Solutions Chapter 11

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.

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 table 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 pro

pay back its original investment. 8.

than the present value of the cash outflows. It also indicates that the project has met its hurdle rate

than the present value of the cash outflows. It also indicates that the project has not merate.

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.

11-2 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.

10. A

rate. If a project generates a $50,000 NPV using a discount or hurdle rate of 10%, this indic

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. I =5%, n = 4 I = 10%, n = 7 I =14%, n = 10 FV of $1 1.2155 1.9487 3.7072 PV of $1 0.8227 0.5132 0.2697 FV of annuity of $1 4.3101 9.4872 19.3373 PV of annuity of $1 3.5460 4.8684 5.2161


Authors' Recommended Solution Time

(Time in minutes)

Mini-exercises

Exercises

Problems

Cases and Projects*

No. Time No. Time No. Time No. Time

1 3 1 5 PA 1 9 1 30 2 4 2 6 PA 2 8 3 3 3 6 PA 3 6 4 3 4 5 PA 4 8 5 4 5 5 PA 5 9 6 4 6 6 PB 1 8 7 3 7 6 PB 2 8 8 4 8 5 PB 3 7 9 4 9 5 PB 4 8

10 4 10 6 PB 5 9 11 3 11 6 12 4 12 6

13 8

* 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).


ANSWERS TO MINI-EXERCISES M111

H 1. Time value of money

F 2. Profitability Index

J 3. Payback period

A, K 4. Net present value method

G 5. Future value

I 6. Preference decision

A, C 7. Internal rate of return method

D 8. Screening decision

B, E 9. Accounting rate of return

M112 Accounting Rate of Return = Annual Net Income / Initial Investment

= ($390,000 / 3) / $920,000 = $130,000 / $920,000 = 14.13% (rounded)

M113 Payback Period = Initial Investment / Annual Net Cash Flow

= $340,000 / $80,000 = 4.25 years

M114 Accounting Rate of Return = Annual Net Income / Initial Investment

= $25,000 / $250,000 = 10%

Payback Period = Initial Investment / Annual Net Cash Flow

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


M115

Year Annual Cash Flow PV Factor (8%) Present Value 0 $( 150,000) - $(150,000.00)

1-6 $ 32,000 4.6229 147,932.80 NPV $( 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. M116 From Excel, the IRR is 0.13% for this project.

Year Cash flow

0 -286500

1 57523

2 57523

3 57523

4 57523

5 57523 0.13% M11-7 Req. 1

Year Annual Cash Flow PV Factor (11%) Present Value 0 $( 400,000) - $(400,000)

1-10 $ 70,000 5.8892 412,244 NPV $ 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.


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.


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,

12%, 4 periods Present value*

PV of future cash flows $78,000 3.0373 $236,909 Original investment (240,000) NPV $(3,091)

* Rounded

Project XYZ: Cash flows Discount factor,

12%, 5 periods Present value*

PV of future cash flows $66,000 3.6048 $237,917 Original investment (230,000) NPV $7,917

* Rounded

M11-12 Project PI Ranking A 1.70 2 B 1.55 3 C 1.89 1


ANSWERS TO EXERCISES E111 Req. 1 Accounting rate of return = Annual Net Income / Initial Investment

= $45,000 / $300,000 = 15%

Req. 2 Payback period = Initial Investment / Annual Net Cash Flow

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

E112 Req. 1 Accounting rate of return = Annual Net Income / Initial Investment

= $53,000 / $510,000 = 10.39% (rounded)

Req. 2 Payback period = 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)


E113 Req. 1

Year

Annual Cash Flow

PV Factor (10%)

Present Value

0 $(1,600,000) - $(1,600,000) 1-8 406,250* 5.3349 2,167,303 8 350,000 0.4665 163,275

NPV $ 730,578 *$250,000 + [($1,600,000 - $350,000) / 8] 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

PV Factor (20%)

Present Value

0 $(1,600,000) - $(1,600,000) 1-8 406,250* 3.8372 1,558,863 8 350,000 0.2326 81,410

NPV $ 40,273 *$250,000 + [($1,600,000 - $350,000) / 8] 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%.


E114 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

PV Factor (12%)

Present Value

0 $(600,000) - $(600,000) 1-8 110,500* 4.9676 548,920 8 100,000 0.4039 40,390

NPV $ (10,690) * $48,000 + [($600,000 - $100,000) / 8] 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%. E115 Answers are shaded below: Net present value Cost of capital Internal rate of return Project 1 0 8% >8% Project 5


E116

Req. 1.

Option 1:

$1,000,000 7.4694 = $7,469,400

Option 2:

$8,000,000 = $8,000,000

Option 3:

$2,000,000 + ($700,000 7.4694) = $7,228,580

Req. 2

Option 2 is the best option because it provides the greatest present value when all options are discounted at 12%. E117 Req. 1 Purchase Option Year Cash Flow PV of $1 (10%) Present Value

0 $(26,500) 1.000 $(26,500.00) 1 (500) 0.9091 (454.55) 2 (500) 0.8264 (413.20) 3 (500) 0.7513 (375.65) 4 (500) 0.6830 (341.50) 5 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).


E118 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

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 Shayleeundertake Project D. E119

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)


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 Discount

factor, 11% Present value*

PV of annual cash flows $80,000 5.1461 $411,688 PV of cost to rebuild 120,000 .6587 (79,044) PV of salvage 0 .4339 0 $332,644 Capital investment (320,000) NPV $12,644

* Rounded

Option B: Cash flows Discount

factor, 11% Present value*

PV of annual cash flows $85,000 5.1461 $437,419 PV of cost to rebuild 0 .6587 0 PV of salvage 24,000 .4339 10,414 $447,833 Capital investment (454,000) NPV $(6,167)

* Rounded


E11-12

Project X Project Y Project Z

Initial investment $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 1.60 2.00 1.97

NPV $5,000 $13,000 $20,000

PI 1.13 1.65 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.


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 Initial Investment

Annual cash flow

Unpaid Investment

1 $112,000 $30,000 $82,000 2 82,000 24,000 58,000 3 58,000 20,000 38,000 4 38,000 14,800 23,200 5 23,200 14,800 8,400 6 8,400 14,800 (6,400) 7 NA NA NA 8 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 PV of $1 (12%)

Present Value*

0 $(112,000) --- $(112,000) 1 30,000 0.8929 26,787 2 24,000 0.7972 19,133 3 20,000 0.7118 14,236 4 14,800 0.6355 9,405 5 14,800 0.5674 8,398 6 14,800 0.5066 7,498 7 14,800 0.4523 6,694 8 14,800 0.4039 5,978 Residual 50,000 0.4039 20,195 NPV $ 6,324 *rounded Req. 3 The machine Granite Company is considering has a large residual value (about

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

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

any downwar


GROUP A PROBLEMS PA111 Req. 1 Accounting Rate of Return = Annual Net Income / Initial Investment

= $37,800 / $420,000 = 9.0%


= 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

PV Factor (11%)

Present Value

0 $(420,000) - $(420,000) 1-10 74,800* 5.8892 440,512 10 50,000 0.3522 17,610

NPV $ 38,122 * $37,800 + [($420,000 - $50,000) / 10] Req. 4

Year

Annual Cash Flow

PV Factor (15%)

Present Value

0 $(420,000) - $(420,000) 1-10 74,800* 5.0188 375,406 10 50,000 0.2472 12,360

NPV $( 32,234) * $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%.


PA112 Req. 1

Current (No Automation) Proposed (Automation)

Production and Sales Volume 80,000 units 120,000 units

Per Unit Total Per Unit Total

Sales Revenue $90 $7,200,000 $90 $10,800,000

Variable Costs:

Direct Materials $18 $18

Direct Labor 25 20

Variable Manufacturing Overhead 10 10

Total Variable Manufacturing Costs 53 48

Contribution Margin $37 2,960,000 $42 5,040,000

Fixed Manufacturing Costs 1,250,000 2,350,000

Net Income $1,710,000 $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%


= 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

PV Factor (15%)

Present Value

0 $(15,000,000) 1.0000 $(15,000,000.00) 1-10 2,430,000* 5.0188 12,195,684.00 10 500,000 0.2472 123,600.00

NPV $( 2,680,716.00) * $980,000 + [($15,000,000 - $500,000) / 10]


PA112 (Continued) Req. 5

Year

Annual Cash Flow

PV Factor (10%)

Present Value

0 $(15,000,000) - $(15,000,000.00) 1-10 2,430,000* 6.1446 14,931,378.00 10 500,000 0.3855 192,750.00

NPV $ 124,128.00 * $980,000 + [($15,000,000 - $500,000) / 10] 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 Beacondetermine the appropriate discount rate, which will determine whether this is an acceptable project.


PA113 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%


= $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 = Initial Investment / Annual Net Cash Flow

= $4,850,000 / $865,000 = 5.61 years (rounded)

Project 2: Payback Period = 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 / (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.


PA113 (Continued) Req. 3 Project 1

Year

Annual Cash Flow

PV Factor (10%)

Present Value

0 $(4,850,000) 1.0000 $ (4,850,000.00) 1-8 865,000 5.3349 4,614,688.50 8 1,000,000 0.4665 466,500.00

NPV $ 231,188.50 Project 2

Year

Annual Cash Flow

PV Factor (10%)

Present Value

0 $(3,400,000) 1.0000 $(3,400,000.00) 1-5 1,105,000* 3.7908 4,188,834.00 5 0 0.00

NPV $ 788,834.00 *($425,000 + [($3,400,000 / 5) Project 3

Year

Annual Cash Flow

PV Factor (10%)

Present Value

0 $(2,875,000) 1.0000 $(2,875,000.00) 1-10 475,000* 6.1446 2,918,685.00 10 125,000 0.3855 48,187.50

NPV $ 91,872.50 *($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.


PA114

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

PV Factor (10%)

Present Value

0 $(110,000) - $(110,000) 1-10 14,200* 6.1446 87,253 10 10,000 0.3855 3,855

NPV $( 18,892) * $4,200 + [($110,000 - $10,000) / 10] Req. 4

Year

Annual Cash Flow

PV Factor (6%)

Present Value

0 ($110,000) - $(110,000) 1-10 14,200* 7.3601 104,513 10 10,000 0.5584 5,584

NPV $ 97 * $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%.


PA115

Req. 1

Option 1:

$1,000,000 = $1,000,000

Option 2:

$92,000 9.8181* = $903,265

Option 3:

$82,000 6.7101** = $550,228

$95,000 (9.8181 - 6.7101)*** = 295,260

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

$845,488

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.


GROUP B PROBLEMS PB111 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

PV Factor (9%)

Present Value

0 $(200,000) - $(200,000) 1-5 57,600* 3.8897 224,047 5 12,000 0.6499 7,799

NPV $ 31,846 * $20,000 + [($200,000 - $12,000) / 5] Req. 4

Year

Annual Cash Flow

PV Factor (15%)

Present Value

0 $(200,000) - $(200,000) 1-5 57,600* 3.3522 193,087 5 12,000 0.4972 5,966

NPV $( 947) * $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%.


PB112 Req. 1

Current (No Automation) Proposed (Automation)

Production and Sales Volume 60,000 units 80,000 units

Per Unit Total Per Unit Total

Sales Revenue $70 $4,200,000 $70 $5,600,000

Variable Costs:

Direct Materials $15 $15

Direct Labor 20 12

Variable Manufacturing Overhead 7 7

Total Variable Manufacturing Costs 42 34

Contribution Margin $28 1,680,000 $36 2,880,000

Fixed Manufacturing Costs 800,000 1,612,500

Net Income $ 880,000 $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)


= 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

PV Factor (15%)

Present Value

0 $(5,800,000) 1.0000 $ (5,800,000.00) 1-8 1,062,500* 4.4873 4,767,756.25 8 400,000 0.3269 130,760.00

NPV $ ( 901,483.75) * [$387,500 + (($5,800,000 - $400,000) / 8)]


PB112 (Continued) Req. 5

Year

Annual Cash Flow

PV Factor (10%)

Present Value

0 $(5,800,000) 1.0000 $ (5,800,000.00) 1-8 1,062,500* 5.3349 5,668,331.25 8 400,000 0.4665 186,600.00

NPV $ 54,931.25 * [$387,500 + (($5,800,000 - $400,000) / 8)] 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%.


PB113 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%


= $1,650,000 / $8,200,000 = 20.12% (rounded)


= $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 = Initial Investment / Annual Net Cash Flow

= $2,700,000 / $975,000 = 2.77 years (rounded)


= 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 / (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.


PB113 (Continued) Req. 3 Project 1

Year

Annual Cash Flow

PV Factor (10%)

Present Value

0 $(2,700,000) 1.0000 $ (2,700,000.00) 1-7 975,000 4.8684 4,746,690.00 7 600,000 0.5132 307,920.00

NPV $2,354,610.00 Project 2

Year

Annual Cash Flow

PV Factor (10%)

Present Value

0 $(8,200,000) 1.0000 $(8,200,000.00) 1-10 2,470,000* 6.1446 15,177,162.00 10 0 0.3855 0.00

NPV $ 6,977,162.00 *[$1,650,000 + ($8,200,000 / 10)] Project 3

Year

Annual Cash Flow

PV Factor (10%)

Present Value

0 $(250,000) 1.0000 $ (250,000.00) 1-10 52,500* 6.1446 322,591.50 10 25,000 0.3855 9,637.50

NPV $ 82,229.00 *($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.


PB114 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

PV Factor (11%)

Present Value

0 $(860,000) - $(860,000) 1-6 206,000* 4.2305 871,483 6 20,000 0.5346 10,692

NPV $ 22,175 * $66,000 + [($860,000 - $20,000) / 6] Req. 4

Year

Annual Cash Flow

PV Factor (12%)

Present Value

0 $(860,000) - $(860,000) 1-6 206,000* 4.1114 846,948 6 20,000 0.5066 10,132

NPV $( 2,920) * $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%.


PB115

Req. 1

Option 1: Present Values

$100,000 = $100,000.00

Option 2:

$10,000 9.8181 = $ 98,181.00

Option 3:

$7,000 6.7101 = $ 46,970.70

+ $10,000 6.7101 0.4632 = 31,081.18

Total = $ 78,051.88 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.


ANSWERS TO SKILLS DEVELOPMENT CASES S 111 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.


S 111 (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 post-MBA 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

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.

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