Solution to Extra Problems - Capital Budgeting Criteria | ACCT 301, Study notes of Accounting

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Solutions to extra problems – capital budgeting criteria SOLUTIONS

1. A project has an initial cost of $43,000 and produces cash inflows of $14,000, $23,000, $30,000 over the next three years, respectively. What is the payback period if the required rate of return is 15 percent? The required rate of return is not relevant. Year CF CF needed after year-end 0 -43,000 43, 1 14,000 43,000 – 14,000 = 29, 2 23,000 29,000 – 23,000 = 6, 3 30,000 6,000 – 30,000 = -24, Payback occurs between 2 and 3 years After 2 years, $6,000 in cash flows are needed In year 3, the expected cash flow is $30, Assume cash flows occur uniformly throughout the year Therefore, it would take ($6,000 / $30,000) = 0.20 of year 3 to reach payback So payback = 2 + 0.20 = 2.20 years
2. A project has an initial cost of $33,000 and produces cash inflows of $10,000, $23,000, $30,000 over the next three years, respectively. What is the discounted payback period if the required rate of return is 15 percent? Year CF DCF = PV(CF) @ 15% DCF needed after year-end 0 -33,000 -33,000 33, 1 10,000 10,000 / 1.15 = 8,695.65 33,000 – 8,695.65 = 24,304. 2 23,000 23,000 / 1.15^2 = 17,391.30 24,304.35 – 17,391.30 = 6,913. 3 30,000 30,000 / 1.15^3 = 19,725.49 6913.05 – 19,725.49 = -12,812. Discounted payback occurs between 2 and 3 years After 2 years, $6,913.05 in discounted cash flows are needed In year 3, the expected discounted cash flow is $19,725. Assume discounted cash flows occur uniformly throughout the year Therefore, it would take ($6,913.05 / $19,725.49) = 0.35 of year 3 to reach discounted payback So discounted payback = 2 + 0.35 = 2.35 years

Solutions to extra problems – capital budgeting criteria

3. You are considering two projects with the following cash flows. Year Project A CF Project B CF 0 -50,000 -75, 1 40,000 30, 2 20,000 40, 3 30,000 50, 4 15,000 20, a. What is the NPV of each project if the cost of capital is 8%? b. What is the NPV of each project if the cost of capital is 15%? c. What is the IRR of each project? a. With an 8 percent discount rate: NPV(A) = [-50,000] + [40,000 / 1.08] + [20,000 / 1.08^2 ] + [30,000 / 1.08^3 ] + [15,000 / 1.08^4 ] = $39, NPV(B) = [-75,000] + [30,000 / 1.08] + [40,000 / 1.08^2 ] + [50,000 / 1.08^3 ] + [20,000 / 1.08^4 ] = $41, Project A: npv(8,-50000,{40000,20000,30000,15000})  39, Project B: npv(8,-75000,{30000,40000,50000,20000})  41, b. With a 15 percent discount rate: NPV(A) = [-50,000] + [40,000 / 1.15] + [20,000 / 1.15^2 ] + [30,000 / 1.15^3 ] + [15,000 / 1.15^4 ] = $28, NPV(B) = [-75,000] + [30,000 / 1.15] + [40,000 / 1.15^2 ]+ [50,000 / 1.15^3 ] + [20,000 / 1.15^4 ] = $25, Project A: npv(15,-50000,{40000,20000,30000,15000})  28, Project B: npv(15,-75000,{30000,40000,50000,20000})  25, c. IRR Project A: 0 = [-50,000] + [40,000/(1+IRR)] + [20,000/(1+IRR)^2 ] + [30,000/(1+IRR)^3 ] + [15,000/(1+IRR)^4 ] irr(-50000,{40000,20000,30000,15000})  45.54, so IRR = 45.54% Project B: 0 = [-75,000] + [30,000/(1+IRR)] + [40,000/(1+IRR)^2 ] + [50,000/(1+IRR)^3 ] + [20,000/(1+IRR)^4 ] irr(-75000,{30000,40000,50000,20000})  31.19, so IRR = 31.19%

Solutions to extra problems – capital budgeting criteria

4. The following table presents information on 5 potential projects with conventional cash flows currently being evaluated by a medium-size clothing retailer. Cash flows are in terms of millions of dollars and the discount rate is the opportunity cost of capital. Project Cash flows (number of years from today) Discount 0 1 2 3 4 rate A -100 15 90 0 25 7% B -100 61 61 0 0 8% C -200 230 0 0 0 6% D -200 60 60 60 60 9% E -200 0 130 130 0 10% a. What is the NPV of each project and which projects should be chosen based on NPV? In millions: NPV(A) = [-100] + [15 / 1.07] + [90 / 1.07^2 ] + [0 / 1.07^3 ] + [25 / 1.07^4 ] = 11. NPV(B) = [-100] + [61 / 1.08] + [61 / 1.08^2 ] + [0 / 1.08^3 ] + [0 / 1.08^4 ] = 8. NPV(C) = [-200] + [230 / 1.06] + [0 / 1.06^2 ] + [0 / 1.06^3 ] + [0 / 1.06^4 ] =16. NPV(D) = [-200] + [60 / 1.09] + [60 / 1.09^2 ] + [60 / 1.09^3 ] + [60 / 1.09^4 ] = -5. NPV(E) = [-200] + [0 / 1.10] + [130 / 1.10^2 ] + [130 / 1.10^3 ] + [0 / 1.10^4 ] = 5. In millions: Project A: npv(7,-100,{15,90,0,25})  11. Project B: npv(8,-100,{61,61,0,0})  8. Project C: npv(6,-200,{230,0,0,0})  16. Project D: npv(9,-200,{60,60,60,60})  -5. Project E: npv(10,-200,{0,130,130,0})  5. Projects A, B, C, and E should be accepted, because they have positive NPV b. How much value would be created by selecting the projects chosen in part a? The amount of value that would be created is the sum of the chosen projects’ NPVs 11.70 + 8.78 + 16.98 + 5.11 = 42.57 (in millions) Note that the most value that can be created would occur when managers choose all projects with positive NPV. Therefore, the maximum amount of value that can be created by the firm would be $42.57 million. Any combination of projects other than A, B, C, and E would result in less value being created.

Solutions to extra problems – capital budgeting criteria

4. Continued c. What is the IRR of each project and which projects should be chosen based on IRR exceeding the cost of capital? Project A: irr(-100,{15,90,0,25})  12.53 percent > 7 percent, so accept project Project B: irr(-100,{61,61,0,0})  14.35 percent > 8 percent, so accept project Project C: irr(-200,{230,0,0,0})  15.00 percent > 6 percent, so accept project Project D: irr(-200,{60,60,60,60})  7.71 percent < 9 percent, so reject project Project E: irr(-200,{0,130,130,0})  11.13 percent > 10 percent, so accept project Projects A, B, C, and E should be accepted, because they have IRR > their cost of capital Note that all of the projects have conventional cash flows, so IRR agrees with NPV. The projects that are accepted with NPV are accepted with IRR and the projects that are rejected by NPV are rejected by IRR. d. How much value would be created by selecting the projects chosen in part c? The amount of value that would be created is the sum of the of the chosen projects’ NPVs 11.70 + 8.78 + 16.98 + 5.11 = 42.57 (in millions) e. What is the payback period of each project and which projects should be chosen if the payback threshold is 2 years? Assume cash flows occur uniformly throughout the year Project A (in millions) Year CF CF needed after year-end 0 -100 100 1 15 100 – 15 = 85 2 90 85 – 90 = - 3 0 4 25 Payback occurs between 1 and 2 years After 1 year, $85 million in cash flows are needed In year 2, the expected cash flow is $90 million Therefore, it would take ($85m / $90m) = 0.94 of year 2 to reach payback So payback = 1 + 0.94 = 1.94 years

Solutions to extra problems – capital budgeting criteria

4. Continued e. Continued Project B (in millions) Year CF CF needed after year-end 0 -100 100 1 61 100 – 61 = 39 2 61 39 – 61 = - 3 0 4 0 Payback occurs between 1 and 2 years After 1 year, $39 million in cash flows are needed In year 2, the expected cash flow is $61 million Therefore, it would take ($39m / $61m) = 0.64 of year 2 to reach payback So payback = 1 + 0.64 = 1.64 years Project C (in millions) Year CF CF needed after year-end 0 -200 200 1 230 200 – 230 = - 2 0 3 0 4 0 Payback occurs between 0 and 1 year After 0 years, $200 million in cash flows are needed In year 1, the expected cash flow is $230 million, which is more than $200 million Therefore, it would take ($200m / $230m) = 0.87 of year 1 to reach payback So payback = 0 + 0.887 = 0.87 years Project D (in millions) Year CF CF needed after year-end 0 -200 200 1 60 200 – 60 = 140 2 60 140 – 60 = 80 3 60 80 – 60 = 20 4 60 20 – 60 = - Payback occurs between 3 and 4 years After 3 years, $20 million in cash flows are needed In year 4, the expected cash flow is $60 million Therefore, it would take ($20m / $60m) = 0.33 of year 4 to reach payback So payback = 3 + 0.33 = 3.33 years

Solutions to extra problems – capital budgeting criteria

4. Continued e. Continued Project E (in millions) Year CF CF needed after year-end 0 -200 200 1 0 200 – 0 = 200 2 130 200 – 130 = 70 3 130 70 – 130 = - 4 0 Payback occurs between 2 and 3 years After 2 years, $70 million in cash flows are needed In year 3, the expected cash flow is $130 million Therefore, it would take ($70m / $130m) = 0.54 of year 3 to reach payback So payback = 2 + 0.54 = 2.54 years Projects A, B, and C should be accepted, because they have payback ≤ 2 years Note that project E, which has a positive NPV is rejected with the payback method. The payback method can lead to positive NPV projects being rejected. Moreover, the payback method can also lead to negative NPV projects being accepted. f. How much value would be created by selecting the projects chosen in part e? The amount of value that would be created is the sum of the of the chosen projects’ NPVs 11.70 + 8.78 + 16.98 = 37.46 (in millions) g. What is the discounted payback period of each project and which projects should be chosen if the discounted payback threshold is 2 years? Assume discounted cash flows occur uniformly throughout the year. However, discount cash flows as if they occur at end of year. Also, discounted cash flows are rounded to one decimal place for simplicity and convenience Project A (in millions) Year CF DCF = PV(CF) @ 7% DCF needed after year-end 0 -100 -100 100 1 15 15 / 1.07 = 14.0 100 – 14.0 = 86. 2 90 90 / 1.07^2 = 78.6 86.0 – 78.6 = 7. 3 0 0 / 1.07^3 = 0 7.4 – 0 = 7. 4 25 25 / 1.07^4 = 19.1 7.4 – 19.1 = -11. Discounted payback occurs between 3 and 4 years After 3 years, $7.4 million in discounted cash flows are needed In year 4, the expected discounted cash flow is $19.1 million Therefore, it would take ($7.4m / $19.1m) = 0.39 of year 4 to reach discounted payback So discounted payback = 3 + 0.39 = 3.39 years

Solutions to extra problems – capital budgeting criteria

4. Continued g. Continued Project B (in millions) Year CF DCF = PV(CF) @ 8% DCF needed after year-end 0 -100 -100 100 1 61 61 / 1.08 = 56.5 100 – 56.5 = 43. 2 61 61 / 1.08^2 = 52.3 43.5 – 52.3 = -8. 3 0 0 / 1.08^3 = 0 7.4 – 0 = 7. 4 0 0 / 1.08^4 = 0 7.4 – 19.1 = -11. Discounted payback occurs between 1 and 2 years After 1 year, $43.5 million in discounted cash flows are needed In year 2, the expected discounted cash flow is $52.3 million Therefore, it would take ($43.5m / $52.3m) = 0.83 of year 2 to reach discounted payback So discounted payback = 1 + 0.83 = 1.83 years Project C (in millions) Year CF DCF = PV(CF) @ 6% DCF needed after year-end 0 -200 -200 200 1 230 230 / 1.06 = 217.0 200 – 217.0 = -17. 2 0 0 / 1.06^2 = 0 3 0 0 / 1.06^3 = 0 4 0 0 / 1.06^4 = 0 Discounted payback occurs between 0 and 1 year After 0 years, $200 million in discounted cash flows are needed In year 1, the expected discounted cash flow is $217.0 million Therefore, it would take ($200m / $217.0m) = 0.92 of year 1 to reach discounted payback So discounted payback = 0 + 0.92 = 0.92 years Project D (in millions) Year CF DCF = PV(CF) @ 9% DCF needed after year-end 0 -200 -200 200 1 60 60 / 1.09 = 55.0 200 – 55.0 = 145. 2 60 60 / 1.09^2 = 50.5 145.0 – 50.5 = 94. 3 60 60 / 1.09^3 = 46.3 94.5 – 46.3 = 48. 4 60 60 / 1.09^4 = 42.5 48.2 – 42.5 = 5. Discounted payback never occurs After 4 years, when the project is over, $5.7 million in discounted cash flows are still needed to reach discounted payback

Solutions to extra problems – capital budgeting criteria

4. Continued g. Continued Project E (in millions) Year CF DCF = PV(CF) @ 10% DCF needed after year-end 0 -200 -200 200 1 0 0 / 1.10 = 0.0 200 – 0.0 = 200. 2 130 130 / 1.10^2 = 107.4 200.0 – 107.4 = 92. 3 130 130 / 1.10^3 = 97.7 92.6 – 97.7 = -5. 4 0 0 / 1.10^4 = 0 Discounted payback occurs between 2 and 3 years After 2 years, $92.6 million in discounted cash flows are needed In year 3, the expected discounted cash flow is $97.7 million Therefore, it would take ($92.6m / $97.7m) = 0.95 of year 3 to reach discounted payback So discounted payback = 2 + 0.95 = 2.95 years Projects B and C should be accepted, because they have discounted payback ≤ 2 years Note that projects A and E, which have positive NPVs are rejected with the discounted payback method. The discounted payback method can lead to positive NPV projects being rejected. However, unlike the payback method, the discounted payback method can not lead to negative NPV projects being accepted. h. How much value would be created by selecting the projects chosen in part g? The amount of value that would be created is the sum of the of the chosen projects’ NPVs 8.78 + 16.98 = 25.76 (in millions) i. Which project is the riskiest? Project E is the riskiest project. It has the highest cost of capital, which is the only relevant piece of information for answering this question. Note that project C is the least risky as it has the lowest cost of capital.

Solutions to extra problems – capital budgeting criteria

5. Villanova Corporation accepts projects that have a payback period of 2.3 years or less. It is currently looking at an opportunity with conventional cash flows that would last for 3 years. The project would require an initial investment of $50,000, produce cash flows of $18,000 in the first year, and produce $26,000 in the second year. What is the lowest amount of cash flows that could be produced in the third year for this project to be accepted? The lowest amount of cash flows that can be produced in the third year that results in a payback period of 2.3 years or less is the cash flow that leads to payback of 2.3 years. All smaller cash flows would lead to the payback period being greater than 2.3 years, so the project would not be accepted. All larger cash flows would lead to the payback period being less than 2.3 years, so the project would be accepted, but there would be a lower cash flow for which the project would still be accepted. After 2 years, the project is expected to produce $18,000 + $26,000 = $44,000 in cumulative cash flows The investment is $50,000, so the project would still need to produce cash flows of $50,000 – $44,000 = $6,000 for payback To just satisfy the payback threshold of 2.3 years, payback must occur at 0.3 of year 3 Therefore, 0.3 = $6,000 / cash flow in year 3 So, cash flow in year 3 = $6,000 / 0.3 = $20, The lowest amount of cash that could be produced in the third year for this project to be accepted is $20,000. More than $20,000 and payback would happen before 2.3 years, and less than $20,000 and payback would take place after 2.3 years.

Solutions to extra problems – capital budgeting criteria

6. Creighton Corporation accepts projects that have a discounted payback period of 2.5 years or less. It is currently looking at an opportunity with conventional cash flows that would last for 3 years and have a discount rate of 9 percent. The project would require an initial investment of $50,000, produce cash flows of $18,000 in the first year, and produce $26,000 in the second year. What is the lowest amount of cash flows that could be produced in the third year for this project to be accepted? The lowest amount of cash flows that can be produced in the third year that results in a discounted payback period of 2.5 years or less is the cash flow that leads to discounted payback of 2.5 years. All smaller cash flows would lead to the discounted payback period being greater than 2.5 years, so the project would not be accepted. All larger cash flows would lead to the discounted payback period being less than 2.5 years, so the project would be accepted, but there would be a lower cash flow for which the project would still be accepted. After 2 years, the project is expected to produce cumulative discounted cash flows of [$18,000 / 1.09] + [$26,000 / 1.09^2 ] = $38,397. The investment is $50,000, so the project would still need to produce discounted cash flows of $50,000 – $38,397.44 = $11,602.56 for discounted payback To just satisfy the discounted payback threshold of 2.5 years, discounted payback must occur at 0.5 of year 3 Therefore, 0.5 = $11,602.56 / discounted cash flow in year 3 So, discounted cash flow in year 3 = $11,602.56 / 0.5 = $23,205. Recall that $23,205.12 is the discounted cash flow in year 3 needed for discounted payback to be 2. years and we want to find the cash flow in year 3 needed for discounted payback to be 2.5 years So, $23,205.12 = the actual cash flow in year 3 / 1.09^3 So, the actual cash flow in year 3 = $23,205.12 × 1.09^3 = $30,051. The lowest amount of cash that could be produced in the third year for this project to be accepted is $30,051.30. More than $30,051.30 and discounted payback would happen before 2.5 years, and less than $30,051.30 and discounted payback would take place after 2.5 years.

Solutions to extra problems – capital budgeting criteria

7. Gonzaga Corporation is currently looking at an opportunity with conventional cash flows that would last for 3 years and have a discount rate of 10 percent. The project would require an initial investment of $50,000, produce cash flows of $18,000 in the first year, and produce $26,000 in the second year. What cash flow would need to be produced in the third year for this project to destroy $2,873.78 in value? If the project destroys $2,873.78 in value, then it has an NPV of -$2,873. NPV = -2,873.78 = [-50,000] + [18,000 / 1.10] + [26,000 / 1.10^2 ] + [CF 3 / 1.10^3 ] So, [CF 3 / 1.10^3 ] = -2,873.78 + 50,000 – [18,000 / 1.10] – [26,000 / 1.10^2 ] So, CF 3 = 1.10^3 × {-2,873.78 + 50,000 – [18,000 / 1.10] – [26,000 / 1.10^2 ]} = 12, The cash flow in the third year of the project would need to be $12,345 in order for this project to destroy $2873.78 in value
8. Morehead Corporation is currently looking at an opportunity with conventional cash flows that would last for 3 years and have a discount rate of 11 percent. The project would require an initial investment of $50,000, produce cash flows of $18,000 in the first year, and produce $26,000 in the second year. What cash flow would need to be produced in the third year for this project to have no effect on value? If the project has no effect on value, then it has an NPV of 0 NPV = 0 = [-50,000] + [18,000 / 1.11] + [26,000 / 1.11^2 ] + [CF 3 / 1.11^3 ] = 0 So, [CF 3 / 1.11^3 ] = 50,000 – [18,000 / 1.11] – [26,000 / 1.11^2 ] So, CF 3 = 1.11^3 × { 50,000 – [18,000 / 1.11] – [26,000 / 1.11^2 ]} = 17,343. The cash flow in the third year of the project would need to be $17,343.75 in order for this project to have no effect on value

Solutions to extra problems – capital budgeting criteria

9. The following table presents information on 9 potential projects with conventional cash flows currently being evaluated by Blue Turtle, Inc. Cash flows are in terms of millions of dollars and the discount rate is the opportunity cost of capital. NPV is the net present value (in millions of dollars), IRR is the internal rate of return, PB is the payback period in terms of years, and DPB is discounted payback period in terms of years. None of the projects are mutually exclusive. Empty cells contain unrevealed values that may be needed to answer questions, not necessarily zeroes. Project Cash flows (number of years from today) (^) Discount 0 1 2 3 4 rate NPV IRR PB DPB A -100 33 33 33 7% 12.11% More than 3 B -100 35 60 0 15 8% -5.13 5.05% 3.33 ∞ C -100 122 0 0 0 10% 10.91 22.00% 0.82 0. D -100 30 30 30 30 9% -2.81 7.71% 3.33 ∞ E -200 0 130 125 0 6% 20.65 10.30% 2. F -200 15 100 15 100 7% -10.10 5.04% 3.70 ∞ G -200 90 180 0 0 17% 20.00% 1.61 1. H -200 70 55 70 55 6% 17.33 9.82% 3.09 3. I -200 0 0 0 300 12% -9.34 10.67% 3.67 ∞ a. How much value would be created in total by selecting all projects with a payback period of 2.60 years or less? We know that projects A, B, D, F, H, and I have payback > 2. We know that projects C and G have payback < 2. We don’t know the payback of project E For project E, the cumulative cash flow after 3 years is 0 + 130 + 125 = 255, so payback is definitely less than 3 years and could possibly be less than or equal to 2.6 years, so we should figure out what it is Investment = 200 After 1 year, 200 – 0 = 200 is needed for payback After 2 years, 200 – 130 = 70 is needed for payback In year 3, the cash flow is 125, so payback = 2 + (70/125) = 2.56 years < 2.60 years Projects E, C, and G have paybacks of 2.60 years or less The amount of value created is the sum of the chosen projects’ NPVs NPV(C) = 10. NPV(E) = 20. NPV(G) = -200 + [90/ 1.17] + [180 / 1.17^2 ] = 8. Project G: npv(17,-200,{90,180})  8. NPV(C) + NPV(E) + NPV(G) = 10.91 + 20.65 + 8.42 = 39.98 (in millions)

Solutions to extra problems – capital budgeting criteria

9. Continued b. Suppose Blue Turtle accepts projects that have a discounted payback period of 3.53 years or less. What is the lowest amount of cash flows that could be produced in the fourth year for project A to be accepted? Find the cash flows such that the discounted payback of project A is 3.53 years. The initial investment is 100 After 3 years, the project is expected to have cumulated discounted cash flows of [33/ 1.07] + [33 / 1.07^2 ] + [33 / 1.07^3 ] = 86. In the fourth year, 100 – 86.60 = 13.40 million in discounted cash flows are needed If cash flows take place through 0.53 of the year, then 0.53 = 13.40 / total DCF in year 4 So, total DCF in year 4 = 13.40 / 0.53 = 25. If the DCF in year 4 = 25.283, then 25.283 = CF 4 / (1.07)^4 So, CF 4 = 25.283 × 1.07^4 = 33.14 million The lowest amount of cash that could be produced in the fourth year for this project to be accepted is $33.14 million. More than $33.14 million and discounted payback would happen before 3.53 years, and less than $33.14 million and discounted payback would take place after 3.53 years. c. Which of the projects is the riskiest? The riskiest project is the one with the highest opportunity cost of capital. That is project G. Remember the opportunity cost of capital is synonymous with cost of capital and appropriate discount rate. Note that the least risky projects are project E and project H, because they have the lowest costs of capital. They have the same cost of capital, so they are equally risky.

Solutions to extra problems – capital budgeting criteria

10. The following table presents information on the expected cash flows of 12 potential projects being evaluated by Mulligan Golf Supplies. For which, if any, of the potential projects, should the internal rate of return (IRR) rule not be used to identify projects that would create value for the firm, because selecting projects where IRR is greater than the cost of capital may not necessarily lead to the selection of a positive NPV project? This question asks about the appropriateness of using the IRR rule. It is not asking about which projects should be chosen. Project Cash flows (number of years from today) 0 1 2 3 4 5 6 A 50,000 -15,000 -20,000 -30,000 -10,000 -40,000 -5, B -50,000 1 1 1 1 1 1 C -50,000 1 0 0 0 0 0 D -50,000 90,000,000 0 0 0 0 0 E -50,000 15,000 20,000 30,000 10,000 40,000 -5, F -50,000 15,000 20,000 -30,000 10,000 40,000 -5, G -50,000 15,000 20,000 -30,000 10,000 40,000 5, H -50,000 15,000 0 -30,000 0 40,000 5, I -50,000 15,000 20,000 30,000 10,000 40,000 5, J -50,000 15,000 0 0 0 40,000 5, K -5 15,000 20,000 30,000 10,000 40,000 5, L 50,000 15,000 20,000 30,000 10,000 -40,000 -5, For projects with conventional cash flows, IRR rule consistently leads to decisions that create value if inputs are accurate and produces the same results as NPV rule for these types of projects. A project with conventional cash flows involves an initial negative investment-related cash flow (C 0 <

1. and subsequent non-negative project-related cash flows (C 1 ≥ 0, C 2 ≥ 0, …, Ct ≥ 0) that can continue for a finite or infinite length of time. The IRR rule does not consistently lead to decisions that create value if cash flows are not conventional. Two important cases occur with:
2. Positive cash flow or flows then negative cash flow or flows
3. Cash flows that flip sign more than once IRR is appropriate for projects with conventional cash flows. The following projects have conventional cash flows: B, C, D, I, J, and K. Note that IRR is an appropriate approach for B and C, even though the projects almost surely would have a negative NPV. Note that IRR is an appropriate approach for D and K, even though the projects almost surely would have a large positive NPV. Note that IRR is an appropriate approach for J, even though the project has some cash flows of zero after time 0 IRR would not be appropriate for projects A and L, because they have a positive cash flow or cash flows followed by a negative cash flow or cash flows. IRR would not be appropriate for projects E, F, G, and H, because they have cash flows that flip sign more than once. All have a negative cash flow at time 0, followed by one or more non-negative cash flows, but then have at least one negative cash flow.

Solutions to extra problems – capital budgeting criteria

11. Wolfpack Technologies is considering a project that is expected to produce net income of $140,000 in the first year, $300,000 in the second year, and -$50,000 in the third and final year. The assets associated with the project are expected to average $800,000. a. What is the average accounting return of the project? b. Should Wolfpack accept the project if the average accounting return threshold is 20%? a. AAR = average net income / average book value of assets Average net income = [140,000 + 300,000 + (-50,000)] / 3 = 130, Average book value of assets = 800, AAR = 130,000 / 800,000 = .1625 = 16.25% b. Since AAR = 16.25% < 20% = threshold, Wolfpack should not accept the project
12. Durham Industries is considering a project that is expected to produce net income of $140,000 in the first year and $300,000 in the second year. The assets associated with the project are expected to average $800,000. The project is expected to last for three years. What is the smallest level of net income that must be earned in the third year such that Durham would accept the project if it applies the average accounting return rule and uses a threshold of 20%? To solve:

1. Find the average net income needed to produce an AAR of 20%. This is the smallest average income that would enable Durham to accept the project. A greater average net income than the one that produces an AAR of 20% would lead to the project being accepted, but it would not be the lowest possible amount consistent with acceptance. A lower average net income than the one that produces an AAR of 20% would lead to the project being rejected.
2. Find the net income needed in year 3 to produce the average net income needed to produce an AAR of 20%.

AAR = average net income / average book value of assets So .20 = average net income / 800, So average net income = .20 × 800,000 = 160, If the average net income for the project is 160,000, then AAR = 20%

Average net income = [140,000 + 300,000 + expected net income in year 3] / 3 = 160, So [140,000 + 300,000 + expected net income in year 3] = 3 × 160,000 =480, So expected net income in year 3 = 480,000 – 140,000 – 300,000 = 40, The smallest level of net income that must be earned in the third year such that Durham would accept the project if it applies the average accounting return rule and uses a threshold of 20% is $40,

Solutions to extra problems – capital budgeting criteria

13. Windy Ridge International is considering a project that is expected to produce net income of $140,000 in the first year, $300,000 in the second year, and $145,000 in the third and final year. What is the largest level of average assets that can be associated with the project such that Windy Ridge would accept the project, if the firm applies the average accounting return rule and uses a threshold of 20%? To solve, find the average assets that would produce an AAR of 20%. This is the largest average assets (also referred to as average book value of assets) that would enable Chester to accept the project. Fewer average assets than the one that produces an AAR of 20% would lead to the project being accepted, but it would not be the lowest possible amount consistent with acceptance. More average assets than the one that produces an AAR of 20% would lead to the project being rejected. AAR = average net income / average book value of assets AAR =. Average net income = [140,000 + 300,000 + 145,000] / 3 = 195, AAR = .20 = 195,000 / average book value of assets So average book value of assets = 195,000 / .20 = 975, The largest level of average assets that can be associated with the project such that Windy Ridge would accept the project if it applies the average accounting return rule and uses a threshold of 20% is $975,000.