Business Finance Final Exam (Chapter 8)

Blinding Light Co. has a project available with the following cash flows: Year Cash Flow 0 −$35,230 1 7,940 2 9,530 3 13,490 4 15,570 5 10,280 What is the project's IRR?

0 = −$35,230 + $7,940/(1 + IRR) + $9,530/(1 + IRR)2 + $13,490/(1 + IRR)3 + $15,570/(1 + IRR)4 + $10,280/(1 + IRR)5 IRR = .1693, or 16.93%

A project will generate annual cash flows of $237,600 for each of the next three years, and a cash flow of $274,800 during the fourth year. The initial cost of the project is $745,600. What is the internal rate of return of this project?

0 = −$745,600 + $237,600/(1 + IRR) + $237,600/(1 + IRR)2 + $237,600/(1 + IRR)3 + $274,800/(1 + IRR)4 IRR = .1198, or 11.98%

What are non-conventional cash flows?

A combination of cash outflows and inflows

There is a project with the following cash flows : Year Cash Flow 0 −$25,700 1 7,500 2 7,950 3 7,350 4 5,600 What is the payback period?

Amount short after 3 years = $25,700 − 7,500 − 7,950 − 7,350 Amount short after 3 years = $2,900 Payback period = 3 + $2,900/$5,600 Payback period = 3.52 years

The net present value profile illustrates how the net present value of an investment is affected by which one of the following?

Discount rate

What is the payback period for a project with the following cash flows? Year Cash Flow 0 -75,000 1 15,000 2 23,000 3 35,000 4 25,000

Payback = 3 + ($75,000 -15,000 -23,000 -35,000)/$25,000 = 3.08 years

The Golden Goose is considering a project with an initial cost of $46,700. The project will produce cash inflows of $10,000 a year for the first two years and $12,000 a year for the following three years. What is the payback period?

Payback = 4 + ($46,700 -10,000 -10,000 -12,000 -12,000)/$12,000 = 4.23 years

EKG, Inc. is considering a new project that will require an initial cash investment of $419,000. The project will produce no cash flows for the first two years. The projected cash flows for Years 3 through 7 are $69,000, $98,000, $109,000, $145,000, and $165,000, respectively. How long will it take the firm to recover its initial investment in this project?

Payback = 5 + ($419,000 -0 -0 -69,000 -98,000 -109,000)/$145,000 = 5.99 years

All of the following are commonly cited reasons for using the Internal Rate of Return, except:

Multiple IRR's allow the company to choose the best one when evaluating projects

Which one of the following methods of analysis is most appropriate to use when two investments are mutually exclusive?

Net present value

What is the first step when calculating the crossover rate?

To calculate the cash flow differences between each project

Year Cash Flow (A) Cash Flow (B) 0 -54,000 -23,000 1 12,700 11,600 2 23,200 11,200 3 27,600 12,500 4 46,500 6,000 Whichever project you choose, if any, you require a rate of return of 14 percent on your investment. If you apply the payback criterion, you will choose Project ______; if you apply the NPV criterion, you will choose Project ______; if you apply the IRR criterion, you will choose Project _____; if you choose the profitability index criterion, you will choose Project ___. Based on your first four answers, which project will you finally choose?

B; A; B; A; A PaybackA = ($54,000 -12,700 -23,200)/$27,600 = 2.66 years PaybackB = ($23,000 -11,600 -11,200)/$12,500 = 2.02 years PIA = ($12,700 / 1.14 + $23,200 / 1.142 + $27,600 / 1.143+ $46,500 / 1.144) / $54,000 = 1.39 PIB = ($11,600 / 1.14 + $11,200 / 1.142 + $12,500 / 1.143+ $6,000 / 1.144) / $23,000 = 1.34 IRRA = - $54,000 + $12,700 / (1 + IRR) + $23,200 / (1 + IRR)2 + $27,600 / (1 + IRR)3 + $46,500 / (1 + IRR)4 = 28.50 percent IRRB =-$23,000 + ($11,600 / (1 + IRR) + $11,200 / (1 + IRR)2 + $12,500 / (1 + IRR)3 + $6,000 / (1 + IRR)4 = 30.94 NPVA = -$54,000 + $12,700 / 1.14 + $23,200 / 1.142 + $27,600 / 1.143 + $46,500 / 1.144 = $21,152.94 NPVB = -$23,000 + $11,600 / 1.14 + $11,200 / 1.142 + $12,500 / 1.143+ $6,000 / 1.144= $7,783.10 The company should select Project A based on net present value. Payback ignores some cash flows and the time value of money. Neither the internal rate of return nor the profitability ratio are reliable methods when projects are mutually exclusive and of differing sizes.

The combination approach for calculating the Modified Internal Rate of Return (MIRR) differs because:

Negative cash flows are discounted back and positive cash flows are compounded forward

A firm evaluates all of its projects by applying the IRR rule. Year Cash Flow 0 -159,000 1 57,000 2 82,000 3 66,000 What is the project's IRR? If the required return is 15 percent, should the firm accept the project?

The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is: 0 = -$159,000 + $57,000 / (1 + IRR) + $82,000 / (1 + IRR)2 + $66,000 / (1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 13.50% No

What does the Modified Internal Rate of Return (MIRR) assume?

The MIRR assumes that cash flows will be reinvested at the cost of capital

According to the video, which of the following are disadvantages of the Average Accounting Return (AAR)?

Time value of money is ignored, An arbitrary benchmark cutoff rate is established, and Market values are not considered

Consider the following cash flows: Year Cash Flow 0 -7,600 1 2,150 2 4,900 3 1,950 4 1,650 What is the payback period for the cash flows?

To calculate the payback period, we need to find the time the project needs to recover its initial investment. After two years, the project has created: $2,150 + 4,900 = $7,050 in cash flows. The project still needs to create another: $7,600 - 7,050 = $550 in cash flows. During the third year, the cash flows from the project will be $1,950. So, the payback period will be 2 years, plus what we still need to make divided by what we will make during the third year. The payback period is: Payback = 2 + ($550 / $1,950) Payback = 2.28 years

Chestnut Tree Farms has identified the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 -40,000 -40,000 1 11,300 17,400 2 14,800 14,100 3 13,700 12,900 4 7,900 2,200 Over what range of discount rates would you choose Project A?

Year Cash Flow (A) Cash Flow (B) A-B 0 -40,000 -40,000 0 1 11,300 17,400 -6,100 2 14,800 14,100 700 3 13,700 12,900 800 4 7,900 2,200 5,700 NPV = 0 = -$6,100 / (1 + IRR) + $700 / (1 + IRR)2 + $800 / (1 + IRR)3 + $5,700 / (1 + IRR)4 IRR = 6.38 percent NPVA =-$40,000 + $11,300 / 1.05 + $14,800 / 1.052 + $13,700 / 1.053 + $7,900 / 1.054 NPVA = $2,519.87 NPVB =-$40,000 + $17,400 / 1.05 + $14,100 / 1.052 + $12,900 / 1.053 + $2,200 / 1.054 NPVB = $2,313.99 Project A is preferred if the discount rate is 6.38 percent, or less.

The modified internal rate of return is specifically designed to address the problems associated with:

unconventional cash flows

The internal rate of return is the:

discount rate that results in a zero net present value for the project

The Average Accounting Return (AAR) Rule states that a company will accept a project that has an average account return that: 3.Award: 10 out of 10.00 points According to the video, which of the following are disadvantages of the Average Accounting Return (AAR)? rev: 11_05_2018_QC_CS-146737 Time value of money is ignored. An arbitrary benchmark cutoff rate is established. Market values are not considered. All of the above. A & C only.

exceeds a pre-determined target average accounting return

Textiles Unlimited has gathered projected cash flows for two projects. At what interest rate would the company be indifferent between the two projects? Which project is better if the required return is 12 percent? Year Cash Flow (A) Cash Flow (B) 0 -105,000 -105,000 1 42,200 52,600 2 34,600 39,400 3 28,700 35,500 4 40,500 30,100

-4.44 percent; B Year Cash Flow (A) Cash Flow (B) A-B 0 -105,000 -105,000 0 1 42,200 52,600 -10,400 2 34,600 39,400 -4,800 3 28,700 35,500 3,200 4 40,500 30,100 10,400 NPV = 0 =[-$10,400 / (1 + IRR)] + [-$4,800 / (1 + IRR)2] + $3,200 / (1 + IRR)3 + $10,400 / (1+ IRR)4 IRR = -4.44 NPVA = -$105,000 + $42,200 / 1.12 + $34,600 / 1.122 + $38,700 / 1.123 + $40,500 / 1.124 = $13,545.86 NPVB = -$105,000 + $52,600 / 1.12 + $39,400 / 1.122 + $35,500 / 1.123+ $30,100 / 1.124= $17,771.02

Based upon the following data: calculate the Average Accounting Return Net Income: Year 1: $ 1,500,000 Year 2: $ 1,200,000 Year 3: $ 1,050,000 Year 4: -$ 1,400,000 Year 5: $ 1,350,000 The starting book value is $11,840,000, which will end with $0, at the end of five years

12.5% Average net income = ($1,500,000 + $1,200,000 + $1,050,000 - $1,400,000 + $1,350,000) / 5 = $740,000 Average book value = (11,840,000 + 0) / 2 = 5,920,000 AAR = 740,000 / 5,920,000 = 12.50%

Mountain Frost is considering a new project with an initial cost of $200,000. The equipment will be depreciated on a straight-line basis to a zero book value over the four-year life of the project. The projected net income for each year is $19,900, $20,800, $24,600, and $16,800, respectively. What is the average accounting return?

AAR = [$19,900 + 20,800 + 24,600 + 16,800)/4]/[$200,000 + 0)/2] AAR = .2053, or 20.53%

he Nifty Fifty is considering opening a new store at a start-up cost of $628,000. The initial investment will be depreciated straight-line to zero over the 15-year life of the project. What is the average accounting rate of return given the following net income projections? Year Net Income 1-5 58,000 6-10 52,000 11-15 44,000

AAR = {[($58,000 ×5) + ($52,000 ×5) + ($44,000 ×5)]/15}/[($628,000 + 0)/2] = .1635, or 16.35 percent

Anderson International Limited is evaluating a project in Erewhon. The project will create the following cash flows: Year Cash Flow 0 -587,000 1 217,000 2 160,000 3 225,000 4 204,000 All cash flows will occur in Erewhon and are expressed in dollars. In an attempt to improve its economy, the Erewhonian government has declared that all cash flows created by a foreign company are "blocked" and must be reinvested with the government for one year. The reinvestment rate for these funds is 4 percent. Assume Anderson uses a required return of 12 percent on this project. What is the NPV of the project? What is the IRR of the project?

First, we need to find the future value of the cash flows for the one year in which they are blocked by the government. So, reinvesting each cash inflow for one year, we find: Year 2 cash flow = $217,000(1.04) = $225,680 Year 3 cash flow = $160,000(1.04) = $166,400 Year 4 cash flow = $225,000(1.04) = $234,000 Year 5 cash flow = $204,000(1.04) = $212,160 So, the NPV of the project is: NPV = -$587,000 + $225,680 / 1.122 + $166,400 / 1.123 + $234,000 / 1.124 + $212,160 / 1.125 NPV = -$19,552.54 And the IRR of the project is: 0 = -$587,000 + $225,680 / (1 + IRR)2 + $166,400 / (1 + IRR)3 + $234,000 / (1 + IRR)4 + $212,160 / (1 + IRR)5 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 10.88%

Professional Properties is considering remodeling the office building it leases to Heartland Insurance. The remodeling costs are estimated at $2.8 million. If the building is remodeled, Heartland Insurance has agreed to pay an additional $820,000 a year in rent for the next five years. The discount rate is 12.5 percent. What is the benefit of the remodeling project to Professional Properties?

NPV = -$2,800,000 + $820,000 ×{1 - [1 / (1 + .125)5]} / .125 NPV = $119,666.04

A project with an initial investment of $455,300 will generate equal annual cash flows over its 11-year life. The project has a required return of 8.6 percent. What is the minimum annual cash flow required to accept the project?

NPV = 0 = −$455,300 + C(PVIFA8.6%, 11) C = $65,645.48

POD has a project with the following cash flows: Year Cash Flows 0 −$273,000 1 145,900 2 163,400 3 128,500 The required return is 8.7 percent. What is the profitability index for this project?

PI = [$145,900/(1 + .087) + $163,400/(1 + .087)2 + $128,500/(1 + .087)3]/$273,000 PI = 1.365

You're trying to determine whether or not to expand your business by building a new manufacturing plant. The plant has an installation cost of $19 million, which will be depreciated straight-line to zero over its four-year life. If the plant has projected net income of $1,835,000, $2,155,000, $2,054,000, and $1,336,000 over these four years, 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 = ($1,835,000 + 2,155,000 + 2,054,000 + 1,336,000) / 4 Average net income = $1,845,000 And the average book value is: Average book value = ($19,000,000 + 0) / 2 Average book value = $9,500,000 So, the AAR for this project is: AAR = Average net income / Average book value AAR = $1,845,000 / $9,500,000 AAR = .1942, or 19.42%

What does mutually exclusive mean?

Taking one project means that we cannot take the other

Mittuch Corp. is evaluating a project with the following cash flows: Year Cash Flow 0 -$ 16,800 1 7,900 2 9,100 3 8,700 4 7,500 5 -4,900 The company uses an interest rate of 9 percent on all of its projects. Calculate the MIRR of the project using all three methods. MIRR Discounting approach Reinvestment approach Combination approach

The MIRR for the project with all three approaches is: Discounting approach: In the discounting approach, we find the value of all cash outflows at Time 0, while any cash inflows remain at the time at which they occur. So, discounting the cash outflows at Time 0, we find: Time 0 cash flow = -$16,800 - $4,900 / 1.095 Time 0 cash flow = -$19,984.66 So, the MIRR using the discounting approach is: 0 = -$19,984.66 + $7,900 / (1 + MIRR) + $9,100 / (1 + MIRR)2 + $8,700 / (1 + MIRR)3 + $7,500 / (1 + MIRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: MIRR = 24.11% Reinvestment approach: In the reinvestment approach, we find the future value of all cash, except the initial cash flow, at the end of the project. So, reinvesting the cash flows to Time 5, we find: Time 5 cash flow = $7,900(1.094) + $9,100(1.093) + $8,700(1.092) + $7,500(1.09) - $4,900 Time 5 cash flow = $36,547.73 So, the MIRR using the reinvestment approach is: 0 = -$16,800 + $36,547.73 / (1 + MIRR)5 $36,547.73 / $16,800 = (1 + MIRR)5 MIRR = ($36,547.73 / $16,800)1/5 - 1 MIRR = .1682, or 16.82% Combination approach: In the combination approach, we find the value of all cash outflows at Time 0, and the value of all cash inflows at the end of the project. So, the value of the cash flows is: Time 0 cash flow = -$16,800 - $4,900 / 1.095 Time 0 cash flow = -$19,984.66 Time 5 cash flow = $7,900(1.094) + $9,100(1.093) + $8,700(1.092) + $7,500(1.09) Time 5 cash flow = $41,447.73 So, the MIRR using the discounting approach is: 0 = -$19,984.66 + $41,447.73 / (1 + MIRR)5 $41,447.73 / $19,984.66 = (1 + MIRR)5 MIRR = ($41,447.73 / $19,984.66)1/5 - 1 MIRR = .1571, or 15.71%

Hodgkiss Enterprises has gathered projected cash flows for two projects. Year Project I Project J 0 -267,000 -267,000 1 113,300 95,200 2 106,400 100,700 3 90,400 102,700 4 79,400 109,700 At what interest rate would the company be indifferent between the two projects? Which project is better if the required return is above this interest rate?

The company would be indifferent between the projects at the crossover rate. To find the crossover rate, we subtract the cash flows from one project from the cash flows of the other project, and find the IRR of the differential cash flows. We will subtract the cash flows from Project J from the cash flows from Project I. It is irrelevant which cash flows we subtract from the other. Subtracting the cash flows, the equation to calculate the IRR for these differential cash flows is: Crossover rate: 0 = $18,100 / (1 + R) + $5,700 / (1 + R)2 - $12,300 / (1 + R)3 - $30,300 / (1 + R)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: R = 26.61% At a lower interest rate, Project J is more valuable because of the higher total cash flows. At a higher interest rate, Project I becomes more valuable since the differential cash flows received in the first two years are larger than the cash flows for Project J. Project I

What is crossover rate?

The discount rate at which we are indifferent between two investments

The Internal Rate of Return (IRR) represents which of the following:

The discount rate that makes the net present value equal to zero

Which one of the following is true if the managers of a firm accept only projects that have a profitability index greater than 1.5?

The firm should increase in value each time it accepts a new project

When choosing between mutually exclusive projects, what is the best method to use?

The highest NPV is always the best option

All of the following are disadvantages of the Payback Period, except:

The method incorporates the time value of money

Seether, Inc., has the following two mutually exclusive projects available. Year Project R Project S 0 -82,000 -101,600 1 28,800 25,400 2 27,800 25,400 3 25,800 40,400 4 19,800 35,400 5 10,600 14,400 What is the crossover rate for these two projects? What is the NPV of each project at the crossover rate? NPV Project R Project S

To find the crossover rate, we subtract the cash flows from one project from the cash flows of the other project, and find the IRR of the differential cash flows. We will subtract the cash flows from Project S from the cash flows from Project R. It is irrelevant which cash flows we subtract from the other. Subtracting the cash flows, the equation to calculate the IRR for these differential cash flows is: 0 = $19,600 + $3,400 / (1 + R) + $2,400 / (1 + R)2 - $14,600 / (1 + R)3 - $15,600 / (1 + R)4 - $3,800 / (1 + R)5 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: R = 9.07% The NPV of the projects at the crossover rate must be equal. The NPV of each project at the crossover rate is: R: NPV = -$82,000 + $28,800 / 1.0907 + $27,800 / 1.09072 + $25,800 / 1.09073 + $19,800 / 1.09074 + $10,600 / 1.09075 NPV = $8,509.34 S: NPV = -$101,600 + $25,400 / 1.0907 + $25,400 / 1.09072 + $40,400 / 1.09073 + $35,400 / 1.09074 + $14,400 / 1.09075 NPV = $8,509.34

Based upon the following data: calculate the crossover rate. Project A Project B Year 1 600 700 Year 2 650 800

16.5% Project A Project B Difference Year 0 -1000 -1200 200 Year 1 600 700 -100 Year 2 650 805 -155 NPV (A-B) = 200 + [-100/(1+R)] + [-155/(1+R)2] When utilizing a financial calculator, the crossover rate is 16.5150%

Based upon the following data: calculate the Discounted Payback Period with a discount rate of 10%. Project A Initial Cost -50,000 Year 1 $ 20,000 Year 2 $ 25,000 Year 3 $ 20,000

2.74 years Project A Discounted Cash Flows Initial Cost -50,000 Year 1 $ 20,000 ($20,000/1.10) = $18,182 Year 2 $ 25,000 ($25,000/1.102) = $20,661 Year 3 $ 20,000 ($20,000/1.103) = $15,026 Payback period Initial cost = $50,000 - $18,182 (year 1) - $20,661 (year 2) =$11,157 remaining after year 2 $11,157/$15,026 (Year 3) = .74 2.74 years

Matterhorn Mountain Gear is evaluating two projects with the following cash flows: Year Project X Project Y 0 −$321,000 −$301,850 1 145,300 136,900 2 162,800 154,100 3 127,900 119,850 What interest rate will make the NPV for the projects equal?

0 = (−$321,000−(−$301,850)) + ($145,300−$136,900)/(1 + IRR) + ($162,800−$119,850)/(1 + IRR)2 + ($127,900−$-109,000)/(1 + IRR)3 0 = −$19,150 + $8,400/(1 + IRR) + $8,700/(1 + IRR)2 + $8,050/(1 + IRR)3 IRR = .1508, or 15.08%

Green Submarine has a project with the following cash flows: Year Cash Flows −$17,850 1 7,080 2 12,650 3 7,950 4 −3,050 The discounting rate is 9 percent and the reinvestment rate is 11 percent. What is the MIRR for this project using the combination approach?

0 = [−$17,850 − $3,050/(1 + .09)4] + $0/(1 + MIRR) + $0/(1 + MIRR)2 + $0/(1 + MIRR)3 + [$7,080(1 + .11)3 + $12,650(1 + .11)2 + $7,950(1 + .11)]/(1 + MIRR)4 MIRR = .1425, or 14.25%

Using the discounting approach, calculate the MIRR of the following cash flows: Assume that the required return on this project is 15% Project A Initial Cost -50 Year 1 175 Year 2 -115

27.74% Project A Modified cash flows Initial Cost -$50 -$50 + (-$115/1.152) = -$137 Year 1 175 $175 Year 2 -$115 $0 (discounted above) Now, calculate the IRR for the modified cash flows above and you get 27.74%

Based upon the following data, which of the following mutually exclusive projects should you choose if your required return is 10%? Year Investment A Investment B 0 −$ 150 −$ 150 1 80 40 2 40 50 3 40 60 4 30 55

Investment B with an NPV of 10.33% -$150 + (40/1.1) + (50/1.12) + (60/1.13) + (55/1.14) = 10.33%

Carland, Inc., has a project available with the following cash flows. If the required return for the project is 7.5 percent, what is the project's NPV? Year Cash Flow 0 −$254,000 1 62,500 2 86,400 3 115,800 4 67,300 5 −11,600

NPV = −$254,000 + $62,500/(1 + .075) + $86,400/(1 + .075)2 + $115,800/(1 + .075)3 + $67,300/(1 + .075)4 − $11,600/(1 + .075)5 NPV = $14,432.90

Soft and Cuddly is considering a new toy that will produce the following cash flows. Should the company produce this toy based on IRR if the firm requires a rate of return of 17.5 percent? Year Cash Flow 0 -132,000 1 97,000 2 42,000 3 28,000

No, because the project's rate of return is 16.45 percent NPV = 0 = -$132,000 + $97,000 / (1 + IRR) + $42,000 / (1 + IRR)2 + $28,000 / (1 + IRR)3 IRR = 16.45 percent The project should be rejected because its IRR is less than the required rate of return

A project that provides annual cash flows of $2,200 for nine years costs $9,100 today. At a required return of 9 percent, what is the NPV of the project? At a required return of 25 percent, what is the NPV of the project? At what discount rate would you be indifferent between accepting the project and rejecting it?

The NPV of a project is the PV of the outflows plus the PV of the inflows. Since the cash inflows are an annuity, the equation for the NPV of this project at a required return of 9 percent is: NPV = -$9,100 + $2,200(PVIFA9%, 9) NPV = $4,089.54 At a required return of 9 percent, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a required return of 25 percent is: NPV = -$9,100 + $2,200(PVIFA25%, 9) NPV = -$1,481.12 At a required return of 25 percent, 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 = -$9,100 + $2,200(PVIFAIRR, 9) IRR = .1920, or 19.20%

The Discounted Payback Period Rule states that a company will accept a project if:

The calculated payback is less than a pre-specified number of years

Consider the following cash flows: Year Cash Flow 0 -28,300 1 15,400 2 13,500 3 9,900 What is the profitability index for the cash flows if the relevant discount rate is 9 percent? What is the profitability index if the discount rate is 14 percent? What is the profitability index if the discount rate is 25 percent?

The profitability index is defined as the PV of the cash inflows divided by the PV of the cash outflows. The equation for the profitability index at a required return of 9 percent is: PI = ($15,400 / 1.09 + $13,500 / 1.092 + $9,900 / 1.093) / $28,300 PI = 1.171 The equation for the profitability index at a required return of 14 percent is: PI = ($15,400 / 1.14 + $13,500 / 1.142 + $9,900 / 1.143) / $28,300 PI = 1.081 The equation for the profitability index at a required return of 25 percent is: PI = ($15,400 / 1.25 + $13,500 / 1.252 + $9,900 / 1.253) / $28,300 PI = .920

You are considering the following two mutually exclusive projects. The crossover point is _____ percent and Project _____ should be accepted at a discount rate of 9 percent. Year Project A Project B 0 -69,000 -69,000 1 13,000 29,000 2 33,000 24,000 3 38,000 27,000

Year Project A Project B A-B 0 -69,000 -69,000 0 1 13,000 29,000 -16,000 2 33,000 24,000 9,000 3 38,000 27,000 11,000 NPV = 0 = -$16,000 / (1 + IRR) + $9,000 / (1 + IRR)2 + $11,000 / (1 + IRR)3 IRR = 15.68 percent NPVA = -$69,000 + $13,000 / 1.09 + $33,000 / 1.092 + $38,000 / 1.093 NPVA = $45.02 NPVB = -$69,000 + $29,000 / 1.09 + $24,000 / 1.092 + $27,000 / 1.093 NPVB = -$1,345.22 The crossover point is 15.68 percent. At 9 percent, Project B has the higher net present value and should be accepted.

An investment has an initial cost of $300,000 and a life of four years. This investment will be depreciated by $60,000 a year and will generate the net income shown below. Should this project be accepted based on the average accounting rate of return (AAR) if the required rate is 9.5 percent? Why or why not? Year Net Income 1 14,500 2 16,900 3 19,600 4 23,700

Yes, because the AAR is greater than 9.5 percent Average net income = ($14,500 + 16,900 + 19,600 + 23,700)/4 = $18,675 Average book value = ($300,000 + 240,000 + 180,000 + 120,000 + 60,000)/5 = $180,000 AAR = $18,675/$180,000 = .1038, or 10.38 percent. The project should be accepted because the AAR is greater than the required return.