Fin 323 Chapter 9 Homework

A project that provides annual cash flows of $17,800 for eight years costs $84,000 today. What is the NPV for the project if the required return is 7 percent? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) NPV $ At a required return of 7 percent, should the firm accept this project? Accept Reject What is the NPV for the project if the required return is 19 percent? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV $ At a required return of 19 percent, should the firm accept this project? Accept Reject At what discount rate would you be indifferent between accepting the project and rejecting it? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Discount rate %

NPV $22289.11, accept NPV $-13612.29 reject Discount Rate 13.49% The NPV of a project is the PV of the inflows minus the PV of the outflows. Since the cash inflows are an annuity, the equation for the NPV of this project at a 7 percent required return is: NPV = -$84,000 + $17,800(PVIFA7%, 8) = $22,289.11 At a 7 percent required return, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a 19 percent required return is: NPV = -$84,000 + $17,800(PVIFA19%, 8) = -$13,612.29 At a 19 percent required return, the NPV is negative, so we would reject the project. We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is: 0 = -$84,000 + $17,800(PVIFAIRR, 8) IRR = 13.49% Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. CFo -$84,000 CFo -$84,000 CFo -$84,000 C01 $17,800 C01 $17,800 C01 $17,800 F01 8 F01 8 F01 9 I = 7% I = 19% IRR CPT NPV CPT NPV CPT 13.49% $22,289.11 -$13,612.29

A firm evaluates all of its projects by applying the IRR rule. A project under consideration has the following cash flows: Year Cash Flow 0 -$ 28,100 1 12,100 2 15,100 3 11,100 If the required return is 15 percent, what is the IRR for this project? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) IRR =? Should the firm accept the project? Yes No

17.45, yes NPV = 0 = -28100 + 12100/(1+r)^1 + 15100/(1+r)^2 + 11100/(1+r)^3 Using trial and error method, IRR = 17.45%

What is the payback period for the following set of cash flows? (Round your answer to 2 decimal places, e.g., 32.16.) Year Cash Flow 0 -$ 5,800 1 1,450 2 1,650 3 2,050 4 1,550 Payback period ? years

3.42 To calculate the payback period, we need to find the time that the project has recovered its initial investment. After three years, the project has created: $1,450 + 1,650 + 2,050 = $5,150 in cash flows. The project still needs to create another: $5,800 - 5,150 = $650 in cash flows. During the fourth year, the cash flows from the project will be $1,550. So, the payback period will be three years, plus what we still need to make divided by what we will make during the fourth year. The payback period is: Payback = 3 + ($650 / $1,550) = 3.42 years

Consider the following two mutually exclusive projects: Year Cash Flow (X) Cash Flow (Y) 0 -$ 19,900 -$ 19,900 1 8,825 10,050 2 9,050 7,775 3 8,775 8,675 Calculate the IRR for each project. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) IRR Project X % Project Y % What is the crossover rate for these two projects? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Crossover rate % What is the NPV of Projects X and Y at discount rates of 0%, 15%, and 25%? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Discount rate Project X Project Y 0% $ $ 15% $ $ 25% $ $

IRR: - Project X: 16.17% - Project Y: 16.31% Crossover Rate: 11.41% Discount Rate @ 0%: - Project X: 6750 - Project Y: 6600 Discount Rate @ 15%: - Project X: 386.72 - Project Y: 422.10 Discount Rate @ 25%: - Project X: -2555.2 - Project Y: -2442.4 Part A: IRR: To calculate IRR, you need to put the value of NPV as 0 and solve for r as follows: Project X: NPV = 0 = -19900 + 8825/(1+r)^1 + 9050/(1+r)^2 + 8775/(1+r)^3 Solving for R we get IRR as = 16.17% IRR (Project X) = 16.17% Project Y: NPV = 0 = -19900 + 10050/(1+r)^1 + 7775/(1+r)^2 + 8675/(1+r)^3 Solving for R we get IRR as = 16.31% IRR (Project Y) = 16.31% Part B: Crossover Rate: Year Project X Project Y Difference 0 -19900 -19900 0 1 8825 10050 -1225 2 9050 7775 1275 3 8775 8675 100 To calculate the cross over rate, you need to calculate rate of return at which the difference in cash flows would be 0 NPV = 0 = 0 -1225/(1+r)^1 + 1275/(1+r)^2 + 100/(1+r)^3 Solving for r, we get crossover rate as 11.41% Crossover Rate = 11.41% Part C: NPV a) 0% Project X = -19900 + 8825/(1+r)^1 + 9050/(1+r)^2 + 8775/(1+r)^3 = 6750 Project Y = -19900 + 10050/(1+0)^1 + 7775/(1+0)^2 + 8675/(1+0)^3 = 6600 b) 15% Project X = -19900 + 8825/(1+.15)^1 + 9050/(1+.15)^2 + 8775/(1+.15)^3 = 386.72 Project Y = -19900 + 10050/(1+.15)^1 + 7775/(1+.15)^2 + 8675/(1+.15)^3 = 422.10 c) 25% Project X = -19900 + 8825/(1+.25)^1 + 9050/(1+.25)^2 + 8775/(1+.25)^3 = -2555.20 Project Y = -19900 + 10050/(1+.25)^1 + 7775/(1+.25)^2 + 8675/(1+.25)^3 = -2442.40

A firm evaluates all of its projects by applying the NPV decision rule. A project under consideration has the following cash flows: Year Cash Flow 0 -$ 28,100 1 12,100 2 15,100 3 11,100 What is the NPV for the project if the required return is 12 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV $ At a required return of 12 percent, should the firm accept this project? Yes No What is the NPV for the project if the required return is 24 percent? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) NPV $ At a required return of 24 percent, should the firm accept this project? Yes No

NPV for the project, if the required return is 12 percent NPV= -28,100+(12,100/1.12)+(15,100/1.12^2)+(11100/1.12^3)= $2641.96 YES, Since the NPV is positive, the firm should accept this project. NPV for the project if the required return is 24 percent NPV= -28,100+(12,100/1.24)+(15,100/1.24^2)+(11100/1.24^3)= $-2699.63 No, Since the NPV is negative, the firm should NOT accept this project.

An investment project provides cash inflows of $600 per year for eight years. What is the project payback period if the initial cost is $1,625? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.) Payback period ? years What is the project payback period if the initial cost is $3,225? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.) Payback period ? years What is the project payback period if the initial cost is $5,100? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.) Payback period ? years

To calculate the payback period, we need to find the time that the project has recovered its initial investment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial cost is $1,625, the payback period is: Payback = 2 + ($425 / $600) = 2.71 years There is a shortcut to calculate the payback period when the future cash flows are an annuity. Just divide the initial cost by the annual cash flow. For the $3,225 cost, the payback period is: Payback = $3,225 / $600 = 5.38 years The payback period for an initial cost of $5,100 is a little trickier. Notice that the total cash inflows after eight years will be: Total cash inflows = 8($600) = $4,800 If the initial cost is $5,100, the project never pays back. Notice that if you use the shortcut for annuity cash flows, you get: Payback = $5,100 / $600 = 8.50 years This answer does not make sense since the cash flows stop after eight years, so again, we must conclude the payback period is never.

Garage, Inc., has identified the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 -$ 29,700 -$ 29,700 1 15,100 4,650 2 13,000 10,150 3 9,550 15,900 4 5,450 17,500 a-1 What is the IRR for each of these projects? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) IRR Project A % Project B % a-2 Using the IRR decision rule, which project should the company accept? Project A Project B a-3 Is this decision necessarily correct? Yes No b-1 If the required return is 12 percent, what is the NPV for each of these projects? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) NPV Project A $ Project B $ b-2 Which project will the company choose if it applies the NPV decision rule? Project A Project B c. At what discount rate would the company be indifferent between these two projects? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Discount rate %

a-1: Project A = 20.14% Project B = 18.34 a-2: Project A a-3: No b-1: 4407 4982 b-2: Project B c. IRR Project A = 20.14% Project B = 18.34% Based on IRR, project A should be chosen as it has a higher IRR compared to other project NPV Project A = 4406.74 Project B = 4982.18 Based on NPV, project B should be chosen as it provides a higher NPV value compared to project A At a discount rate of 19.09%, the company will be indifferent between the two projects Project A Project B Year Cash Flow Year Cash Flow 0 -29700 0 -29700 1 15100 1 4650 2 13000 2 10150 3 9550 3 15900 4 5450 4 17500 Let rA be the rate of return which makes NPV of Project A equals zero. That is -29700 + 15100/(1+rA) + 13000/(1+rA)^2 + 9550/(1+rA)^3 + 5450/(1+rA)^4 = 0 Let rA = 20%, then LHS is equal to = -29700 + 15100/(1.20) + 13000/(1.20)^2 + 9550/(1.20)^3 + 5450/(1.20)^4 = -29700 + 15100/(1.20) + 13000/1.44 + 9550/1.728 + 5450/2.0736 = -29700 + 12583.33 + 9027.78 + 5526.62+ 2628.28 = 66.01 Let rA be equal to 21%, then LHS is equal to = -29700 + 15100/(1.21) + 13000/(1.21)^2 + 9550/(1.21)^3 + 5450/(1.21)^4 = -29700 + 15100/1.21 + 13000/1.4641 + 9550/1.771561 + 5450/2.143589 = -29700+12479.34+8879.18+5390.73+2542..46 = -408.30 rA = 0.20 + [((66.01)*(0.20-0.21))/(-408.3-66.01)] =0.20 + (-0.6601/-474.31) = 0.20 + 0.00139 = 0.20139 or 20.14% Let rB be the rate of return where NPV will be zero. Then -29700 + 4650/(1+rB) + 10150/(1+rB)^2 + 15900/(1+rB)^3 + 17500/(1+rB)^4 = 0 Let rB = 18%, then LHS will be = -29700 + 4650/(1.18) + 10150/(1.18)^2 + 15900/(1.18)^3 + 17500/(1.18)^4 = -29700 + 4650/1.18 + 10150/1.3924 + 15900/1.643032 + 17500/1.938778 = -29700 + 3940.678 + 7289.572+9677.231+9026.305 = 233.786 Let rB = 19%, then LHS would be = -29700 + 4650/(1.19) + 10150/(1.19)^2 + 15900/(1.19)^3 + 17500/(1.19)^4 = -29700 + 4650/1.19 + 10150/1.4161 + 15900/1.685159 + 17500/2.005339 = -29700 + 3907.563 + 7167.573 + 9435.311 + 8726.703 = -462.850 rB = 0.18 + [((233.786)*(0.18 - 0.19))/(-462.85-233.786)] rB = 0.18 + (-2.33786/-696.636) rB = 0.18 + 0.003356 = 0.183356 or 18.34% Project A Year 0 1 2 3 4 Cash Flows -29700 15100 13000 9550 5450 Discount Factor (1/1.12^year) 1 0.892857 0.797194 0.71178 0.635518 Discounted Flows -29700 13482.14 10363.52 6797.501 3463.574 Net Present Value of Project A 4406.74 Project B Year 0 1 2 3 4 Cash Flows -29700 4650 10150 15900 17500 Discount Factor (1/1.12^year) 1 0.892857 0.797194 0.71178 0.635518 Discounted Flows -29700 4151.786 8091.518 11317.31 11121.57 Net Present Value of Project B 4982.18 Calculation of discount rate at which the company will be indifferent between two projects NPV of project A at 18.34% Year 0 1 2 3 4 Cash Flows -29700 15100 13000 9550 5450 Discount Factor (1/1.1834^year) 1 0.845023 0.714064 0.6034 0.509887 Discounted Flows -29700 12759.84 9282.826 5762.47 2778.883 Net Present Value of Project A 884.02 NPV of project B at 20.14% Year 0 1 2 3 4 Cash Flows -29700 4650 10150 15900 17500 Discount Factor (1/1.2014^year) 1 0.832362 0.692827 0.576683 0.480009 Discounted Flows -29700 3870.484 7032.193 9169.259 8400.16 Net Present Value of Project B -1227.90 r = 0.1834 + [((884.02) * (0.1834-0.2014))/(-1227.90-884.02)] = 0.1834 + (-15.91236/-2111.92) = 0.1834 + 0.007535 = 0.190935 or 19.09%

The Sloan Corporation is trying to choose between the following two mutually exclusive design projects: Year Cash Flow (I) Cash Flow (II) 0 -$ 65,000 -$ 17,900 1 30,000 9,650 2 30,000 9,650 3 30,000 9,650 a-1 If the required return is 12 percent, what is the profitability index for both projects? (Do not round intermediate calculations. Round your answers to 3 decimal places, e.g., 32.161.) Profitability Index Project I Project II a-2 If the company applies the profitability index decision rule, which project should the firm accept? Project I Project Il b-1 What is the NPV for both projects? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) NPV Project I $ Project II $ b-2 If the company applies the NPV decision rule, which project should it take? Project I Project II

a-1: Project I: 1.11 Project II: 1.29 a-2: Project II b-1: Project I: 7054.94 Project II: 5277.67 b-2: Project I //\\//\\//\\//\\//\\//\\ Cash Flow (i) Year CashFlow PV Factor@ 12% PV 0 (65,000) 1.0000 (65,000.00) 1 30,000 0.8929 26,785.71 2 30,000 0.7972 23,915.82 3 30,000 0.7118 21,353.41 NPV 7,054.94 PI= NPV + Initial Investment/ Initial Investment= $7,054.94+65,000/65,000=1.11 Cash Flow (ii) Year CashFlow PV Factor@ 12% PV 0 (17,900) 1.0000 (17,900.00) 1 9,650 0.8929 8,616.07 2 9,650 0.7972 7,692.92 3 9,650 0.7118 6,868.68 NPV 5,277.67 PI= NPV + Initial Investment/ Initial Investment= $5,277.67+17,900/17,900=1.29 a-1If the required return is 12 percent, what is the profitability index for both projects Profitability Index Project I-1.11 Project II--1.29 a-2) If the company applies the profitability index decision rule, which project should the firm accept? Project II b-1) What is the NPV for both projects? Profitability Index Project I-$7,054.94 Project II--$5,277.67 b-2) If the company applies the NPV decision rule, which project should it take? Project I

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 -$ 344,000 -$ 49,000 1 51,000 24,600 2 71,000 22,600 3 71,000 20,100 4 446,000 15,200 Whichever project you choose, if any, you require a 15 percent return on your investment. a-1 What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Payback period Project A years Project B years a-2 If you apply the payback criterion, which investment will you choose? Project A Project B b-1 What is the discounted payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Discounted payback period Project A years Project B years b-2 If you apply the discounted payback criterion, which investment will you choose? Project A Project B c-1 What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) NPV Project A $ Project B $ c-2 If you apply the NPV criterion, which investment will you choose? Project A Project B d-1 What is the IRR for each project? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) IRR Project A % Project B % d-2 If you apply the IRR criterion, which investment will you choose? Project A Project B e-1 What is the profitability index for each project? (Do not round intermediate calculations and round your answers to 3 decimal places, e.g., 32.161.) Profitability index Project A Project B e-2 If you apply the profitability index criterion, which investment will you choose? Project A Project B f. Based on your answers in (a) through (e), which project will you finally choose?

a. The payback period for each project is: A: 3 + ($151,000 / $446,000) = 3.34 years B: 2 + ($1,800 / $20,100) = 2.09 years The payback criterion implies accepting Project B because it pays back sooner than Project A. b. The discounted payback for each project is: A: $51,000 / 1.15 + $71,000 / 1.152 + $71,000 / 1.153 = $144,717.68 $446,000 / 1.154 = $255,001.95 Discounted payback = 3 + ($344,000 - 144,717.68) / $255,001.95 = 3.78 years B: $24,600 / 1.15 + $22,600 / 1.152 = $38,480.15 $20,100 / 1.153 = $13,216.08 Discounted payback = 2 + ($49,000 - 38,480.15) / $13,216.08 = 2.80 years The discounted payback criterion implies accepting Project B because it pays back sooner than A. c. The NPV for each project is: A: NPV = -$344,000 + $51,000 / 1.15 + $71,000 / 1.152 + $71,000 / 1.153 + $446,000 / 1.154 NPV = $55,719.63 B: NPV = -$49,000 + $24,600 / 1.15 + $22,600 / 1.152 + $20,100 / 1.153 + $15,200 / 1.154 NPV = $11,386.88 The NPV criterion implies we accept Project A because Project A has a higher NPV than Project B. d. The IRR for each project is: A: $344,000 = $51,000 / (1 + IRR) + $71,000 / (1 + IRR)2 + $71,000 / (1 + IRR)3 + $446,000 / (1 + IRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 20.43% B: $49,000 = $24,600 / (1 + IRR) + $22,600 / (1 + IRR)2 + $20,100 / (1 + IRR)3 + $15,200 / (1 + IRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 27.05% The IRR decision rule implies we accept Project B because the IRR for B is greater than the IRR for A. e. The profitability index for each project is: A: PI = ($51,000 / 1.15 + $71,000 / 1.152 + $71,000 / 1.153 + $446,000 / 1.154) / $344,000 = 1.162 B: PI = ($24,600 / 1.15 + $22,600 / 1.152 + $20,100 / 1.153 + $15,200 / 1.154) / $49,000 = 1.232 The profitability index criterion implies we accept Project B because its PI is greater than Project A's. f. The final decision should be based on the NPV since it does not have the ranking problem associated with the other capital budgeting techniques. Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. CF(A) c. d. e. CFo -$344,000 CFo -$344,000 CFo $0 C01 $51,000 C01 $51,000 C01 $51,000 F01 1 F01 1 F01 1 C02 $71,000 C02 $71,000 C02 $71,000 F02 2 F02 2 F02 2 C03 $446,000 C03 $446,000 C03 $446,000 F03 1 F03 1 F03 1 I = 15% IRR CPT I = 15% NPV CPT 20.43% NPV CPT $55,719.63 $399,719.63 PI = $399,719.63 / $344,000 = 1.162 CF(B) c. d. e. CFo -$49,000 CFo -$49,000 CFo $0 C01 $24,600 C01 $24,600 C01 $24,600 F01 1 F01 1 F01 1 C02 $22,600 C02 $22,600 C02 $22,600 F02 1 F02 1 F02 1 C03 $20,100 C03 $20,100 C03 $20,100 F03 1 F03 1 F03 1 C04 $15,200 C04 $15,200 C04 $15,200 F04 1 F04 1 F04 1 I = 15% IRR CPT I = 15% NPV CPT 27.05% NPV CPT $11,386.88 $60,386.88 PI = $60,386.88 / $49,000 = 1.232 f. The final decision should be based on the NPV since it does not have the ranking problem associated with the other capital budgeting techniques.

Year Cash Flow 0 -$ 17,200 1 9,500 2 8,400 3 4,900 What is the profitability index for the set of cash flows if the relevant discount rate is 10 percent? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) Profitability index What is the profitability index for the set of cash flows if the relevant discount rate is 15 percent? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) Profitability index What is the profitability index for the set of cash flows if the relevant discount rate is 22 percent? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) Profitability index

Profitability Index @10% = 1.12 Profitability Index @15% = 1.04 Profitability Index @22% = 0.94 //\\//\\//\\//\\//\\//\\ \\ Profitability Index @10% // PI = PV of future cash flows / investment, investment =$17200 PV = (9500/(1+0.1)) + (8400/(1+0.1)^2 + 4900/(1+0.1)^3 = 8636.37 + 6942.15 + 3681.44 = 19259.97 So, PI = 19259.97/17200 = 1.119 or 1.12% \\ Profitability Index @ 15% // PV = (9500/(1+0.15)) + (8400/(1+0.15)^2 + 4900/(1+0.15)^3 =8260.84 + 6351.61 + 3221.83 So, PI = 17834.3/17200 = 1.037 or 1.04% \\ Profitability Index @22% // PV = (9500/(1+0.22)) + (8400/(1+0.22)^2 + 4900/(1+0.22)^3 =7786.89 + 5643.64 + 2698.46 =16128.994 So, PI = 16128.944/17200 = 0.938 or 0.94%