 $ 12,000 $ 10,000 $ 8,000 $ 18,000 b. Net Cash Flow Present Value of Present Value of Year [from part (a)] $1 at 12% Net Cash Flow 2012 $14, $12, , , , , , , , ,206 Total present value of cash flows... $44,480 Investment in delivery truck... Net present value of delivery truck... 48,000 $ (3,520) 463

5 Ex (FIN MAN); Ex (MAN) (Concluded) 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 negative. Thus, this analysis does not support investment in the truck. Ex (FIN MAN); Ex (MAN) a. (in millions) Annual revenues... $58 Total expenses... $32 Less noncash depreciation expense... 7 Annual cash expenses Annual net cash flow... $33 *Annual depreciation expense, $210 million/30 years $7 million per year b. (in millions, except present value factor) Annual net cash flow... $ 33 Present value of an annuity of $1 at 14% for 30 periods * Present value of hotel project cash flows, rounded... $ 231 Less hotel construction costs... Net present value of hotel project... $ *From Appendix A in the text c. The present value of the hotel s operating cash flows exceeds the construction costs by $21 million. That is, the net present value is positive. Therefore, construction of the new hotel can be supported by this analysis. 464

6 Ex (FIN MAN); Ex (MAN) a. Cash inflows: Hours of operation... 1,400 Revenue per hour... $ Revenue per year... $ 147,000 Cash outflows: Hours of operation... 1,400 Fuel cost per hour... $38.00 Labor cost per hour Total fuel and labor costs per hour... $72.00 Fuel and labor costs per year... (100,800) Maintenance costs per year... (9,000) Annual net cash flow... $ 37,200 b. Annual net cash flow (at the end of each of five years)... $ 37,200 Present value of annuity of $1 at 10% for five periods Present value of annual net cash flows... $ 141,025 Less amount to be invested... Net present value ,000 $ 21,025 c. Yes. Easton 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%. d [(Hrs. $105) (Hrs. $72) $9,000] $120,000 (Hrs. $398) (Hrs. $273) $34,119 $120,000 Hrs. $125 $154,119 Hrs. 1,233 (rounded) Thus, the bulldozer operating hours must exceed 1,233 annually in order for the investment to be justified. 465

7 Ex (FIN MAN); Ex (MAN) a. Revenues (3, days $280)... $ 322,560,000 Less: Variable expenses (3, days $95)... (109,440,000) Fixed expenses (other than depreciation)... (65,000,000) Annual net cash flow... $ 148,120,000 b. Present value of annual net cash flows ($148,120, ) $836,878,000 Present value of residual value ($100,000, )... 32,200,000 Total present value... $869,078,000 Initial investment... Net present value ,000,000 $119,078,000 Ex (FIN MAN); Ex (MAN) a. Present Value Index Present value index of Mason City: Present value index of Cedar Rapids: Total Present Value of Net Cash Flow $455,900 $485,000 $565,760 $544, b. The analysis supports investing in Cedar Rapids because the present value index is greater than one. The Mason City investment is not supported. 466

8 Ex (FIN MAN); Ex (MAN) a. Annual net cash flow Sewing Machine: $100,980 1,700 hours 110 incremental baseballs $0.54 per baseball Annual net cash flow Packing Machine: $40,000 1,600 hours $25 labor cost saved per hour Sewing Machine: Annual net cash flow (at the end of each of 8 years)... $100,980 Present value of an annuity of $1 at 15% for 8 years (Exhibit 2) Present value of annual net cash flows... $453,097 Less amount to be invested ,000 Net present value... $ 93,097 Packing Machine: Annual net cash flow (at the end of each of 8 years)... $ 40,000 Present value of an annuity of $1 at 15% for 8 years (Exhibit 2) Present value of annual net cash flows... $179,480 Less amount to be invested... Net present value ,000 $ 59,480 b. Present Value Index Total Present Value of Net Cash Flow Present value index of the sewing machine: $453,097 $360, Present value index of the packing machine: $179,480 $120, 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 triple the investment that the packing machine does ($360,000 vs. $120,000), for less than double extra net present value ($93,097 vs. $59,480). Thus, the present value index indicates the packing machine is favored. If there were sufficient capital for both investments, then they would both be attractive opportunities. This solution does not consider the alternative use of remaining cash, which is an additional complexity beyond the scope of this text. 467

9 Ex (FIN MAN); Ex (MAN) $36,800* a. Average rate of return on investment: 13.3% $552,000/2 *The annual earnings are equal to the cash flow less the annual depreciation expense, shown as follows: $92,000 ($552,000/10 years) $36,800 b. Cash payback period: $ 552, 000 $ 92, years c. Present value of annual net cash flows ($92, *)... $565,340 Amount to be invested ,000 Net present value... $ 13,340 *Present value of an annuity of $1 at 10% for 10 periods from Exhibit 2. Ex (FIN MAN); Ex (MAN) $2,500,000 a. Payback period: 5 years $500,000 b. Net present value: Present value factor for an annuity of $1, 10 periods at 10%: Net present value (6.145 $500,000) $2,500,000 $572,500 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 company to hire engineers and support personnel to keep the machines running, to program the software, and to debug new programs. The operators will require new training. Thus, extensive training costs will likely be incurred. It would not be surprising to see a large portion of the direct labor savings lost by hiring expensive indirect labor support for the technology. 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. 468

10 Ex (FIN MAN); Ex (MAN) a. Present Value Factor for an Annuity of $1 for 6 Periods AnnualNet Cash Flow $45,420 $12, b. 15% Row 6 in Exhibit 2. The column associated with the factor is 15%. Ex (FIN MAN); Ex (MAN) a. Present Value Factor for an Annuity of $1 for 10 Periods AnnualNet Cash Flow $400 million $70.8 million is the present value of an annuity factor for 10 years at 12% from Exhibit 2; thus, the internal rate of return on the cash flows for 10 years is 12%. b. There are many uncertainties that could adversely impact a project of this scale and scope. There are uncertainties affecting the initial investment and the annual cash flow assumptions. Regarding the initial investment, the construction cost could be higher than $400 million due to delays, labor issues, and other construction site problems. The annual cash flow assumptions could be adversely impacted by uncertainties such as, 1. warm weather conditions, or no snow. 2. recessionary economic conditions that reduce the demand for ski holidays. 3. competitor property improvements that siphon demand from the project. 4. increased fuel costs that increase the cost of travel to ski resorts, thus reducing demand from non-local patrons. 5. industry overbuilding that causes a price war to maintain volume. 469

11 Ex (FIN MAN); Ex (MAN) a. Delivery Truck Cash received from additional delivery (61,000 bags $0.40)... $24,400 Cash used for operating expenses (21,000 miles $0.70)... 14,700 Net cash flow for delivery truck... $ 9,700 Present Value Factor for an Annuity of $1 for 7 Periods AnnualNet Cash Flow $ 44, 271 $ 9, Internal Rate of Return 12% (from text Exhibit 2 for 7 periods) Bagging Machine Direct labor savings (3.0 hrs./day $16/hr. 250 days/yr.)... $12,000 Present Value Factor for an Annuity of $1 for 7 Periods AnnualNet Cash Flow $49,920 $12, Internal Rate of Return 15% (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 bagging machine investments. The internal rate of return for the bagging machine is 15%, while the delivery truck is 12% (detailed analysis available). The delivery truck fails to exceed our minimum rate of return requirement of 13%. 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. 470

12 Ex (FIN MAN); Ex (MAN) a. Present value of annual net cash flows ($27, *)... $121,149 Amount to be invested ,136 Net present value... $ (12,987) *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 AnnualNet Cash Flow $134,136 $27, Internal Rate of Return 12% (from text Exhibit 2) Ex (FIN MAN); Ex (MAN) 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. In addition, 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. 471

13 Ex (FIN MAN); Ex (MAN) Processing Mill Present Value Net Cash Present Value of Year of $1 at 15% Flow Net Cash Flow $ 280,000 $ 243, , , , , , ,400 4 (residual value) , ,200 Total... $1,330,000 $ 911,700 Amount to be invested... (840,000) Net present value... $ 71,700 Electric Shovel Present Value Net Cash Present Value of Year of $1 at 15% Flow Net Cash Flow $ 350,000 $ 304, , , , , , ,600 Total... $1,275,000 $ 919,200 Amount to be invested... (840,000) Net present value... $ 79,200 The net present value of both proposals is positive; thus, both pieces of equipment are acceptable. However, the net present value of the electric shovel exceeds that of the processing mill. Thus, the electric shovel 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. 472

14 Ex (FIN MAN); Ex (MAN) a. Blending Equipment Equal annual cash flows for Years $ 16,000 Present value of a $1 annuity at 10% for five periods Present value of operating cash flows... $ 60,656 Residual value at end of fifth year... $ 10,000 Present value of $1 at 10% for five periods Present value of residual value... 6,210 Total present value of cash flows... $ 66,866 Amount to be invested... (60,000) Net present value... $ 6,866 Computer System Equal annual cash flows for Years $ 20,000 Present value of a $1 annuity at 10% for five periods Present value of cash flows... $ 75,820 Amount to be invested... (70,000) Net present value... $ 5,820 b. Present value index of blending equipment: $66,866 $60, Present value index of computer system: $ 75, 820 $ 70, Both the net present value calculations in part (a) and the present value index calculations in part (b) suggest that the blending equipment should be selected between the two options if there is sufficient capital for only one project investment. 473

15 PROBLEMS Prob. 25 1A (FIN MAN); Prob. 10 1A (MAN) 1. a. Average annual rate of return for both projects: $36,000/5 $64,000 $0 /2 $7, % $32,000 b. Net present value analysis: Present Present Value of Value of Net Cash Flow Net Cash Flow Year $1 at 12% Greenhouse Skid Loader Greenhouse Skid Loader $ 35,000 $ 20,000 $31,255 $17, ,000 20,000 19,925 15, ,000 20,000 14,240 14, ,000 20,000 6,360 12, ,000 20,000 5,670 11,340 Total... $100,000 $100,000 $77,450 $72,100 Amount to be invested... 64,000 64,000 Net present value... $13,450 $ 8, 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 greenhouse offers a larger net present value. The greenhouse has a larger net present value because larger cash flows occur earlier in time compared to the skid loader. Thus, if only one of the two projects can be accepted, the greenhouse would be the more attractive. 474

16 Prob. 25 2A (FIN MAN); Prob. 10 2A (MAN) 1. a. Cash payback period for both projects: 2 years (the year in which accumulated net cash flows equal $700,000), shown as follows: Plant Expansion Retail Store Expansion Net Cash Cumulative Net Cash Cumulative Year Flow Net Cash Flow Year Flow Net Cash Flow 1 $350,000 $350,000 1 $360,000 $360, , , , ,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 15% Expansion Expansion Expansion Expansion $ 350,000 $ 360,000 $304,500 $313, , , , , , ,000 92,120 92, , ,000 51,480 57, ,000 60,000 34,790 29,820 Total... $1,000,000 $1,000,000 $747,490 $749,380 Amount to be invested , ,000 Net present value... $ 47,490 $ 49, The report can take many forms and should include, as a minimum, the following 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 expansion 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. 475

17 Prob. 25 3A (FIN MAN); Prob. 10 3A (MAN) 1. New Maintenance Yard Present Value Net Cash Present Value of Year of $1 at 20% Flow Net Cash Flow $ 6,000,000 $ 4,998, ,800,000 3,331, ,500,000 2,605,500 Total... $15,300,000 $ 10,934,700 Amount to be invested... Net present value... 12,000,000 $ (1,065,300) Route Expansion Present Value Net Cash Present Value of Year of $1 at 20% Flow Net Cash Flow $12,000,000 $ 9,996, ,000,000 7,634, ,500,000 5,500,500 Total... $32,500,000 $ 23,130,500 Amount to be invested... Net present value... 20,000,000 $ 3,130,500 Acquire Railcars Present Value Net Cash Present Value of Year of $1 at 20% Flow Net Cash Flow $22,000,000 $ 18,326, ,500,000 12,839, ,000,000 9,264,000 Total... $56,500,000 $ 40,429,000 Amount to be invested... Net present value... 36,000,000 $ 4,429,

18 Prob. 25 3A (FIN MAN); Prob. 10 3A (MAN) (Concluded) 2. Present Value Index Total Present Value of Net Cash Flow Present value index of new maintenance yard: $10,934,700 $12,000, * Present value index of route expansion: Present value index of acquire railcars: *Rounded $23,130,500 $20,000,000 $40,429,000 $36,000, * 1.12* 3. The route expansion has the largest present value index. Although acquire railcars has the largest net present value, it returns less present value per dollar invested than does the route expansion, as revealed by the present value indexes (1.16 to 1.12). (The present value index for the maintenance yard is less than 1, indicating that it does not meet the minimum rate of return standard.) 477

19 Prob. 25 4A (FIN MAN); Prob. 10 4A (MAN) 1. a. Generating Unit: Annual net cash flow (at the end of each of 4 years)... $ 370,000 Present value of an annuity of $1 at 6% for 4 years (Exhibit 2) Present value of annual net cash flows... $1,282,050 Less amount to be invested... Net present value... 1,172,900 $ 109,150 Distribution Network Expansion: Annual net cash flow (at the end of each of 4 years)... $280,000 Present value of an annuity of $1 at 6% for 4 years (Exhibit 2) Present value of annual net cash flows... $970,200 Less amount to be invested... Net present value ,360 $119,840 b. Present Value Index Total Present Value of Net Cash Flow $1,282,050 Present value index of the generating unit: 1.09* $1,172,900 $970,200 Present value index of the distribution network expansion: 1.14* $850,360 *Rounded 2. a. Present Value Factor for an Annuity of $1 AnnualNet Cash Flow Generating unit: $1,172, $370,000 $850,360 Distribution network expansion: $280,000 b. Internal rate of return (determined from Exhibit 2 for 4 years in text) Generating unit: 10% Distribution network expansion: 12% 478

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