HW 9

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 -$34,000 1 15,000 2 17,000 3 13,000 If the required return is 14 percent, what is the IRR for this project? Should the firm accept the project?

CFo -$34,000 C01 $15,000 F01 1 C02 $17,000 F02 1 C03 $13,000 F03 1 IRR CPT 15.80% Since the IRR is greater than the required return, we would accept the project.

An investment under consideration has a payback of seven years and a cost of $685,000. Assume the cash flows are conventional. If the required return is 11 percent, what is the worst-case NPV?

CFo -$685,000 C01 $0 F01 6 C02 $685,000 F02 1 I = 11% NPV CPT -$355,063.99

A firm evaluates all of its projects by applying the NPV decision rule. A project under consideration has the following cash flows: YearCash Flow0-$34,000 1 15,000 2 17,000 3 13,000 a. What is the NPV of the project if the required return is 11 percent? b. At a required return of 11 percent, should the firm accept this project? c. What is the NPV of the project if the required return is 24 percent? d. At a required return of 24 percent, should the firm accept this project?

CFo-$34,000 CFo-$34,000 C01 $15,000 C01 $15,000 F01 1 F01 1 C02 $17,000 C02 $17,000 F02 1 F02 1 C03 $13,000 C03 $13,000 F03 1 F03 1 I = 11% I = 24% NPV CPT NPV CPT $2,816.58 -$4,028.70

A project that provides annual cash flows of $11,700 for nine years costs $63,000 today. What is the NPV for the project if the required return is 8 percent? At a required return of 8 percent, should the firm accept this project? What is the NPV for the project if the required return is 20 percent? At a required return of 20 percent, should the firm accept this project? At what discount rate would you be indifferent between accepting the project and rejecting it?

CFo-$63,000 CFo-$63,000 CFo-$63,000 C01 $11,700 C01 $11,700 C01 $11,700 F01 9 F01 9 F01 9 I = 8% I = 20% IRR CPT NPV CPT NPV CPT 11.72% $10,088.59 -$15,837.69 a. $10,088.59 b. -$15,837.69 c. 11.72%

Bruin, Inc., has identified the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 -$37,500 -$37,500 1 17,300 5,700 2 16,200 12,900 3 13,800 16,300 4 7,600 27,500 a-1.What is the IRR for each of these projects? a-2.Using the IRR decision rule, which project should the company accept? a-3.Is this decision necessarily correct? b-1.If the required return is 11 percent, what is the NPV for each of these projects? NPV Project A Project B b-2.Which project will the company choose if it applies the NPV decision rule? c.At what discount rate would the company be indifferent between these two projects?

Calculator Solution: Project A CFo -$37,500 CFo -$37,500 C01 $17,300 C01 $17,300 F01 1 F01 1 C02 $16,200 C02 $16,200 F02 1 F02 1 C03 $13,800 C03 $13,800 F03 1 F03 1 C04 $7,600 C04 $7,600 F04 1 F04 1 IRR CPT I = 11% 19.71% NPV CPT $6,330.67 Project B CFo -$37,500 CFo -$37,500 C01 $5,700 C01 $5,700 F01 1 F01 1 C02 $12,900 C02 $12,900 F02 1 F02 1 C03 $16,300 C03 $16,300 F03 1 F03 1 C04 $27,500 C04 $27,500 F04 1 F04 1 IRR CPT I = 11% 18.76% NPV CPT $8,138.59 Crossover rate CFo $0 C01 $11,600 F01 1 C02 $3,300 F02 1 C03 -$2,500 F03 1 CO4 -$19,900 FO4 1 IRR CPT 16.48% Examining the IRRs of the projects, we see that the IRRA is greater than the IRRB, so IRR decision rule implies accepting Project A. This may not be a correct decision; however, because the IRR criterion has a ranking problem for mutually exclusive projects. To see if the IRR decision rule is correct or not, we need to evaluate the project NPVs. The NPVB is greater than the NPVA, so we should accept Project B.

The Sloan Corporation is trying to choose between the following two mutually exclusive design projects: Year Cash Flow (I) Cash Flow (II) 0 -$63,000 -$15,500 1 28,900 7,900 2 28,900 7,900 3 28,900 7,900 a-1.If the required return is 10 percent, what is the profitability index for both projects? a-2.If the company applies the profitability index decision rule, which project should the firm accept? b-1.What is the NPV for both projects? b-2.If the company applies the NPV decision rule, which project should it take?

Calculator Solution: Project I CFo $0 CFo -$63,000 C01 $28,900 C01 $28,900 F01 3 F01 3 I = 10% I = 10% NPV CPT NPV CPT $71,870.02 $8,870.02 PI = $71,870.02/$63,000 = 1.141 Project II CFo $0 CFo -$15,500 C01 $7,900 C01 $7,900 F01 3 F01 3 I = 10% I = 10% NPV CPT NPV CPT $19,646.13 $4,146.13 PI = $19,646.13/$15,500 = 1.267 The profitability index decision rule implies that we accept Project II, since PIII is greater than PII. The NPV decision rule implies accepting Project I, since the NPVI is greater than the NPVII.

You're trying to determine whether to expand your business by building a new manufacturing plant. The plant has an installation cost of $13.5 million, which will be depreciated straight-line to zero over its four-year life. If the plant has projected net income of $1,570,000, $1,684,200, $1,716,300, and $1,097,400 over these four years, respectively, what is the project's average accounting return (AAR)?

Our definition of AAR is the average net income divided by the average book value. The average net income for this project is: Average net income = ($1,570,000 + 1,684,200 + 1,716,300 + 1,097,400)/4 Average net income = $1,516,975 And the average book value is: Average book value = ($13,500,000 + 0)/2 Average book value = $6,750,000 So, the AAR for this project is: AAR = Average net income/Average book value AAR = $1,516,975/$6,750,000 AAR = .2247, or 22.47%

Bronco, Inc., imposes a payback cutoff of three years for its international investment projects. YearCash Flow (A) Cash Flow (B) 0 -$35,000 -$45,000 1 12,000 11,000 2 17,000 13,000 3 14,000 16,000 4 9,000 255,000 What is the payback period for both projects? Which project should the company accept?

Project A has total cash flows of $29,000 after Year 2, so the cash flows are short by $6,000 of recapturing the initial investment, so the payback for Project A is: Payback = 2 + ($6,000/$14,000) Payback = 2.43 years Project B has cash flows of: Cash flows = $11,000 + 13,000 + 16,000 Cash flows = $40,000 during the first three years. The cash flows are still short by $5,000 of recapturing the initial investment, so the payback for Project B is: Payback = 3 + ($5,000/$255,000) Payback = 3.02 years Using the payback criterion and a cutoff of three years, accept Project A and reject Project B.

An investment project costs $17,000 and has annual cash flows of $4,700 for six years. a.What is the discounted payback period if the discount rate is zero percent? b.What is the discounted payback period if the discount rate is 5 percent? c.What is the discounted payback period if the discount rate is 19 percent?

R = 0%: 3 + ($2,900/$4,700) = 3.62 years Discounted payback = Regular payback = 3.62 years R = 5%: $4,700/1.05 + $4,700/1.05^2 + $4,700/1.05^3 + $4,700/1.05^4 = $16,665.97 $4,700/1.05^5 = $3,682.57 Discounted payback = 4 + ($17,000-16,665.97)/$3,682.57 Discounted payback = 4.09 years R = 19%: $4,700(PVIFA19%,6) = $16,025.95 The project never pays back.

An investment has an installed cost of $527,630. The cash flows over the four-year life of the investment are projected to be $212,200, $243,800, $203,500, and $167,410, respectively. a.If the discount rate is zero, what is the NPV? b.If the discount rate is infinite, what is the NPV? c.At what discount rate is the NPV just equal to zero?

a. At a zero discount rate (and only at a zero discount rate), the cash flows can be added together across time. So, the NPV of the project at a zero percent required return is: NPV = -$527,630 + 212,200 + 243,800 + 203,500 + 167,410 NPV = $299,280 b. If the required return is infinite, future cash flows have no value. Even if the cash flow in one year is $1 trillion, at an infinite rate of interest, the value of this cash flow today is zero. If the future cash flows have no value today, the NPV of the project is the cash flow today, so at an infinite interest rate: NPV = -$527,630 c. CF0-$527,630 C01 $212,200 F01 1 C02 $243,800 F02 1 C03 $203,500 F03 1 C04 $167,410 F04 1 IRR CPT 21.76%

NPVProject Anot attemptedProject Bnot attemptedConsider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 -$364,000 -$52,000 1 46,000 25,000 2 68,000 22,000 3 68,000 21,500 4 458,000 17,500 Whichever project you choose, if any, you require a return of 11 percent on your investment. a-1. What is the payback period for each project? a-2. If you apply the payback criterion, which investment will you choose? b-1. What is the discounted payback period for each project? Discounted payback period: Project A: Years Project B: Years b-2. If you apply the discounted payback criterion, which investment will you choose? c-1. What is the NPV for each project? NPV Project A : Project B : c-2. If you apply the NPV criterion, which investment will you choose? d-1. What is the IRR for each project? IRR Project A : % Project B : % d-2. If you apply the IRR criterion, which investment will you choose? e-1. What is the profitability index for each project? Profitability index Project A: Project B: e-2. If you apply the profitability index criterion, which investment will you choose? 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 + ($182,000/$458,000) = 3.40 years B: 2 + ($5,000/$21,500) = 2.23 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: $46,000/1.11 + $68,000/1.11^2 + $68,000/1.11^3 = $146,352.78 $458,000/1.11^4 = $301,698.79 Discounted payback = 3 + ($364,000 - 146,352.78)/$301,698.79 Discounted payback = 3.72 years B: $25,000/1.11 + $22,000/1.11^2 = $40,378.22 $21,500/1.11^3 = $15,720.61 Discounted payback= 2 + ($52,000-40,378.22)/$15,720.61 Discounted payback = 2.74 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 = -$364,000 + $46,000/1.11 + $68,000/1.11^2 + $68,000/1.11^3 + $458,000/1.11^4 NPV = $84,051.57 B: NPV = -$52,000 + $25,000/1.11 + $22,000/1.11^2 + $21,500/1.11^3 + $17,500/1.11^4 NPV = $15,626.62 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: $364,000 = $46,000/(1 + IRR) + $68,000/(1 + IRR)^2 + $68,000/(1 + IRR)^3+ $458,000/(1 + IRR)^4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 18.14% B: $52,000 = $25,000/(1 + IRR) + $22,000/(1 + IRR)^2 + $21,500/(1 + IRR)^3+ $17,500/(1 + IRR)^4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 25.29% IRR decision rule implies we accept Project B because IRR for B is greater than IRR for A. e. The profitability index for each project is: A: PI = ($46,000/1.11 + $68,000/1.11^2 + $68,000/1.11^3 + $458,000/1.11^4)/$364,000 PI = 1.231 B: PI = ($25,000/1.11 + $22,000/1.11^2 + $21,500/1.11^3 + $17,500/1.11^4)/$52,000 PI = 1.301 Profitability index criterion implies we accept Project B because the PI for B is greater than the PI for A. 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: CF(A) c. d. e. CFo-$364,000 CFo-$364,000 CFo$0 C01 $46,000 C01 $46,000 C01$46,000 F01 1 F01 1 F01 1 C02 $68,000 C02 $68,000 C02 $68,000 F02 2 F02 2 F02 2 C03 $458,000 C03 $458,000 C03 $458,000 F03 1 F03 1 F03 1 I = 11% IRR CPT I = 11% NPV CPT 18.14% NPV CPT $84,051.57 $448,051.57 PI = $448,051.57/$364,000 = 1.231 CF(B) c. d. e. CFo-$52,000 CFo-$52,000 CFo$0 C01 $25,000 C01 $25,000 C01$25,000 F01 1 F01 1 F01 1 C02 $22,000 C02 $22,000 C02 $22,000 F02 1 F02 1 F02 1 C03 $21,500 C03 $21,500 C03 $21,500 F03 1 F03 1 F03 1 C04 $17,500 C04 $17,500 C04 $17,500 F04 1 F04 1 F04 1 I = 11% IRR CPT I = 11% NPV CPT 25.29% NPV CPT $15,626.62 $67,626.62 PI = $67,626.62/$52,000 = 1.301