3.11 - BEC 3 Capital Budgeting: Internal Rate of Return

**49. The internal rate of return is the a. Rate of interest that equates the present value of cash outflows and the present value of cash in-flows. b. Minimum acceptable rate of return for a proposed investment. c. Risk-adjusted rate of return. d. Required rate of return.

49. (a) The requirement is to identify a description of the application of the internal rate of return. Answer (a) is correct because the IRR is the interest rate that equates the present value of the future cash inflows with the present value of the future cash outflows.

**50. As used in capital budgeting analysis, the internal rate of return uses which of the following items in its computation? Net incremental investment; Incremental average operating income; Net annual cash flows a. Yes No Yes b. Yes Yes No c. No No Yes d. No Yes Yes

50. (a) The requirement is to identify the items used in the computation of the internal rate of return. Answer (a) is correct because the IRR uses the net incremental investment and the net annual cash flows. However, it does not include the incremental average operating income.

**51. An organization is using capital budgeting techniques to compare two independent projects. It could accept one, both, or neither of the projects. Which of the following statements is true about the use of net present value (NPV) and internal rate of return (IRR) methods for evaluating these two projects? a. NPV and IRR criteria will always lead to the same accept or reject decision for two independent projects. b. If the first project's IRR is higher than the organization's cost or capital, the first project will be accepted but the second project will not. c. If the NPV criterion leads to accepting or rejecting the first project, one cannot predict whether the IRR criterion will lead to accepting or rejecting the first project. d. If the NPV criterion leads to accepting the first project, the IRR criterion will never lead to accepting the first project.

51. (a) The requirement is to compare NPV and IRR. Answer (a) is correct because NPV and IRR criteria will always lead to the same accept or reject decision. Answer (b) is incorrect because if the second project's internal rate of return is higher than the first project's, the organization would accept the second project based on IRR.

Items 52 and 53 are based on the following information: A firm, with an 18% cost of capital, is considering the following projects (on January 1, 2011): Jan. 1, 2011, Cash outflow (000's omitted) Dec. 31, 2015, Cash inflow (000's omitted) Project internal rate of return Project A $3,500 $7,400 15% Project B 4,000 9,950 ? Present Value of $1 Due at End of "N" Periods N 12% 14% 15% 16% 18% 20% 22% 4 .6355 .5921 .5718 .5523 .5158 .4823 .4230 5 .5674 .5194 .4972 .4761 .4371 .4019 .3411 6 .5066 .4556 .4323 .4104 .3704 .3349 .2751 52. Using the net present value method, Project A's net present value is a. $316,920 b. $0 c. $(265,460) d. $(316,920)

52. (c) The requirement is to calculate the net present value of Project A. Answer (c) is correct. The December 31, 2015 cash inflow is five years from the present cash outflow, and the net present value method uses the firm's cost of capital of 18%. The present value factor for 18% for 5 years is .4371, and $7,400,000 times .4371 equals $3,234,540, which is $265,460 less than the present cash outflow of $3,500,000. Answer (a) is incorrect because this answer discounts the cash inflow at the correct discount rate (18%), but for four years instead of five. Answer (b) is incorrect because this answer discounts the cash inflow at 15% (the project's internal rate of return) instead of at 18% (the cost of capital), which the net present value method uses. Answer (d) is incorrect because this answer discounts the cash inflow at the correct discount rate (18%), but for four years instead of five, and also subtracts the cash outflow from the cash inflow, instead of vice versa.

Items 52 and 53 are based on the following information: A firm, with an 18% cost of capital, is considering the following projects (on January 1, 2011): Jan. 1, 2011, Cash outflow (000's omitted) Dec. 31, 2015, Cash inflow (000's omitted) Project internal rate of return Project A $3,500 $7,400 15% Project B 4,000 9,950 ? Present Value of $1 Due at End of "N" Periods N 12% 14% 15% 16% 18% 20% 22% 4 .6355 .5921 .5718 .5523 .5158 .4823 .4230 5 .5674 .5194 .4972 .4761 .4371 .4019 .3411 6 .5066 .4556 .4323 .4104 .3704 .3349 .2751 53. Project B's internal rate of return is closest to a. 15% b. 18% c. 20% d. 22%

53. (c) The requirement is to estimate Project B's internal rate of return. Answer (c) is correct because 20% is the rate of return that equates the cash inflows with the cash outflows. The present value of 20% for 5 years is .4019, which multiplied by $9,950,000 equals $3,998,905. Therefore, the net present value of the project approximates $0 using the 20% rate.

Items 54 thru 57 are based on the following information: An organization has four investment proposals with the following costs and expected cash inflows: Expected Cash Inflows Project Cost End of year 1 End of year 2 End of year 3 A Unknown $10,000 $10,000 $10,000 B $20,000 5,000 10,000 15,000 C 25,000 15,000 10,000 5,000 D 30,000 20,000 Unknown 20,000 Additional information Discount rate Number of periods Present value of $1 due at the end of n periods [PVIF] Present value of an annuity of $1 per period for n periods [PVIFA] 5% 1 0.9524 0.9524 5% 2 0.9070 1.8594 5% 3 0.8638 2.7232 10% 1 0.9091 0.9091 10% 2 0.8264 1.7355 10% 3 0.7513 2.4869 15% 1 0.8696 0.8696 15% 2 0.7561 1.6257 15% 3 0.6575 2.2832 54. If Project A has an internal rate of return (IRR) of 15%, then it has a cost of a. $8,696 b. $22,832 c. $24,869 d. $27,232

54. (b) The requirement is to calculate the cost of the project from its cash flow information. Answer (b) is correct. The internal rate of return is the discount rate that sets the net present value of the project to zero, so the present value of the costs equals the present value of the cash inflows. The cost of Project A can be calculated by determining the present value of the annual annuity of $10,000 cash flows discounted at 15%. Therefore, the cost of the investment is $22,832 ($10,000 × 2.2832). Answer (a) is incorrect because this solution uses the present value interest factor of 15%, one period rather than the present value interest factor for an annuity. Answer (c) is incorrect because this solution is obtained using a 10% rather than a 15% discount rate. Answer (d) is incorrect because this solution is obtained using a 5% rather than a 15% discount rate.

Items 54 thru 57 are based on the following information: An organization has four investment proposals with the following costs and expected cash inflows: Expected Cash Inflows Project Cost End of year 1 End of year 2 End of year 3 A Unknown $10,000 $10,000 $10,000 B $20,000 5,000 10,000 15,000 C 25,000 15,000 10,000 5,000 D 30,000 20,000 Unknown 20,000 Additional information Discount rate Number of periods Present value of $1 due at the end of n periods [PVIF] Present value of an annuity of $1 per period for n periods [PVIFA] 5% 1 0.9524 0.9524 5% 2 0.9070 1.8594 5% 3 0.8638 2.7232 10% 1 0.9091 0.9091 10% 2 0.8264 1.7355 10% 3 0.7513 2.4869 15% 1 0.8696 0.8696 15% 2 0.7561 1.6257 15% 3 0.6575 2.2832 55. If the discount rate is 10%, the net present value (NPV) of Project B is a. $4,079 b. $6,789 c. $9,869 d. $39,204

55. (a) The requirement is to calculate the net present value of Project B. Answer (a) is correct because the net present value is the present value of the cash inflows less the cost of the project. The net present value of the future inflows is $24,079 [($5,000 × .9091) + ($10,000 × .8264) + ($15,000 × .7513)]. Therefore, the net present value of the project is $4,079 ($24,079 - $20,000). Answer (b) is incorrect because this solution is obtained using a 5%, rather than a 10%, discount rate. Answer (c) is incorrect because this is the net present value of Project A at a 10% discount rate. Answer (d) is incorrect because this solution is obtained using the present value interest factor for annuities.

Items 54 thru 57 are based on the following information: An organization has four investment proposals with the following costs and expected cash inflows: Expected Cash Inflows Project Cost End of year 1 End of year 2 End of year 3 A Unknown $10,000 $10,000 $10,000 B $20,000 5,000 10,000 15,000 C 25,000 15,000 10,000 5,000 D 30,000 20,000 Unknown 20,000 Additional information Discount rate Number of periods Present value of $1 due at the end of n periods [PVIF] Present value of an annuity of $1 per period for n periods [PVIFA] 5% 1 0.9524 0.9524 5% 2 0.9070 1.8594 5% 3 0.8638 2.7232 10% 1 0.9091 0.9091 10% 2 0.8264 1.7355 10% 3 0.7513 2.4869 15% 1 0.8696 0.8696 15% 2 0.7561 1.6257 15% 3 0.6575 2.2832 56. The payback period of Project C is a. 0 years. b. 1 year. c. 2 years. d. 3 years.

56. (c) The requirement is to calculate the payback period of Project C. Answer (c) is correct because after two years, the cumulative cash inflows for Project C are exactly equal to the initial investment outlay, $25,000 ($15,000 + 10,000). Answer (a) is incorrect because the payback period would be zero only if a project had no cost or provided immediate cash inflows in excess of the investment outlay. Project C does not provide an immediate payback of its investment cost. Answer (b) is incorrect because after one year, the cumulative cash inflows for Project C are only $15,000 versus an initial investment outlay of $25,000. The project has not yet recovered its costs. Answer (d) is incorrect because Project C pays back its initial investment outlay in only two years.

Items 54 thru 57 are based on the following information: An organization has four investment proposals with the following costs and expected cash inflows: Expected Cash Inflows Project Cost End of year 1 End of year 2 End of year 3 A Unknown $10,000 $10,000 $10,000 B $20,000 5,000 10,000 15,000 C 25,000 15,000 10,000 5,000 D 30,000 20,000 Unknown 20,000 Additional information Discount rate Number of periods Present value of $1 due at the end of n periods [PVIF] Present value of an annuity of $1 per period for n periods [PVIFA] 5% 1 0.9524 0.9524 5% 2 0.9070 1.8594 5% 3 0.8638 2.7232 10% 1 0.9091 0.9091 10% 2 0.8264 1.7355 10% 3 0.7513 2.4869 15% 1 0.8696 0.8696 15% 2 0.7561 1.6257 15% 3 0.6575 2.2832 57. If the discount rate is 5% and the discounted payback period of Project D is exactly two years, then the year two cash inflow for Project D is a. $5,890 b. $10,000 c. $12,075 d. $14,301

57. (c) The requirement is to calculate the year 2 cash inflow for Project D. Answer (c) is correct. The discounted payback period is the length of time required for discounted cash flows to recover the cost of the investment. The year 2 cash inflow for Project D that is consistent with a discounted payback period of 2 years can be calculated as follows: Investment cost = present value of year 1 and 2 cash inflows $30,000 = $20,000 × (.9524) + year 2 cash inflow × (0.9070) Year 2 cash inflow = [$30,000 - ($20,000 × .9524)] ÷ 0.9070 = $12,075. Answer (c) is incorrect because this solution is obtained using the present value interest factor for annuities. Answer (b) is incorrect because this solution is based on the regular payback period. Since the cash inflow in year 1 is $20,000, Project D pays back its $30,000 cost in two years if the cash inflow in year 2 is $10,000. Answer (d) is incorrect because this solution is obtained using a 10%, rather than a 5%, discount rate.

58. Tam Co. is negotiating for the purchase of equipment that would cost $100,000, with the expectation that $20,000 per year could be saved in after-tax cash costs if the equipment were acquired. The equipment's estimated useful life is ten years, with no residual value, and would be depreciated by the straight-line method. Tam's predetermined minimum desired rate of return is 12%. Present value of an annuity of 1 at 12% for ten periods is 5.65. Present value of 1 due in ten periods at 12% is .322. In estimating the internal rate of return, the factors in the table of present values of an annuity should be taken from the columns closest to a. 0.65 b. 1.30 c. 5.00 d. 5.65

58. (c) The internal rate of return (IRR) determines the rate of discount at which the present value of the future cash flows will exactly equal the investment outlay. It is computed by setting up the following equation Initial investment = TVMF × Cash flows and solving for the time value of money factor (TVMF). The IRR can then be found by locating the TVMF for (n) periods in the present value of an ordinary annuity table and tracing to the top of that column to find the rate of return. The problem asks for the TVMF for the IRR of the equipment, which is calculated as follows: $100,000 = TVMF × $20,000 5.00 = TVMF In estimating the IRR, the factors in the table of present values of an annuity should be taken from the columns closest to 5.00.

59. How are the following used in the calculation of the internal rate of return of a proposed project? Ignore income tax considerations. Residual sales value of project Depreciation expense a. Exclude Include b. Include Include c. Exclude Exclude d. Include Exclude

59. (d) The internal rate of return of a proposed project includes the residual sales value of a project but not the depreciation expense. This is true because the residual sales value represents a future cash flow whereas depreciation expense (ignoring income tax considerations) provides no cash inflow or outflow.

60. Neu Co. is considering the purchase of an investment that has a positive net present value based on Neu's 12% hurdle rate. The internal rate of return would be a. 0 b. 12% c. > 12% d. < 12%

60. (c) The relationship between the NPV method and the IRR method can be summarized as follows: NPV IRR NPV > 0 IRR > Discount rate NPV = 0 IRR = Discount rate NPV < 0 IRR < Discount rate Since the problem states that Neu Co. has a positive net present value on the investment, then the internal rate of return would be > 12%.

61. Bennet Inc. uses the net present value method to evaluate capital projects. Bennet's required rate of return is 10%. Bennet is considering two mutually exclusive projects for its manufacturing business. Both projects require an initial outlay of $120,000 and are expected to have a useful life of four years. The projected after-tax cash flows associated with these projects are as follows: Year; Project X; Project Y 1 $40,000 $10,000 2 40,000 20,000 3 40,000 60,000 4 40,000 80,000 Total $160,000 $170,000 Assuming adequate funds are available, which of the following project options would you recommend that Bennet's management undertake? a. Project X only. b. Project Y only. c. Projects X and Y. d. Neither project.

61. (a) The requirement is to determine which mutually exclusive investment should be accepted. Answer (a) is correct because Project X has the higher net present value as calculated below. Net present value of Project X = $6,800 = ($40,000 × 3.170) - $120,000 Net present value of Project Y = $5,310 = [($10,000 × 0.909) + ($20,000 × 0.826) + ($60,000 × 0.751) + ($80,000 × 0.683)] - $120,000

Items 62 thru 64 are based on the following information: Capital Invest Inc. uses a 12% hurdle rate for all capital expenditures and has done the following analysis for four projects for the upcoming year. Project 1 Project 2 Project 3 Project 4 Initial capital outlay $200,000 $298,000 $248,000 $272,000 Annual net cash inflows Year 1 $65,000 $100,000 $80,000 $ 95,000 Year 2 70,000 135,000 95,000 125,000 Year 3 80,000 90,000 90,000 90,000 Year 4 40,000 65,000 80,000 60,000 Net present value (3,798) 4,276 14,064 14,662 Profitability index 98% 101% 106% 105% Internal rate of return 11% 13% 14% 15% ** 62. Which project(s) should Capital Invest Inc. undertake during the upcoming year assuming it has no budget restrictions? a. All of the projects. b. Projects 1, 2, and 3. c. Projects 2, 3, and 4. d. Projects 1, 3, and 4.

62. (c) The requirement is to select the projects that should be undertaken assuming no budget constraints. Answer (c) is correct because the company should undertake all projects with a positive net present value. This would include Projects 2, 3, and 4. Answers (a), (b), and (d) are incorrect because Project 1 has a negative net present value and should not be undertaken.

Items 62 thru 64 are based on the following information: Capital Invest Inc. uses a 12% hurdle rate for all capital expenditures and has done the following analysis for four projects for the upcoming year. Project 1 Project 2 Project 3 Project 4 Initial capital outlay $200,000 $298,000 $248,000 $272,000 Annual net cash inflows Year 1 $65,000 $100,000 $80,000 $ 95,000 Year 2 70,000 135,000 95,000 125,000 Year 3 80,000 90,000 90,000 90,000 Year 4 40,000 65,000 80,000 60,000 Net present value (3,798) 4,276 14,064 14,662 Profitability index 98% 101% 106% 105% Internal rate of return 11% 13% 14% 15% ** 63. Which project(s) should Capital Invest Inc. undertake during the upcoming year if it has only $600,000 of funds available? a. Projects 1 and 3. b. Projects 2, 3, and 4. c. Projects 2 and 3. d. Projects 3 and 4.

63. (d) The requirement is to select the projects that should be undertaken assuming the company has only $600,000 available. Answer (d) is correct because Projects 3 and 4 have the highest NPV, profitability indexes, and IRRs, so they are the most profitable projects. Answer (a) is incorrect because Project 1 has a negative net present value. Answer (b) is incorrect because it violates the $600,000 restriction. Answer (c) is incorrect because the combined NPV of Projects 2 and 3 is less than the combined NPV of Projects 3 and 4.

Items 62 thru 64 are based on the following information: Capital Invest Inc. uses a 12% hurdle rate for all capital expenditures and has done the following analysis for four projects for the upcoming year. Project 1 Project 2 Project 3 Project 4 Initial capital outlay $200,000 $298,000 $248,000 $272,000 Annual net cash inflows Year 1 $65,000 $100,000 $80,000 $ 95,000 Year 2 70,000 135,000 95,000 125,000 Year 3 80,000 90,000 90,000 90,000 Year 4 40,000 65,000 80,000 60,000 Net present value (3,798) 4,276 14,064 14,662 Profitability index 98% 101% 106% 105% Internal rate of return 11% 13% 14% 15% **64. Which project(s) should Capital Invest Inc. undertake during the upcoming year if it has only $300,000 of capital funds available? a. Project 1. b. Projects 2, 3, and 4. c. Projects 3 and 4. d. Project 3.

64. (d) The requirement is to identify the project(s) that should be undertaken assuming the company has only $300,000 available. Answer (d) is correct; because Project 3 has the highest profitability index and a positive NPV, it should be undertaken. The profitability index provides a good measure for comparing investments of different amounts because it provides an indication of the NPV per dollar invested. Answer (a) is incorrect because it has a negative NPV. Answers (b) and (c) are incorrect because they violate the $300,000 constraint.