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FNAN 303 Solutions to test bank problems – capital budgeting criteria Some answers may be slightly different than provided solutions due to rounding 1. Central Concrete is evaluating a project that would last for 4 years. The project’s cost of capital is 12.26 percent and the expected cash flows are presented in the table. What is the net present value of the project? Years from today 0 1 2 3 4 Expected cash flow (in $) -1,100 9,400 7,000 -7,600 9,000 A. An amount equal to or greater than $1,000 but less than $2,000 B. An amount equal to or greater than $2,000 but less than $3,000 C. An amount equal to or greater than $3,000 but less than $4,000 D. An amount less than $1,000 or an amount equal to or greater than $4,000 E. The amount can not be determined or does not exist because the cash flows are not conventional NPV = [-1,100] + [9,400/1.1226] + [7,000/1.12262] + [-7,600/1.12263] + [-9,000/1.12264] = 1,789 npv(12.26,-1100,{9400,7000,-7600,-9000}) $1,789 Answer: A $1,789 is an amount equal to or greater than $1,000 but less than $2,000 1 FNAN 303 Solutions to test bank problems – capital budgeting criteria 2. Area Forests is evaluating a project that would cost $137,000 today. The project is expected to produce annual cash flows of $8,920 forever with the first annual cash flow expected in 1 year. The cost of capital associated with the project is 8.47 percent and the project’s internal rate of return is 6.51 percent. What is the net present value of the project? (Fall 2017, test 3, question 1) Step 1: expected cash flows are given C0 = -137,000 C1 = C2 = C3 = … = 8,920 Step 2: cost of capital is given as 8.47% The IRR is not relevant for computing NPV Step 3: compute NPV Can not use npv function with financial calculator – there are an infinite number of cash flows NPV = C0 + [C1 / (1+r)] + [C2 / (1+r)2] + ... C1, C2, C3, … represent a fixed perpetuity with annual cash flows of $8,920 and r = .0847 So [C1 / (1+r)] + [C2 / (1+r)2] + ... = (C / r) = ($8,920 / .0847) NPV = -137,000 + (8,920 / .0847) = -137,000 + 105,313 = -31,687 2 FNAN 303 Solutions to test bank problems – capital budgeting criteria 3. Wooden Forests is evaluating a project that would require an initial investment of $900,000 today. The project is then expected to produce annual cash flows that grow by 1.80 percent per year forever. The first annual cash flow is expected in 1 year and is expected to be $65,000. The project’s internal rate of return is 9.02 percent and its cost of capital is 9.32 percent. What is the net present value (NPV) of the project? (Fall 2012, test 3, question 7) Step 1: expected cash flows are given C0 = -900,000 C1 = 65,000 g = .0180 Step 2: cost of capital is given as 9.32% The IRR is not relevant for computing NPV Step 3: compute NPV Can not use npv function with financial calculator – there are an infinite number of cash flows NPV = C0 + [C1 / (1+r)] + [C2 / (1+r)2] + ... C1, C2, C3, … represent a growing perpetuity with C1 = $65,000, r = .0932, and g = .0180 So [C1 / (1+r)] + [C2 / (1+r)2] + ... = [C / (r – g)] = [$65,000 / (.0932 – .0180)] = [$65,000 / .0752] NPV = -900,000 + [65,000 / .0752] = -900,000 + 864,362 = -35,638 3 FNAN 303 Solutions to test bank problems – capital budgeting criteria 4. Karim’s Kabobs is evaluating a project that would last for 3 years. The project’s cost of capital is 9.7 percent; its NPV is $6,700; and the expected cash flows are presented in the table. What is X? Years from today 0 1 2 3 Expected cash flow (in $) -65,000 52,000 -12,000 X A. An amount equal to or greater than $28,000 but less than $36,000 B. An amount equal to or greater than $36,000 but less than $44,000 C. An amount equal to or greater than $44,000 but less than $52,000 D. An amount less than $36,000 or an amount equal to or greater than $52,000 E. The amount can not be determined or does not exist because the cash flows are not conventional (Spring 2011, test 3, question 7) (Fall 2011, test 3, question 8) (Fall 2012, final, question 13) (Spring 2013, test 3, question 7) (Spring 2014, test 3, question 7) (Spring 2017, test 3, question 4) NPV = [C0] + [C1 / (1 + r)] + [C2 / (1 + r)2] + [C3 / (1 + r)3] NPV = 6,700 C0 = -65,000 C1 = 52,000 C2 = -12,000 C3 = X r = .097 6,700 = [-65,000] + [52,000 / 1.097] + [-12,000 / 1.0972] + [X / 1.0973] 6,700 = [-65,000] + [47,402] + [-9,972] + [X / 1.0973] 6,700 = -27,570 + [X / 1.0973] 6,700 + 27,570 = [X / 1.0973] 34,270 = [X / 1.0973] X = C3 = 34,270 × 1.0973 = 45,241 Answers may differ slightly due to rounding Answer: C $45,241 is an amount equal to or greater than $44,000 but less than $52,000 4 FNAN 303 Solutions to test bank problems – capital budgeting criteria 5. Graphco Rackets is considering a project that is expected to cost $5,800 today; produce a cash flow of $8,900 in 4 years, and have an NPV of $300. What is the cost of capital for the project? (Fall 2015, test 3, question 3) (Fall 2016, test 3, question 3) NPV = [C0] + [C1 / (1+r)] + [C2 / (1+r)2] + [C3 / (1+r)3] + [C4 / (1+r)4] In this case, 300 = [-5,800] + [0 / (1+r)] + [0 / (1+r)2] + [0 / (1+r)3] + [8,900 / (1+r)4] = [-5,800] + [8,900 / (1+r)4] So 300 + 5,800 = 8,900 / (1+r)4 = 6,100 So (1 + r)4 = 8,900 / 6,100 And 1 + r = [(8,900 / 6,100)(1/4)] = 1.0990 So r = .0990 = 9.90% 5 FNAN 303 Solutions to test bank problems – capital budgeting criteria 6. Viny Jungles is evaluating a project that would cost $765,100 today. The project is expected to produce annual cash flows of $59,100 forever with the first annual cash flow expected in 1 year. The NPV of the project is $5,200. What is the cost of capital of the project? Can not use the npv function with financial calculator – there are an infinite number of CFs NPV = C0 + [C1 / (1+r)] + [C2 / (1+r)2] + ... r is the cost of capital by definition, as the sum of the present values of all expected cash flows is NPV when the discount rate is the cost of capital In this case, NPV = 5,200 C0 = -765,100 C1 = C2 = C3 = … = 59,100 C1, C2, C3, … represent a fixed perpetuity with annual cash flows of $59,100 So [C1 / (1+r)] + [C2 / (1+r)2] + ... = (C / r) = ($59,100 / r) So 5,200 = -765,100 + (59,100 / r) So 5,200 + 765,100 = 59,100 / r So 770,300 = 59,100 / r So r = 59,100 / 770,300 = 0.0767 = 7.67% 6 FNAN 303 Solutions to test bank problems – capital budgeting criteria 7. Which of the following assertions is true if we define a “good” project as creating value, a “bad” project as destroying value, the “right” decision as accepting a “good” project or rejecting a “bad” project, and the “wrong” decision as rejecting a “good” project or accepting a “bad” project? A. Using net present value (NPV) always leads to the “right” decision for “good” projects when projects have conventional cash flows and using NPV always leads to the “right” decision for “bad” projects when projects have conventional cash flows B. Using net present value (NPV) always leads to the “right” decision for “good” projects when projects have conventional cash flows and using NPV can lead to the “wrong” decision for “bad” projects when projects have conventional cash flows C. Using net present value (NPV) can lead to the “wrong” decision for “good” projects when projects have conventional cash flows and using NPV always leads to the “right” decision for “bad” projects when projects have conventional cash flows D. Using net present value (NPV) can lead to the “wrong” decision for “good” projects when projects have conventional cash flows and using NPV can lead to the “wrong” decision for “bad” projects when projects have conventional cash flows Using net present value (NPV) always leads to the “right” decision for “good” projects when projects have conventional cash flows Regardless of the pattern of expected cash flows, net present value and the NPV rule always lead to the “right” decision for both “good” and “bad” projects, which means that “good” projects are accepted and “bad” projects are rejected Using NPV always leads to the “right” decision for “bad” projects when projects have conventional cash flows Regardless of the pattern of expected cash flows, net present value and the NPV rule always lead to the “right” decision for both “good” and “bad” projects, which means that “good” projects are accepted and “bad” projects are rejected Answer: A. Using net present value (NPV) always leads to the “right” decision for “good” projects when projects have conventional cash flows and using NPV always leads to the “right” decision for “bad” projects when projects have conventional cash flows 7 FNAN 303 Solutions to test bank problems – capital budgeting criteria 8. Which of the following assertions is true if we define a “good” project as creating value, a “bad” project as destroying value, the “right” decision as accepting a “good” project or rejecting a “bad” project, and the “wrong” decision as rejecting a “good” project or accepting a “bad” project? A. Using net present value (NPV) can lead to the “wrong” decision for “good” projects when projects do not have conventional cash flows and using NPV can lead to the “wrong” decision for “bad” projects when projects do not have conventional cash flows B. Using net present value (NPV) can lead to the “wrong” decision for “good” projects when projects do not have conventional cash flows and using NPV always leads to the “right” decision for “bad” projects when projects do not have conventional cash flows C. Using net present value (NPV) always leads to the “right” decision for “good” projects when projects do not have conventional cash flows and using NPV can lead to the “wrong” decision for “bad” projects when projects do not have conventional cash flows D. Using net present value (NPV) always leads to the “right” decision for “good” projects when projects do not have conventional cash flows and using NPV always leads to the “right” decision for “bad” projects when projects do not have conventional cash flows (Spring 2016, test 3, question 4) Using net present value (NPV) always leads to the “right” decision for “good” projects when projects do not have conventional cash flows Regardless of the pattern of expected cash flows, net present value and the NPV rule always lead to the “right” decision for both “good” and “bad” projects, which means that “good” projects are accepted and “bad” projects are rejected Using NPV always leads to the “right” decision for “bad” projects when projects do not have conventional cash flows Regardless of the pattern of expected cash flows, net present value and the NPV rule always lead to the “right” decision for both “good” and “bad” projects, which means that “good” projects are accepted and “bad” projects are rejected Answer: D. Using net present value (NPV) always leads to the “right” decision for “good” projects when projects do not have conventional cash flows and using NPV always leads to the “right” decision for “bad” projects when projects do not have conventional cash flows 8 FNAN 303 Solutions to test bank problems – capital budgeting criteria 9. What is the internal rate of return for a project that is expected to cost $1,410 today; produce a cash flow of $1,620 in 3 years; and have a net present value of $100? (Spring 2014, test 3, question 8) (Fall 2014, test 3, question 7) 0 = C0 + [C1/(1+IRR)] + [C2/(1+IRR)2] + [C3/(1+IRR)3] In this case, 0 = -1,410 + [0/(1+IRR)] + [0/(1+IRR)2] + [1,620 / (1 + IRR)3] So 0 + 1,410 = 1,620 / (1 + IRR)3 And 1,410 = 1,620 / (1 + IRR)3 So (1,620 / 1,410) = (1 + IRR)3 So [(1 + IRR)3](1/3) = (1 + IRR) = (1,620 / 1,410)(1/3) So IRR = [(1,620 / 1,410)(1/3)] – 1 = .0474 = 4.74% Note: irr (-1410,{0,0,1620} 4.74% 9 FNAN 303 Solutions to test bank problems – capital budgeting criteria 10. Wooden Forests is evaluating a project that would require an initial investment of $54,300 today. The project is expected to produce annual cash flows of $6,200 each year forever with the first annual cash flow expected in 1 year. The NPV of the project is $3,700. What is the IRR of the project? (Fall 2013, test 3, question 9) (Spring 2015, test 2, question 10) (Spring 2016, test 3, question 5) Can not use the irr function with financial calculator – there are an infinite number of cash flows By definition of IRR: 0 = C0 + [C1 / (1+IRR)] + [C2 / (1+IRR)2] + ... In this case, C0 = -54,300 C1 = C2 = C3 = … = 6,200 C1, C2, C3, … represent a fixed perpetuity with annual cash flows of $6,200 So [C1 / (1+IRR)] + [C2 / (1+IRR)2] + ... = (C / IRR) = ($6,200 / IRR) So 0 = -54,300 + (6,200 / IRR) So 54,300 = 6,200 / IRR So IRR = 6,200 / 54,300 = 0.1142 = 11.42% Note that the NPV is not relevant to finding IRR, since IRR is the discount rate at which the present value of the expected cash flows is 0. 10 FNAN 303 Solutions to test bank problems – capital budgeting criteria 11. FiberTech is evaluating a project that would last for 3 years. The project’s internal rate of return is 9.71 percent; its NPV is $6,700; and the expected cash flows are presented in the table. What is X? Years from today 0 1 2 3 Expected cash flow (in $) -65,000 52,000 13,000 X (Fall 2017, test 3, question 2) Since we know the IRR, but not the cost of capital, the NPV is irrelevant to finding X. 0 = [C0] + [C1 / (1 + IRR)] + [C2 / (1 + IRR)2] + [C3 / (1 + IRR)3] C0 = -65,000 C1 = 52,000 C2 = 13,000 C3 = X IRR = .0971 0 = [-65,000] + [52,000 / 1.0971] + [13,000 / 1.09712] + [X / 1.09713] 0 = [-65,000] + [47,398] + [10,801] + [X / 1.09713] 0 = -6,801 + [X / 1.09713] 6,801 = [X / 1.09713] X = C3 = 6,801 × 1.09713 = 8,981 Answers may differ slightly due to rounding 11 FNAN 303 Solutions to test bank problems – capital budgeting criteria 12. Which of the following assertions is true if we define a “good” project as creating value, a “bad” project as destroying value, the “right” decision as accepting a “good” project or rejecting a “bad” project, and the “wrong” decision as rejecting a “good” project or accepting a “bad” project? A. Using internal rate of return (IRR) and the IRR rule always leads to the “right” decision when projects have conventional cash flows and using IRR always leads to the “right” decision when projects have non-conventional cash flows B. Using internal rate of return (IRR) and the IRR rule always leads to the “right” decision when projects have conventional cash flows and using IRR can lead to the “wrong” decision when projects have non-conventional cash flows C. Using internal rate of return (IRR) and the IRR rule can lead to the “wrong” decision when projects have conventional cash flows and using IRR always leads to the “right” decision when projects have non-conventional cash flows D. Using internal rate of return (IRR) and the IRR rule can lead to the “wrong” decision when projects have conventional cash flows and using IRR can lead to the “wrong” decision when projects have non-conventional cash flows (Fall 2013, test 3, question 8) Answer: B. Using internal rate of return (IRR) and the IRR rule always leads to the “right” decision when projects have conventional cash flows and using IRR can lead to the “wrong” decision when projects have non-conventional cash flows When cash flows are conventional, IRR always leads to the “right” decision for both “good” and “bad” projects, which means that “good” projects are accepted and “bad” projects are rejected When cash flows are not conventional, IRR can lead to the “wrong” decision for both “good” and “bad” projects, which means that “good” projects can be rejected and “bad” projects can be accepted 12 FNAN 303 Solutions to test bank problems – capital budgeting criteria 13. Mulberry is analyzing a project with conventional cash flows that is expected to last for 3 years. The cost of capital for the project is 5.8 percent. The internal rate of return (IRR) of the project is between 7.1 percent and 7.5 percent. The initial investment today is $10,200; the expected cash flow in 1 year is $4,700; the expected cash flow in 2 years is $3,600; and the expected cash flow in 3 years is X. Which of the following statements is true? A. The NPV of the project is a positive number B. The NPV of the project is equal to zero C. The NPV of the project is a negative number D. Without knowing X, it is not clear whether the NPV of the project is a positive number, zero, or a negative number E. Without knowing the IRR, it is not clear whether the NPV of the project is a positive number, zero, or a negative number (Spring 2011, test 3, question 8) (Fall 2014, test 3, question 8) (Spring 2017, test 3, question 5) Answer: A. The NPV of the project is a positive number Recall that for projects with conventional cash flows, IRR rule (which states that if IRR > cost of capital, then project should be accepted, IRR < cost of capital, then project should be rejected, and if IRR = cost of capital, then firm should be indifferent) always leads to acceptance of projects that create value and always leads to rejection of projects that destroy value. The IRR rule produces same results as NPV rule for these types of projects. In this case, the project has conventional cash flows and IRR, which is at least 7.1 percent, is greater than the cost of capital for the project, which is 5.8 percent, so NPV > 0. We do not need to know what X is to answer this question 13 FNAN 303 Solutions to test bank problems – capital budgeting criteria 14. Yumberry is analyzing a project with conventional cash flows that is expected to last for 3 years. The cost of capital for the project is 5.8 percent. The internal rate of return (IRR) of the project is between 4.1 percent and 4.5 percent. The initial investment today is $10,200; the expected cash flow in 1 year is $4,700; the expected cash flow in 2 years is $3,600; and the expected cash flow in 3 years is X. Which of the following statements is true? A. The NPV of the project is a positive number B. The NPV of the project is equal to zero C. The NPV of the project is a negative number D. Without knowing X, it is not clear whether the NPV of the project is a positive number, zero, or a negative number E. Without knowing the IRR, it is not clear whether the NPV of the project is a positive number, zero, or a negative number (Spring 2011, test 3, question 8) (Fall 2014, test 3, question 8) (Spring 2017, test 3, question 5) Answer: C. The NPV of the project is a negative number Recall that for projects with conventional cash flows, IRR rule (which states that if IRR > cost of capital, then project should be accepted, IRR < cost of capital, then project should be rejected, and if IRR = 0, then firm should be indifferent) always leads to acceptance of projects that create value and always leads to rejection of projects that destroy value. The IRR rule produces same results as NPV rule for these types of projects. In this case, the project has conventional cash flows and IRR, which is at most 4.5 percent, is less than the cost of capital for the project, which is 5.8 percent, so NPV < 0. We do not need to know what X is to answer this question 14 FNAN 303 Solutions to test bank problems – capital budgeting criteria 15. For how many of the projects described in the table is it appropriate to use the internal rate of return (IRR) rule to analyze whether the project should be accepted or rejected? Expected cash flows (number of years from today) Project 0 1 2 3 Cost of capital A -34 13 13 13 6.3% B -57 7 8 9 9.6% C -29 3 3 41 4.7% D 41 19 19 -4 5.2% E -51 35 35 -12 8.1% F -64 64 0 0 7.0% Answer: 4 The IRR rule can be used when cash flows are conventional. The IRR can not be used when cash flows are not conventional. Conventional cash flows involve a negative cash flow at time 0 followed by all non0negative cash flows with at least on positive cash flow. These projects have conventional cash flows, so IRR can be used: A, B, C, & F These projects do not have conventional cash flows, so IRR can not be used: D & E 15 FNAN 303 Solutions to test bank problems – capital budgeting criteria 16. The following table presents information on a potential project currently being evaluated by Erie Shipping. Which assertion about statement 1 and statement 2 is true? Expected cash flows (number of years from today) Cost of capital 0 1 2 3 4 -76,000 38,000 29,000 7,000 11,000 8.2% Statement 1: Erie Shipping would accept the project based on the project’s net present value (NPV) and the NPV rule Statement 2: Erie Shipping would accept the project based on the project’s payback period and the payback rule if the payback threshold is 3.25 years A. Statement 1 is true and statement 2 is true B. Statement 1 is true and statement 2 is false C. Statement 1 is false and statement 2 is true D. Statement 1 is false and statement 2 is false (Spring 2012, final, question 12) (Spring 2014, test 3, question 9) (Fall 2014, test 3, question 9) (Spring 2015, test 2, question 11) (Spring 2016, test 3, question 6) Answer: C. statement 1 is false and statement 2 is true NPV - Statement 1 is false NPV = [-76,000] + [38,000 / 1.082] + [29,000 / 1.0822] + [7,000 / 1.0823] + [11,000 / 1.0824] = -$2,557 npv(8.2,-76000,{38000,29000,7000,11000}) -$2,557 Reject the project, because it has a negative NPV Payback - Statement 2 is true Assume expected cash flows occur uniformly throughout the year Year Expected CF Expected CF needed after year-end 0 -76,000 76,000 1 38,000 76,000 – 38,000 = 38,000 2 29,000 38,000 – 29,000 = 9,000 3 7,000 9,000 – 7,000 = 2,000 4 11,000 2,000 – 11,000 = -9,000 Payback occurs between 3 and 4 years After 3 years, 2,000 in expected cash flows are needed In year 4, the expected cash flow is $11,000 Therefore, it would take ($2,000 / $11,000) = 0.18 of year 4 to reach payback So payback = 3 + 0.18 = 3.18 years Accept the project, because its payback period is 3.18 years, which is less than the threshold of 3.25 years 16 FNAN 303 Solutions to test bank problems – capital budgeting criteria 17. The following table presents information on a potential project currently being evaluated by Macklemore Thrift Shops. Which of the assertions about statement 1 and statement 2 is true? Expected cash flows (number of years from today) Cost of capital 0 1 2 3 4 -$98,000 $56,000 $25,000 $27,000 $3,000 7.20% Statement 1: Macklemore Thrift Shops would accept the project based on the project’s internal rate of return (IRR) and the IRR rule Statement 2: Macklemore Thrift Shops would accept the project based on the project’s payback period and the payback rule if the payback threshold is 2.50 years A. Statement 1 is true and statement 2 is true B. Statement 1 is true and statement 2 is false C. Statement 1 is false and statement 2 is true D. Statement 1 is false and statement 2 is false (Spring 2013, final, question 13) (Fall 2015, test 3, question 5) (Fall 2015, final, question 10) (Spring 2017, final, question 10) Answer: B. Statement 1 is true and statement 2 is false IRR - Statement 1 is true irr(-98000,{56000,25000,27000,3000}) 7.31 percent > 7.20 percent = cost of capital Accept the project, because IRR > cost of capital Payback - Statement 2 is false Assume expected cash flows occur uniformly throughout the year Year Expected CF Expected CF needed after year-end 0 -98,000 98,000 1 56,000 98,000 – 56,000 = 42,000 2 25,000 42,000 – 25,000 = 17,000 3 27,000 17,000 – 27,000 = -10,000 4 3,000 Payback occurs between 2 and 3 years After 2 years, $17,000 in expected cash flows are needed In year 3, the expected cash flow is $27,000 Therefore, it would take ($17,000 / $27,000) = 0.63 of year 3 to reach payback So payback = 2 + 0.63 = 2.63 years Reject the project, because its payback period is 2.63 years, which is greater than the threshold of 2.50 years 17 FNAN 303 Solutions to test bank problems – capital budgeting criteria 18. The following table presents information on a potential project currently being evaluated by Book Jacket. Which one of the assertions about statement 1 and statement 2 is true? Expected cash flows (number of years from today) Cost of capital 0 1 2 3 4 -90,000 44,000 50,000 18,000 5,000 10.2% Statement 1: Book Jacket would accept the project based on the project’s net present value (NPV) and the NPV rule Statement 2: Book Jacket would accept the project based on the project’s discounted payback period and the discounted payback rule if the discounted payback threshold is 2.55 years A. Statement 1 is true and statement 2 is true B. Statement 1 is true and statement 2 is false C. Statement 1 is false and statement 2 is true D. Statement 1 is false and statement 2 is false (Fall 2010, test 3, question 9) (Spring 2017, test 3, question 6) Answer: B. Statement 1 is true and statement 2 is false NPV - Statement 1 is true NPV = -90,000 + [44,000/1.102] + [50,000/1.1022] + [18,000/1.1023] + [5,000/1.1024] = 7,940 npv(10.2,-90000,{44000,50000,18000,5000}) $7,940 Accept the project, because it has a positive NPV Discounted payback - Statement 2 is false Assume discounted expected cash flows occur uniformly throughout the year. However, discount expected cash flows as if they occur at end of year. Also, discounted expected cash flows are rounded to the nearest dollar for simplicity and convenience. Year Expected CF Expected DCF = PV Expected DCF needed after year-end (expected CF) @ 10.2% 0 -90,000 -90,000 90,000 1 44,000 44,000 / 1.102 = 39,927 90,000 – 39,927 = 50,073 2 50,000 50,000 / 1.1022 = 41,172 50,073 – 41,172 = 8,901 3 18,000 18,000 / 1.1023 = 13,450 8,901 – 13,450 = -4,549 4 5,000 5,000 / 1.1024 = 3,390 Discounted payback occurs between 2 and 3 years After 2 years, 8,901 in discounted expected cash flows are needed In year 3, the expected discounted cash flow is $13,450 Therefore, it would take ($8,901 / $13,450) = 0.66 of year 3 to reach discounted payback So discounted payback = 2 + 0.66 = 2.66 years Reject the project, because its discounted payback period is 2.66 years, which is greater than the threshold of 2.55 years 18 FNAN 303 Solutions to test bank problems – capital budgeting criteria 19. The following table presents information on a potential project currently being evaluated by Kasual Kat. Which one of the assertions about statement 1 and statement 2 is true? Expected cash flows (number of years from today) Cost of capital 0 1 2 3 4 -95,000 11,000 84,000 34,000 1,000 11.60% Statement 1: Kasual Kat would accept the project based on the project’s internal rate of return (IRR) and the IRR rule Statement 2: Kasual Kat would accept the project based on the project’s discounted payback period and the discounted payback rule if the discounted payback threshold is 2.65 years A. Statement 1 is true and statement 2 is true B. Statement 1 is true and statement 2 is false C. Statement 1 is false and statement 2 is true D. Statement 1 is false and statement 2 is false (Fall 2011, test 3, question 9) (Spring 2012, test 3, question 9) (Fall 2016, test 3, question 4) Answer: B. Statement 1 is true and statement 2 is false IRR - Statement 1 is true irr(-95000,{11000,84000,34000,1000}) 15.57 percent > 11.60 percent = cost of capital Accept the project, because IRR > cost of capital Discounted payback - Statement 2 is false Assume discounted expected cash flows occur uniformly throughout the year. However, discount expected cash flows as if they occur at end of year. Also, discounted expected cash flows are rounded to the nearest dollar for simplicity and convenience. Year Expected CF Expected DCF = PV Expected DCF needed after year-end (expected CF) @ 11.60% 0 -95,000 -95,000 95,000 1 11,000 11,000 / 1.1160 = 9,857 95,000 – 9,857 = 85,143 2 84,000 84,000 / 1.11602 = 67,445 85,143 – 67,445 = 17,698 3 3 34,000 34,000 / 1.1160 = 24,462 17,698 – 24,462 = -6,764 4 1,000 Not relevant Discounted payback occurs between 2 and 3 years After 2 years, 17,698 in discounted expected cash flows are needed In year 3, the expected discounted cash flow is $24,462 Therefore, it would take ($17,698 / $24,462) = 0.72 of year 3 to reach discounted payback So discounted payback = 2 + 0.72 = 2.72 years Reject the project using discounted payback, because its discounted payback period is 2.72 years, which is greater than the threshold of 2.65 years 19 FNAN 303 Solutions to test bank problems – capital budgeting criteria 20. The following table presents information on a potential project currently being evaluated by Snow Day Amusements. Which one of the assertions about statement 1 and statement 2 is true? Expected cash flows (number of years from today) Cost of capital 0 1 2 3 4 -50,000 33,000 11,000 35,000 9,000 14.3% Statement 1: Snow Day Amusements would accept the project based on the project’s payback period and the payback rule if the payback threshold is 2.25 years Statement 2: Snow Day Amusements would accept the project based on the project’s discounted payback period and the discounted payback rule if the discounted payback threshold is 2.60 years A. Statement 1 is true and statement 2 is true B. Statement 1 is true and statement 2 is false C. Statement 1 is false and statement 2 is true D. Statement 1 is false and statement 2 is false (Spring 2011, test 3, question 9) (Fall 2012, test 3, question 9) (Spring 2013, test 3, question 9) (Fall 2013, test 3, question 10) (Spring 2015, final, question 14) (Spring 2016, final, question 7) (Fall 2017, test 3, question 3) Answer: A. Statement 1 is true and statement 2 is true Payback - Statement 1 is true Year Expected CF 0 -50,000 1 33,000 2 11,000 3 35,000 4 9,000 Expected CF needed after year-end 50,000 50,000 – 33,000 = 17,000 17,000 – 11,000 = 6,000 6,000 – 35,000 = -29,000 Payback occurs between 2 and 3 years After 2 years, 6,000 in expected cash flows are needed In year 3, the expected cash flow is $35,000 Therefore, it would take ($6,000 / $35,000) = 0.17 of year 3 to reach payback So payback = 2 + 0.17 = 2.17 years Accept the project using payback, because its payback period is 2.17 years, which is less than the threshold of 2.25 years Discounted payback - Statement 2 is true Assume discounted expected CFs occur uniformly throughout the year. However, discount expected CFs as if they occur at end of year. Also, discounted expected CFs are rounded to the nearest dollar for simplicity and convenience. Year Expected CF Expected DCF = PV Expected DCF needed after year-end (expected CF) @ 14.3% 0 -50,000 -50,000 50,000 1 33,000 33,000 / 1.143 = 28,871 50,000 – 28,871 = 21,129 2 11,000 11,000 / 1.1432 = 8,420 21,129 – 8,420 = 12,709 3 35,000 35,000 / 1.1433 = 23,438 12,709 – 23,438 = -10,729 4 9,000 Not relevant Discounted payback occurs between 2 and 3 years After 2 years, 12,709 in discounted expected cash flows are needed In year 3, the expected discounted cash flow is $23,438 Therefore, it would take ($12,709 / $23,438) = 0.54 of year 3 to reach discounted payback So discounted payback = 2 + 0.54 = 2.54 years Accept the project using discounted payback, because its discounted payback period is 2.54 years, which is less than the threshold of 2.60 years 20 FNAN 303 Solutions to test bank problems – capital budgeting criteria 21. Indicate whether each of the following 8 statements is true or false. Statement 1: 1A Tech would accept project A based on the project’s net present value and the net present value rule if project A has a net present value of $912 Statement 2: 2B Tech would accept project B based on the project’s net present value and the net present value rule if project B has a net present value of -$3,257 Statement 3: 3C Tech would accept project C, which has conventional cash flows, based on the project’s internal rate of return and the internal rate of return rule if project C has an internal rate of return of 12.32 percent and a cost of capital of 13.65 percent Statement 4: 4D Tech would accept project D, which has conventional cash flows, based on the project’s internal rate of return and the internal rate of return rule if project D has an internal rate of return of 14.67 percent and a cost of capital of 11.72 percent Statement 5: 5E Tech would accept project E, which has conventional cash flows, based on the project’s payback period and the payback rule if project E has a payback period of 2.82 years and the payback threshold is 2.86 years Statement 6: 6F Tech would accept project F, which has conventional cash flows, based on the project’s payback period and the payback rule if project F has a payback period of 4.56 years and the payback threshold is 4.53 years Statement 7: 7G Tech would accept project G, which has conventional cash flows, based on the project’s discounted payback period and the discounted payback rule if project G has a discounted payback period of 3.71 years and the discounted payback threshold is 3.67 years Statement 8: 8H Tech would accept project H, which has conventional cash flows, based on the project’s discounted payback period and the discounted payback rule if project H has a discounted payback period of 2.43 years and the discounted payback threshold is 2.48 years Statement 1 is true Accept project A, because it has a positive NPV Statement 2 is false Reject project B, because it has a negative NPV Statement 3 is false Reject project C, because its IRR is less than its cost of capital Statement 4 is true Accept project D, because its IRR is greater than its cost of capital Statement 5 is true Accept project E, because its payback period is less than the payback threshold Statement 6 is false Reject project F, because its payback period is greater than the payback threshold Statement 7 is false Reject project G, because its discounted payback period is greater than the discounted payback threshold Statement 8 is true Accept project H, because its discounted payback period is less than the discounted payback threshold 21 FNAN 303 Solutions to test bank problems – capital budgeting criteria 22. Which of the following assertions is true if all payback and discounted payback thresholds are a finite, positive number of years (such as 0.6 years or 3.9 years, but not -4.5 years or infinity), and all projects have conventional cash flows? A. Projects with negative NPV can sometimes be accepted using the payback rule and projects with negative NPV can sometimes be accepted using the discounted payback rule B. Projects with negative NPV can sometimes be accepted using the payback rule and projects with negative NPV are never accepted using the discounted payback rule C. Projects with negative NPV are never accepted using the payback rule and projects with negative NPV can sometimes be accepted using the discounted payback rule D. Projects with negative NPV are never accepted using the payback rule and projects with negative NPV are never accepted using the discounted payback rule E. None of the above assertions is true (Spring 2010, test 4, question 3) (Spring 2011, final, question 12) Answer: B. Projects with negative NPV can sometimes be accepted using the payback rule and projects with negative NPV are never accepted using the discounted payback rule If NPV < 0, then discounted payback is infinite, and it is therefore not possible to accept negative-NPV projects using the discounted payback approach if all discounted payback thresholds are a finite, positive number of years If NPV < 0, the payback period can still be a finite, positive number of years, so it is therefore possible to accept negative-NPV projects using the payback approach For example, a project that requires an investment of $110, pays $110 in 1 year, and has a cost of capital of 10%, would have a negative NPV (-110 + 110/1.10 = -10), but payback would be 1 year, and would therefore be accepted if the payback threshold was 1 year or greater. 22 FNAN 303 Solutions to test bank problems – capital budgeting criteria 23. Which of the following assertions is true if all payback and discounted payback thresholds are a finite, positive number of years (such as 0.6 years or 3.9 years, but not -4.5 years or infinity), and all projects have conventional cash flows? A. Projects with positive NPV are never rejected using the payback rule and projects with positive NPV are never rejected using the discounted payback rule B. Projects with positive NPV are never rejected using the payback rule and projects with positive NPV can sometimes be rejected using the discounted payback rule C. Projects with positive NPV can sometimes be rejected using the payback rule and projects with positive NPV are never rejected using the discounted payback rule D. Projects with positive NPV can sometimes be rejected using the payback rule and projects with positive NPV can sometimes be rejected using the discounted payback rule E. None of the above assertions is true (Spring 2014, test 3, question 10) (Fall 2016, test 3, question 5) Answer: D. Projects with positive NPV can sometimes be rejected using the payback rule and projects with positive NPV can sometimes be rejected using the discounted payback rule If a project with positive NPV has substantial expected cash flows that occur after the payback threshold, then it could be rejected. For example, a firm with a payback threshold of 1 year would reject a project with a cost of capital of 10%, an investment of $100 today, and an expected cash flow to the firm of $1 million in 3 years, despite having a positive and relatively large NPV. If a project with positive NPV has substantial expected cash flows that occur after the discounted payback threshold, then it could be rejected. For example, a firm with a discounted payback threshold of 1 year would reject a project with a cost of capital of 10%, an investment of $100 today, and an expected cash flow to the firm of $1 million in 3 years, despite having a positive and relatively large NPV. 23 FNAN 303 Solutions to test bank problems – capital budgeting criteria 24. The managers of Logical Balance Financial have evaluated five potential projects. Each project has conventional cash flows. Based on the information in the table and this paragraph, which one of the projects is the riskiest? Cost of Net present Payback Discounted Internal rate capital value period payback period of return Project (in %) (in $ millions) (in years) (in years) (in %) A 11.0 0.2 7.6 8.1 11.1 B 7.1 53.3 5.6 8.7 13.5 C 13.2 12.6 2.4 3.2 13.4 D 6.7 8.9 5.8 8.2 14.3 E 9.2 -1.5 2.1 ∞ 8.6 (Fall 2009, final, question 10) (Spring 2010, final, question 17) (Fall 2010, final, question 10) (Fall 2011, test 3, question 10) (Spring 2012, test 3, question 10) (Spring 2015, test 2, question 12) (Fall 2017, final, question 10) Project C is the riskiest. Project C has the highest cost of capital, which is the only relevant piece of information for answering this question. Higher cost of capital higher risk. 24 FNAN 303 Solutions to test bank problems – capital budgeting criteria 25. The managers of Logical Balance Financial have evaluated five potential projects. Each project has conventional cash flows. Based on the information in the table and this paragraph, which one of the projects is the safest? Cost of Net present Payback Discounted Internal rate capital value period payback period of return Project (in %) (in $ millions) (in years) (in years) (in %) A 11.0 0.2 7.6 8.1 11.1 B 7.1 53.3 5.6 8.7 13.5 C 13.2 12.6 2.4 3.2 13.4 D 6.7 8.9 5.8 8.2 14.3 E 9.2 -1.5 2.1 ∞ 8.6 (Fall 2012, test 3, question 10) (Spring 2013, test 3, question 10) (Spring 2014, final, question 10) (Fall 2014, final, question 12) (Fall 2016, final, question 10) Project D is the safest. Project D has the lowest cost of capital, which is the only relevant piece of information for answering this question. Lower cost of capital lower risk. 25