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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

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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

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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

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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

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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%

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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%

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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

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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

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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%

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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.

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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

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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

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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

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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

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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...