Solutions Chapter 11

Chapter 11 Capital Budgeting

ANSWERS TO QUESTIONS 1. Screening decisions require managers to determine whether a proposed capital investment meets a minimum criteria or threshold set by the company. Preference decisions require a choice among several alternatives. 2. Independent projects are unrelated to one another, so that investing in one project does not preclude or affect the choice about investing in the other alternatives. Mutually exclusive projects involve a choice among competing alternatives, where selection of one project implies rejection of all the other alternatives. 3. The time value of money refers to the fact that a $1 today is worth more than a $1 in the future. The dollar you receive today can be invested. So long as the investment earns a positive return, you will have more than $1 in the future 4. Non-discounting methods do not incorporate the time value of money, while discounting methods do incorporate the time value of money. Discounting methods are considered superior because they recognize that a $1 today is worth more than a $1 in the future. 5. A hurdle rate is the minimum return that a project must generate in order to be considered an acceptable investment. Projects that do not meet or exceed a company’s hurdle rate are not acceptable and should be rejected. 6. Net income includes non-cash expenses such as depreciation. This distinction is important because some methods use net income while others utilize cash flow. 7. The payback period is the amount of time it will take for a project to “pay for itself” or pay back its original investment. 8. A positive NPV indicates that the present value of a project’s cash inflows is greater than the present value of the cash outflows. It also indicates that the project has met its hurdle rate, since the project’s internal rate of return is higher than the hurdle rate. A negative NPV indicates that the present value of a project’s cash inflows is less than the present value of the cash outflows. It also indicates that the project has not met its hurdle rate, since the project’s internal rate of return is less than the hurdle rate. 9. An annuity factor is used for cash flows that occur evenly across a number of years, while a PV factor is used for cash flows that occur in a single year. Managerial Accounting, 2/e

11-1

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

10. A positive NPV occurs when a project’s IRR is greater than the company’s hurdle rate. A negative NPV occurs when a project’s IRR is less than the company’s hurdle rate. If a project generates a $50,000 NPV using a discount or hurdle rate of 10%, this indicates that the project’s IRR is greater than 10%. 11. The NPV method is generally preferred over the internal rate of return because the NPV method assumes that future cash flows will be reinvested at the minimum required rate of return. In contrast, the IRR method assumes that future cash flows will be reinvested to earn the same internal rate of return, which is a less realistic assumption. 12. The profitability index is the ratio of the present value of future cash flows divided by the initial investment. A profitability index greater than one means that a project has a positive NPV, since the present value of the future cash flows is greater than the initial investment. 13. In future value of a single amount problems, you will be asked to calculate how much money you will have in the future as the result of investing a certain amount in the present. The present value of a single amount is the worth to you today of receiving that amount sometime in the future. 14. From Future Value of $1 table where n=10 and i = 10%: factor = 2.5937 $10,000 x 2.5937 = $25,937. Thus, $10,000 invested today at 10% will be $25,937 in 10 years. 15. From Present Value of $1 table where n = 10 and i = 10%; factor = 0.3855 $8,000 x 0.3855 = $3,084. Thus, a contract that pays $8,000 in 10 years is worth $3,084 today. 16. The PV of annuity table can be used when the cash flows are equal for each year. The PV of $1 must be used when the cash flows are uneven from year to year. 17.

FV of $1 PV of $1 FV of annuity of $1 PV of annuity of $1

11-2

I =5%, n = 4 I = 10%, n = 7 I =14%, n = 10 1.2155 1.9487 3.7072 0.8227 0.5132 0.2697 4.3101 9.4872 19.3373 3.5460 4.8684 5.2161

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

Authors' Recommended Solution Time (Time in minutes)

Mini-exercises No. Time 1 3 4 2 3 3 3 4 4 5 4 6 3 7 4 8 4 9 4 10 3 11 4 12

Exercises No. Time 5 1 6 2 6 3 5 4 5 5 6 6 6 7 5 8 5 9 10 6 11 6 12 6 13 8

Problems No. Time 9 PA−1 8 PA−2 6 PA−3 8 PA−4 9 PA−5 8 PB−1 8 PB−2 7 PB−3 8 PB−4 9 PB−5

Cases and Projects* No. Time 1 30

* Due to the nature of cases, it is very difficult to estimate the amount of time students will need to complete them. As with any open-ended project, it is possible for students to devote a large amount of time to these assignments. While students often benefit from the extra effort, we find that some become frustrated by the perceived difficulty of the task. You can reduce student frustration and anxiety by making your expectations clear, and by offering suggestions (about how to research topics or what companies to select).

Managerial Accounting, 2/e

11-3

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

ANSWERS TO MINI-EXERCISES M11−1 H F J A, K G I A, C D B, E

1. Time value of money 2. Profitability Index 3. Payback period 4. Net present value method 5. Future value 6. Preference decision 7. Internal rate of return method 8. Screening decision 9. Accounting rate of return

M11−2 Accounting Rate of Return = Annual Net Income / Initial Investment = ($390,000 / 3) / $920,000 = $130,000 / $920,000 = 14.13% (rounded)

M11−3 Payback Period

= Initial Investment / Annual Net Cash Flow = $340,000 / $80,000 = 4.25 years

M11−4 Accounting Rate of Return = Annual Net Income / Initial Investment = $25,000 / $250,000 = 10% Payback Period

11-4

= Initial Investment / Annual Net Cash Flow = Initial Investment / (Net Income + Depreciation) = $250,000 / ($25,000 + $40,000) = 3.85 years

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

M11−5 Year 0 1-6 NPV

Annual Cash Flow $( 150,000) $ 32,000

PV Factor (8%) 4.6229

Present Value $(150,000.00) 147,932.80 $( 2,067.20)

The negative NPV shows that the present value of the future cash inflows for the project is less than the original investment it requires. A negative NPV suggests the project is unacceptable.

M11−6 From Excel, the IRR is 0.13% for this project. Year 0 1 2 3 4 5

Cash flow -286500 57523 57523 57523 57523 57523

0.13%

M11-7 Req. 1 Year 0 1-10 NPV

Annual Cash Flow $( 400,000) $ 70,000

PV Factor (11%) 5.8892

Present Value $(400,000) 412,244 $ 12,244

The positive NPV shows that the present value of the future cash inflows for the project is greater than the original investment it requires. A positive NPV suggests that a project is acceptable. Req. 2 The internal rate of return (IRR) on the project must be greater than 11% because the NPV of the project is positive.

Managerial Accounting, 2/e

11-5

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

M11-8 Profitability Index = PV of Future Cash Flows / Initial Investment PI for Project A = $265,000 / $110,000 = 2.4091 (rounded) PI for Project B = $400,000 / $220,000 = 1.8182 (rounded) PI for Project C = $115,000 / $112,000 = 1.0268 (rounded) Project A has the highest profitability index and is the preferred option, Project B would be the 2nd preference, and Project C is the least preferred.

M11-9 $100,000

=

$100,000

+ $50,000  0.9434

=

47,170

+ $ 20,000  11.4699

=

229,398

Total

=

$376,568

M11-10 $30,000  14.4866

=

$434,598

$15,000  45.7620

=

$686,430

It is much better to save $15,000 for 20 years.

11-6

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

M 11-11 Tremaine Company should select project XYZ because it has a positive NPV based on the following analysis: Project ABC: Cash flows

Discount factor, Present value* 12%, 4 periods $78,000 3.0373 $236,909 (240,000) $(3,091)

PV of future cash flows Original investment NPV * Rounded Project XYZ:

Cash flows PV of future cash flows Original investment NPV

Discount factor, Present value* 12%, 5 periods $66,000 3.6048 $237,917 (230,000) $7,917

* Rounded

M11-12 Project A B C

PI 1.70 1.55 1.89

Managerial Accounting, 2/e

Ranking 2 3 1

11-7

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

ANSWERS TO EXERCISES E11−1 Req. 1 Accounting rate of return

Req. 2 Payback period

E11−2 Req. 1 Accounting rate of return

Req. 2 Payback period

11-8

= Annual Net Income / Initial Investment = $45,000 / $300,000 = 15% = Initial Investment / Annual Net Cash Flow = Initial Investment / (Net Income + Depreciation) = $300,000 / [$45,000 + (($300,000 - $100,000) / 5 years)] = 3.53 years

= Annual Net Income / Initial Investment = $53,000 / $510,000 = 10.39% (rounded) = Initial Investment / Annual Net Cash Flow = Initial Investment/(Net Income + Depreciation) = $510,000 / [$53,000 + (($510,000 - $50,000) / 8 years)] = $510,000 / ($53,000 + $57,500) = 4.62 years (rounded)

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

E11−3 Req. 1 Year Annual Cash Flow 0 $(1,600,000) 1-8 406,250* 8 350,000 NPV *$250,000 + [($1,600,000 - $350,000) / 8]

PV Factor (10%) 5.3349 0.4665

Present Value $(1,600,000) 2,167,303 163,275 $ 730,578

The positive NPV shows that the present value of the future cash inflows for the project is greater than the original investment it requires. A positive NPV suggests that a project is acceptable. Req. 2 The internal rate of return must be greater than 10% since the project yields a positive NPV using a 10% discount rate. Req. 3 Year Annual Cash Flow 0 $(1,600,000) 1-8 406,250* 8 350,000 NPV *$250,000 + [($1,600,000 - $350,000) / 8]

PV Factor (20%) 3.8372 0.2326

Present Value $(1,600,000) 1,558,863 81,410 $ 40,273

Req. 4 The internal rate of return must be slightly higher than 20% because the NPV is positive. Optional: If you use Excel to calculate the exact IRR, you will find that the IRR is 20.79%.

Managerial Accounting, 2/e

11-9

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

E11−4 Req. 1 Accounting Rate of Return = Annual Net Income / Initial Investment = $48,000 / $600,000 = 8% Req. 2 Payback Period

= Initial Investment / Annual Net Cash Flow = Initial Investment / (Net Income + Depreciation) = $600,000 / ($48,000 + [($600,000 - $100,000) / 8] = 5.43 years

Req. 3 Year Annual Cash Flow 0 $(600,000) 1-8 110,500* 8 100,000 NPV * $48,000 + [($600,000 - $100,000) / 8]

PV Factor (12%) 4.9676 0.4039

Present Value $(600,000) 548,920 40,390 $ (10,690)

Req. 4 Since the NPV is negative when using a 12% discount rate, the internal rate of return on the project must be less than 12%. Estimate is around 11%. The actual IRR using Excel (not required) is 11.52%.

E11−5 Answers are shaded below:

Project 1 Project 2 Project 3 Project 4 Project 5 Project 6

Net present value 0 the cost of capital. If the NPV is < 0, the internal rate of return must be < the cost of capital.

11-10

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

E11−6 Req. 1. Option 1: $1,000,000  7.4694

=

$7,469,400

=

$8,000,000

=

$7,228,580

Option 2: $8,000,000 Option 3: $2,000,000 + ($700,000  7.4694) Req. 2 Option 2 is the best option because it provides the greatest present value when all options are discounted at 12%.

E11−7 Req. 1 Purchase Option Year 0 1 2 3 4 5

Cash Flow PV of $1 (10%) Present Value $(26,500) 1.000 $(26,500.00) (500) 0.9091 (454.55) (500) 0.8264 (413.20) (500) 0.7513 (375.65) (500) 0.6830 (341.50) 10,500 0.6209 6,519.45 NPV = $(21,565.45)

Lease Option PV of annuity of $1 (i = 10%, n = 5) = 3.7908 NPV of Lease Option = $3,480 x 3.7908 = $(13,191.98) Req. 2 Harold should choose to lease the car since leasing has a lower cost (higher NPV).

Managerial Accounting, 2/e

11-11

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

E11−8 Req. 1 No, Shaylee cannot invest in all of the projects because the company has $2 million available, but the total investment for all four projects combined is $2,310,000. Therefore, Shaylee must choose from among the four options.

Req. 2 Profitability Index = PV of Future Cash Flows / Initial Investment PI for Project A = $765,000 / $415,000 = 1.8434 (rounded) PI for Project B = $415,000 / $230,000 = 1.8043 (rounded) PI for Project C = $1,200,000 / $720,000 = 1.6667 (rounded) PI for Project D = $1,560,000 / $945,000 = 1.6508 (rounded) Shaylee’s order of preference based on profitability index is: Project A Project B Project C Project D Given its $2 million available, Shaylee can only invest in Projects A, B, and C. These 3 projects will require $1,365,000 of Shaylee’s capital which doesn’t leave enough to undertake Project D.

E11−9 Req. 1 $8,000 x 2.1589 = $17,271.20 Req. 2 $17,271.20 – $8,000 = $9,271.20 (time value of money, or interest) Req. 3 2013: $8,000 x 8% = $640 (interest) 2014: ($8,000 + $640) x 8% = $691.20 (interest) 11-12

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

E11-10 Req. 1 FV of annuity of $1 (i = 8%, n = 10): 14.4866 $15,000 x 14.4866 = $217,299 after 10 years Req. 2 $17,500 x 14.4866 = $253,515.50 after 10 years Req. 3 FV of annuity of $1 (i = 10%, n = 10): 15.9374 $15,000 x 15.9374 = $239,061 after 10 years E11-11 Tulsa should select Option A because it has a higher NPV. Option A: Cash flows PV of annual cash flows PV of cost to rebuild PV of salvage Capital investment NPV

Discount Present value* factor, 11% $80,000 5.1461 $411,688 120,000 .6587 (79,044) 0 .4339 0 $332,644 (320,000) $12,644

* Rounded Option B: Cash flows PV of annual cash flows PV of cost to rebuild PV of salvage Capital investment NPV

Discount Present value* factor, 11% $85,000 5.1461 $437,419 0 .6587 0 24,000 .4339 10,414 $447,833 (454,000) $(6,167)

* Rounded

Managerial Accounting, 2/e

11-13

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

E11-12 Project X Initial investment

Project Y

Project Z

$40,000

$20,000

$50,000

Annual cash inflows

25,000

10,000

25,400

PV of cash inflows

45,000

33,000

70,000

Payback NPV PI

1.60 $5,000 1.13

2.00 $13,000 1.65

1.97 $20,000 1.40

Req. 1 Based on the payback, the investment manager would rank the projects as: X, Z, Y. Req. 2 Based on the NPV, the investment manager would rank the projects as: Z, Y, X. Req. 3 Based on the profitability index, the investment manager would rank the projects as: Y, Z, X. Req. 4 Since limited investment funds are available, the investment manager should recommend that the company prioritize the products based on the profitability index: Y, Z, X.

11-14

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

E11-13 Req. 1 No, Granite Company would not invest in the new machine because, as shown below, the payback period is about mid-way through the 6th year. Year 1 2 3 4 5 6 7 8

Initial Investment $112,000 82,000 58,000 38,000 23,200 8,400 NA NA

Annual cash Unpaid Investment flow $30,000 $82,000 24,000 58,000 20,000 38,000 14,800 23,200 14,800 8,400 14,800 (6,400) NA NA NA NA

Req. 2 Yes, Granite Company would accept the investment if the NPV method is used because the project results in a net positive amount of cash when using a 12% return. Year

Cash Flow

0 1 2 3 4 5 6 7 8 Residual NPV *rounded

$(112,000) 30,000 24,000 20,000 14,800 14,800 14,800 14,800 14,800 50,000

PV of $1 (12%) --0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 0.4039

Present Value* $(112,000) 26,787 19,133 14,236 9,405 8,398 7,498 6,694 5,978 20,195 $ 6,324

Req. 3 The machine Granite Company is considering has a large residual value (about 45% of the machine’s price) that the company will receive at the end of 8 years. The NPV method includes this large cash flow in the calculations, but the payback method ignores anything that happens after the payback period. Management will want to exercise caution when considering this machine’s NPV. A small downward change in the estimated residual value will cause the NPV to become negative. For this reason, management may want to review its estimates for accuracy. Req. 4 Since the machine has a positive NPV at 12%, it would have an even larger NPV if the company’s cost of capital was 10%. This larger NPV could act as a buffer against any downward revisions in the machine’s estimated cash flows or residual value.

Managerial Accounting, 2/e

11-15

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

GROUP A PROBLEMS PA11−1 Req. 1 Accounting Rate of Return = Annual Net Income / Initial Investment = $37,800 / $420,000 = 9.0% Req. 2 Payback Period

= Initial Investment / Annual Net Cash Flow = Initial Investment / (Net Income + Depreciation) = $420,000 / ($37,800 + [($420,000 - $50,000) / 10] = $420,000 / $74,800 = 5.62 years

Req. 3 Year Annual Cash Flow 0 $(420,000) 1-10 74,800* 10 50,000 NPV * $37,800 + [($420,000 - $50,000) / 10]

PV Factor (11%) 5.8892 0.3522

Present Value $(420,000) 440,512 17,610 $ 38,122

PV Factor (15%) 5.0188 0.2472

Present Value $(420,000) 375,406 12,360 $( 32,234)

Req. 4 Year Annual Cash Flow 0 $(420,000) 1-10 74,800* 10 50,000 NPV * $37,800 + [($420,000 - $50,000) / 10] Req. 5 The internal rate of return for this project must be between 11% and 15%, since the NPV is positive at 11% and negative at 15%. The IRR using Excel (not required) is 13.03%.

11-16

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PA11−2 Req. 1 Production and Sales Volume Sales Revenue Variable Costs: Direct Materials Direct Labor Variable Manufacturing Overhead Total Variable Manufacturing Costs Contribution Margin Fixed Manufacturing Costs Net Income

Current (No Automation) 80,000 units Per Unit Total $90 $7,200,000 $18 25 10 53 $37

2,960,000 1,250,000 $1,710,000

Proposed (Automation) 120,000 units Per Unit Total $90 $10,800,000 $18 20 10 48 $42

5,040,000 2,350,000 $2,690,000

Automation would generate a total increase in net income of $980,000. Req. 2 Accounting Rate of Return = Annual Net Income / Initial Investment = $980,000 / $15,000,000 = 6.53% Req. 3 Payback Period

= Initial Investment / Annual Net Cash Flow = Initial Investment / (Net Income + Depreciation) = $15,000,000 / ($980,000 + [($15,000,000 - $500,000) / 10] = $15,000,000 / $2,430,000 = 6.17 years

Req. 4 Year Annual Cash Flow 0 $(15,000,000) 1-10 2,430,000* 10 500,000 NPV * $980,000 + [($15,000,000 - $500,000) / 10]

Managerial Accounting, 2/e

PV Factor (15%) 1.0000 5.0188 0.2472

Present Value $(15,000,000.00) 12,195,684.00 123,600.00 $( 2,680,716.00)

11-17

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PA11−2 (Continued) Req. 5 PV Factor (10%) 6.1446 0.3855

Year Annual Cash Flow 0 $(15,000,000) 1-10 2,430,000* 10 500,000 NPV * $980,000 + [($15,000,000 - $500,000) / 10]

Present Value $(15,000,000.00) 14,931,378.00 192,750.00 $ 124,128.00

Req. 6 The answer to this question depends on the assumed required rate of return. The project has a positive NPV using a discount rate of 10%, but a negative NPV using a discount rate of 15%. We need to know what Beacon’s cost of capital is in order to determine the appropriate discount rate, which will determine whether this is an acceptable project.

11-18

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PA11−3 Req. 1 Project 1: Annual Net Income = Annual Cash Flow – Depreciation = [$865,000 – (($4,850,000 – 1,000,000) / 8 years)] =$383,750 Accounting Rate of Return = Annual Net Income / Initial Investment = $383,750 / $4,850,000 = 7.91% Project 2: Accounting Rate of Return = Annual Net Income / Initial Investment = $425,000 / $3,400,000 = 12.50% Project 3: Accounting Rate of Return = Annual Net Income / Initial Investment = $200,000 / $2,875,000 = 6.96% (rounded) Based on the accounting rates of return, Project 2 is the best. Project 1 is the second best, while Project 3 gives the lowest accounting rate of return. Req. 2 Project 1: Payback Period

Project 2: Payback Period

Project 3: Payback Period

= Initial Investment / Annual Net Cash Flow = $4,850,000 / $865,000 = 5.61 years (rounded)

= Initial Investment / Annual Net Cash Flow = Initial Investment / (Net Income + Depreciation) = $3,400,000 / ($425,000 + [($3,400,000 / 5)] = $3,400,000 / $1,105,000 = 3.08 years (rounded)

= Initial Investment / Annual Net Cash Flow = Initial Investment / (Net Income + Depreciation) = $2,875,000 / ($200,000 + [($2,875,000 - $125,000) / 10] = $2,875,000 / $475,000 = 6.05 years rounded

Based on payback period, Project 2 is preferred, Project 1 is the second preference, while Project 3 has the longest payback period. Managerial Accounting, 2/e

11-19

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PA11−3 (Continued) Req. 3 Project 1 Year 0 1-8 8 NPV

Annual Cash Flow $(4,850,000) 865,000 1,000,000

PV Factor (10%) 1.0000 5.3349 0.4665

Present Value $ (4,850,000.00) 4,614,688.50 466,500.00 $ 231,188.50

PV Factor (10%) 1.0000 3.7908

Present Value $(3,400,000.00) 4,188,834.00 0.00 $ 788,834.00

PV Factor (10%) 1.0000 6.1446 0.3855

Present Value $(2,875,000.00) 2,918,685.00 48,187.50 $ 91,872.50

Project 2 Year Annual Cash Flow 0 $(3,400,000) 1-5 1,105,000* 5 0 NPV *($425,000 + [($3,400,000 / 5) Project 3 Year Annual Cash Flow 0 $(2,875,000) 1-10 475,000* 10 125,000 NPV *($200,000 + [($2,875,000 - $125,000) / 10]

Req. 4 Profitability Index = PV of Future Cash Flows / Initial Investment PI for Project 1

= $5,081,188.50 / $4,850,000 = 1.0477 (rounded)

PI for Project 2

= $4,188,834 / $3,400,000 = 1.2320 (rounded)

PI for Project 3

= $2,966,872.50 / $2,875,000 = 1.0320 (rounded)

The projects should be prioritized as follows: Project 2 ranks highest with a profitability index of 1.2320. Project 1 ranks second highest with a profitability index of 1.0477. Project 3 ranks last with a profitability index of 1.0320. 11-20

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PA11−4 Req. 1 Accounting Rate of Return = Annual Net Income / Initial Investment = $4,200 / $110,000 = 3.82% (rounded) Req. 2 Payback Period

= Initial Investment / (Net Income + Depreciation) = $110,000 / ($4,200 + [($110,000 - $10,000) / 10] = $110,000 / $14,200 = 7.75 years

Req. 3 Year Annual Cash Flow 0 $(110,000) 1-10 14,200* 10 10,000 NPV * $4,200 + [($110,000 - $10,000) / 10]

PV Factor (10%) 6.1446 0.3855

Present Value $(110,000) 87,253 3,855 $( 18,892)

PV Factor (6%) 7.3601 0.5584

Present Value $(110,000) 104,513 5,584 $ 97

Req. 4 Year Annual Cash Flow 0 ($110,000) 1-10 14,200* 10 10,000 NPV * $4,200 + [($110,000 - $10,000) / 10] Req. 5 The internal rate of return for this project must be between 6% and 10% since the NPV is negative at 10% and positive at 6%. Based on the absolute dollar value of the NPV, it should be very close to 6%. The IRR using Excel (not required) is 6.02%.

Managerial Accounting, 2/e

11-21

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PA11−5 Req. 1 Option 1: $1,000,000

=

$1,000,000

=

$903,265

$82,000  6.7101**

=

$550,228

$95,000  (9.8181 - 6.7101)***

=

295,260

Option 2: $92,000  9.8181* Option 3:

* 9.8181 is the PV of $1 Annuity for 20 years

$845,488

**6.7101 is the PV of $1 Annuity for 10 years. *** (9.8181 – 6.7101) is the PV of $1 Annuity for years 11-20.

Req. 2 Option 1 is the best because it gives you the highest return. The time value of money makes a dollar received today worth more than a dollar received one year from now; therefore, option one is the best because you receive the greatest value.

11-22

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

GROUP B PROBLEMS PB11−1 Req. 1 Accounting Rate of Return = Annual Net Income / Initial Investment = $20,000 / $200,000 = 10.00% Req. 2 Payback period

= Initial Investment / (Net Income + Depreciation) = $200,000 / ($20,000 + [($200,000 - $12,000) / 5] = $200,000 / $57,600 = 3.47 years (rounded)

Req. 3 Year Annual Cash Flow 0 $(200,000) 1-5 57,600* 5 12,000 NPV * $20,000 + [($200,000 - $12,000) / 5]

PV Factor (9%) 3.8897 0.6499

Present Value $(200,000) 224,047 7,799 $ 31,846

PV Factor (15%) 3.3522 0.4972

Present Value $(200,000) 193,087 5,966 $( 947)

Req. 4 Year Annual Cash Flow 0 $(200,000) 1-5 57,600* 5 12,000 NPV * $20,000 + [($200,000 - $12,000) / 5] Req. 5 The internal rate of return for this project must be between 9% and 15% since the NPV is negative at 15% and positive at 9%. Based on the absolute dollar value of the NPV, it should be very close to 15%. The IRR using Excel (not required) is 14.80%.

Managerial Accounting, 2/e

11-23

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PB11−2 Req. 1 Production and Sales Volume Sales Revenue Variable Costs: Direct Materials Direct Labor Variable Manufacturing Overhead Total Variable Manufacturing Costs Contribution Margin Fixed Manufacturing Costs Net Income

Current (No Automation) 60,000 units Per Unit Total $70 $4,200,000 $15 20 7 42 $28

1,680,000 800,000 $ 880,000

Proposed (Automation) 80,000 units Per Unit Total $70 $5,600,000 $15 12 7 34 $36

2,880,000 1,612,500 $1,267,500

Automation would generate a total increase in annual net income of $387,500. Req. 2 Accounting Rate of Return = Annual Net Income / Initial Investment = $387,500 / $5,800,000 = 6.68% (rounded) Req. 3 Payback Period

= Initial Investment / Annual Net Cash Flow = Initial Investment / (Net Income + Depreciation) = $5,800,000 / [$387,500 + (($5,800,000 - $400,000) / 8)] = $5,800,000 / $1,062,500 = 5.46 years (rounded)

Req. 4

Year Annual Cash Flow 0 $(5,800,000) 1-8 1,062,500* 8 400,000 NPV * [$387,500 + (($5,800,000 - $400,000) / 8)]

11-24

PV Factor (15%) 1.0000 4.4873 0.3269

Present Value $ (5,800,000.00) 4,767,756.25 130,760.00 $ ( 901,483.75)

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PB11−2 (Continued) Req. 5 Year Annual Cash Flow 0 $(5,800,000) 1-8 1,062,500* 8 400,000 NPV * [$387,500 + (($5,800,000 - $400,000) / 8)]

PV Factor (10%) 1.0000 5.3349 0.4665

Present Value $ (5,800,000.00) 5,668,331.25 186,600.00 $ 54,931.25

Req. 6 Gondola should carefully consider whether it should invest in automation since the NPV is negative using a 15% discount rate. When using a 10% discount rate, the NPV is relatively small. It also has a relatively low accounting rate of return and long payback period. The IRR using Excel (not required) is 10.25%.

Managerial Accounting, 2/e

11-25

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PB11−3 Req. 1 Project 1: Annual Net Income = Annual Cash Flow – Depreciation = [$975,000 – (($2,700,000 – 600,000) / 7 years)] = $675,000 Accounting Rate of Return = Annual Net Income / Initial Investment = $675,000 / $2,700,000 = 25% Project 2: Accounting Rate of Return = Annual Net Income / Initial Investment = $1,650,000 / $8,200,000 = 20.12% (rounded) Project 3: Accounting Rate of Return = Annual Net Income / Initial Investment = $30,000 / $250,000 = 12% Based on the accounting rates of return, Project 1 is the best. Project 2 is the second best, while Project 3 gives the lowest accounting rate of return. Req. 2 Project 1: Payback Period

Project 2: Payback Period

Project 3: Payback Period

= Initial Investment / Annual Net Cash Flow = $2,700,000 / $975,000 = 2.77 years (rounded)

= Initial Investment / Annual Net Cash Flow = Initial Investment / (Net Income + Depreciation) = $8,200,000 / ($1,650,000 + ($8,200,000 / 10)) = $8,200,000 / $2,470,000 = 3.32 years rounded

= Initial Investment / Annual Net Cash Flow = Initial Investment / (Net Income + Depreciation) = $250,000 / ($30,000 + ($250,000 - $25,000) / 10)) = $250,000 / $52,500 = 4.76 years rounded

Based on payback period, Project 1 is preferred, Project 2 is the second preference, while Project 3 has the longest payback period.

11-26

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PB11−3 (Continued) Req. 3 Project 1 Year 0 1-7 7 NPV

Annual Cash Flow $(2,700,000) 975,000 600,000

PV Factor (10%) 1.0000 4.8684 0.5132

Present Value $ (2,700,000.00) 4,746,690.00 307,920.00 $2,354,610.00

PV Factor (10%) 1.0000 6.1446 0.3855

Present Value $(8,200,000.00) 15,177,162.00 0.00 $ 6,977,162.00

PV Factor (10%) 1.0000 6.1446 0.3855

Present Value $ (250,000.00) 322,591.50 9,637.50 $ 82,229.00

Project 2 Year Annual Cash Flow 0 $(8,200,000) 1-10 2,470,000* 10 0 NPV *[$1,650,000 + ($8,200,000 / 10)] Project 3 Year Annual Cash Flow 0 $(250,000) 1-10 52,500* 10 25,000 NPV *($30,000 + [($250,000 - $25,000) / 10

Req. 4 Profitability Index = PV of Future Cash Flows / Initial Investment PI for Project 1 = $5,054,610 / $2,700,000 = 1.8721 (rounded) PI for Project 2 = $15,177,162 / $8,200,000 = 1.8509 (rounded) PI for Project 3 = $332,229 / $250,000 = 1.3289 (rounded) The projects should be prioritized as follows: Project 1 ranks highest with a profitability index of 1.8721. Project 2 ranks second highest with a profitability index of 1.8509. Project 3 ranks last with the lowest profitability index of 1.3289. Managerial Accounting, 2/e

11-27

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PB11−4 Req. 1 Accounting Rate of Return = Annual Net Income / Initial Investment = $66,000 / $860,000 = 7.67% (rounded) Req. 2 Payback Period

= Initial Investment / (Net Income + Depreciation) = $860,000 / ($66,000 + [($860,000 - $20,000) / 6] = $860,000 / $206,000 = 4.17 years (rounded)

Req. 3 Year Annual Cash Flow 0 $(860,000) 1-6 206,000* 6 20,000 NPV * $66,000 + [($860,000 - $20,000) / 6]

PV Factor (11%) 4.2305 0.5346

Present Value $(860,000) 871,483 10,692 $ 22,175

PV Factor (12%) 4.1114 0.5066

Present Value $(860,000) 846,948 10,132 $( 2,920)

Req. 4 Year Annual Cash Flow 0 $(860,000) 1-6 206,000* 6 20,000 NPV * $66,000 + [($860,000 - $20,000) / 6] Req. 5 The internal rate of return for this project must be between 11% and 12% because the NPV is positive using an 11% discount rate and slightly negative using a 12% discount rate. The IRR using Excel (not required) is 11.88%.

11-28

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

PB11−5 Req. 1 Option 1: $100,000

Present Values =

$100,000.00

=

$ 98,181.00

$7,000  6.7101

=

$ 46,970.70

+ $10,000  6.7101  0.4632

=

31,081.18

Total

=

$ 78,051.88

Option 2: $10,000  9.8181 Option 3:

Req. 2 Option 1 is the best because it gives the highest return. The time value of money makes a dollar received today worth more than a dollar received one year from now; therefore, Option 1 is the best because it yields the greatest present value.

Managerial Accounting, 2/e

11-29

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

ANSWERS TO SKILLS DEVELOPMENT CASES S 11−1 The solution to this problem may vary slightly over time and depending on the assumptions the student makes about the rate of increase in future salary. The following table shows the comparison of Arizona State and Harvard that were obtained in July of 2008. The numbers may change as Forbes updates the website with more recent information.

Req. 1 The expected five-year gain from an MBA at Arizona State is $77,149, which is slightly higher than at BYU. The primary difference is the lower cost of in-state tuition at ASU vs. BYU. However, the expected growth rate in salary was lower at ASU than BYU. Forbes provides a default value for these numbers based on the median increase salary changes reported in survey data. Students are allowed to modify these numbers if they want.

11-30

Solutions Manual

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.

S 11−1 (Continued) Req. 2 The expected five-year gain from an MBA at Harvard is substantially higher than at BYU, in spite of a much higher tuition rate. Part of the difference is the higher postMBA salary. The bigger effect comes from the anticipated growth in the post-MBA salary, which is 11.4% at Harvard versus only 6.2% at BYU. Interestingly the payback period at Harvard and BYU is similar because most of the salary benefit comes after the payback period is over. Req. 3 Out of pocket costs include the tuition and fees. Opportunity costs include the salary values and the time value of money. Req. 4 The time value of money calculations will penalize the Harvard option more than the ASU option. The reason is that Harvard requires greater up-front costs. While the salary benefits are greater from an MBA at Harvard, these benefits happen further down the road, and thus are worth less in today’s dollars. Req. 5 The $45,000 pre-MBA salary is not relevant to the decision about which MBA program to attend, because it will be the same under any of the alternatives. Once Greg has decided to get an MBA, his current salary is not relevant to the decision about which school to choose. Req. 6 If Greg was deciding whether to keep his job or get an MBA, his current salary would be relevant to that decision, because it is an opportunity cost associated with getting an MBA. He must give up his current salary in order to go to school.

Managerial Accounting, 2/e

11-31

© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.