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Problems Review Exam 2 BADM 115 Fall 2008 Professor Isabelle Bajeux-Besnainou Expected dividend yield
i
.
If D1 = $2.00, g (which is constant) = 6%, and P0 = $40, what is the stocks expected dividend yield for the coming year? a. 5.0% b. 6.0% c. 7.0% d. 8.0% e. 9.0%
Constant growth valuation
ii
.
A stock is expected to pay a dividend of $1 at the end of the year. The required rate of return is rs = 11%, and the expected constant growth rate is 5%. What is the current stock price? a. $16.67 b. $18.83 c. $20.00 d. $21.67 e. $23.33
Preferred stock valuation
iii
.
Mark Walker Inc plans to issue preferred stock with a perpetual annual dividend of $2 per share and a par value of $25. If the required return on this stock is currently 8%, what should be the stocks market value? a. $22.00 b. $23.00 c. $24.00 d. $25.00 e. $26.00
Future price of a constant growth stock
iv
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Damon Enterprises' stock currently sells for $25 per share. The stocks dividend is projected to increase at a constant rate of 7% per year. The required rate of return on the stock, rs, is 10%. What is Damon's expected price 4 years from today? a. $30.21 b. $31.65 c. $32.77 d. $33.89 e. $34.45
Constant growth valuation; CAPM
v
.
The Lashgari Company is expected to pay a dividend of $1 per share at the end of the year, and that dividend is expected to grow at a constant rate of 5% per year in the future. The company's beta is 1.2, the market risk premium is 5%, and the risk-free rate is 3%. What is the company's current stock price? a. $15.00 b. $20.00 c. $25.00 d. $30.00 e. $35.00
Constant growth dividend
vi
.
Wald Inc's stock has a required rate of return of 10%, and it sells for $40 per share. Wald's dividend is expected to grow at a constant rate of 7% per year. What is the expected yearend dividend, D1? a. $0.90 b. $1.00 c. $1.10 d. $1.20 e. $1.30
Constant growth stock
vii
.
Thames Inc.s most recent dividend was $2.40 per share (D0 = $2.40). The dividend is expected to grow at a rate of 6% per year. The risk-free rate is 5% and the market risk premium is 4%. If the companys beta is 1.3, what is the price of the stock today? a. $72.14 b. $57.14 c. $40.00 d. $68.06 e. $60.57
Component cost of retained earnings: CAPM
viii
.
Assume that you are a consultant to Thornton Inc., and you have been provided with the following data: rRF = 5.5%; RPM = 6.0%; and b = 0.8. What is the cost of equity from retained earnings based on the CAPM approach? a. 9.65% b. 9.91% c. 10.08% d. 10.30% e. 10.49%
Component cost of retained earnings: DCF, D1
ix
.
Assume that you are a consultant to Morton Inc., and you have been provided with the following data: D1 = $1.00; P0 = $25.00; and g = 6% (constant). What is the cost of equity from retained earnings based on the DCF approach?
a. 9.79% b. 9.86% c. 10.00% d. 10.20% e. 10.33% Cost of retained earnings: bond-yield-plus-risk premium
x
.
P. Daves Inc. hired you as a consultant to help them estimate their cost of equity. The yield on the firms bonds is 6.5%, and Daves' investment bankers believe that the cost of equity can be estimated using a risk premium of 4.0%. What is an estimate of Daves' cost of equity from retained earnings? a. 9.77% b. 10.02% c. 10.19% d. 10.33% e. 10.50%
Component cost of debt
xi
.
Several years ago the Haverford Company sold a $1,000 par value bond that now has 25 years to maturity and an 8.00% annual coupon that is paid quarterly. The bond currently sells for $900.90, and the companys tax rate is 40%. What is the component cost of debt for use in the WACC calculation? a. 5.40% b. 5.73% c. 5.98% d. 6.09% e. 6.24%
Component cost of new common stock, based on DCF, D1
xii
.
Wagner Lumber Company hired you to help them estimate their cost of capital. You were provided with the following data: D1 = $1.25; P0 = $40; g = 6% (constant); and F = 5%. The firm must issue new stock; what is the cost of equity raised by selling new common stock? a. 9.29% b. 9.40% c. 9.62% d. 9.85% e. 9.99%
Retained earnings breakpoint
xiii
.
Crum International's target capital structure calls for 80% debt and 20% equity. The company expects to have $3 million of net income this year, and 60% of the net income will be paid out in dividends. How large can the firms capital budget be this year before it will have to issue new common stock? a. $5.5 million b. $6.0 million c. $6.3 million
d. $6.8 million e. $7.1 million
Cost of retained earnings: risk premium, CAPM, and DCF
xiv
.
Malko Inc. hired you as a consultant to help them estimate their cost of capital. You have been provided with the following data. (1): rd = yield on the firms bonds = 6.5% and risk premium over own debt cost = 4%. (2) rRF = 5.5%, RPM = 5.5%, and b = 1.0. (3) D1 = $1.20; P0 = $40.00 and g = 7% (constant). You were asked to estimate the cost of equity based on the three most commonly used methods and then to indicate the difference between the highest and lowest of these estimates. What is this difference? a. 0.90% b. 1.00% c. 1.10% d. 1.20% e. 1.30%
Capital components
xv
.
Which of the following statements is CORRECT? a. Because of tax effects, an increase in the risk-free rate will have a greater effect on the after-tax cost of debt than on the cost of common stock. b. When calculating the cost of preferred stock, companies must adjust for taxes, because dividends paid on preferred stock are deductible by the paying corporation. c. When calculating the cost of debt, a company needs to adjust for taxes, because interest payments are deductible by the paying corporation. d. If a companys beta increases, this will increase the cost of equity used to calculate the WACC, but only if the company does not have enough retained earnings to take care of its equity financing and hence needs to issue new stock. e. Higher flotation costs reduce investor returns, and that leads to a reduction in a companys WACC.
Factors influencing WACC
xvi
.
Maese Sisters Inc has been paying out all of its earnings as dividends, and hence has no retained earnings. This same situation is expected to persist in the future. The company uses the CAPM to calculate its cost of equity. Its target capital structure consists of common stock, preferred stock, and debt. Which of the following events would reduce the WACC? a. b. c. d. e. The flotation costs associated with issuing new common stock increase. The market risk premium declines. The companys beta increases. Expected inflation increases. The flotation costs associated with issuing preferred stock increase.
WACC
xvii
.
Dobson Dairies has a capital structure consisting of 60% debt and 40% common stock. The companys CFO has obtained the following information:
The before-tax YTM on the companys bonds is 8%. The companys common stock is expected to pay a $3.00 dividend at year end (D 1 = $3.00), and the dividend is expected to grow at a constant rate of 7% a year. The common stock currently sells for $60 a share. Assume the firm will be able to use retained earnings to fund the equity portion of its capital budget. The companys tax rate is 40%.
What is the companys WACC? a. 12.00% b. 8.03% c. 9.34% d. 8.00% e. 7.68%
NPV (constant cash flows; 5 years)
xviii
.
Tapley Dental Associates is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected. WACC = 10% Year: Cash flows: a. b. c. d. e. $116.73 $123.15 $128.47 $131.96 $137.24 01 -$1,000 2 $300 $300 3 $300 4 $300 5 $300
IRR (constant cash flows; 3 years)
xix
.
Blanchford Enterprises is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's projected IRR can be less than the WACC (and even negative), in which case it will be rejected. Year: Cash flows: a. 16.20% b. 16.65% c. 17.10% 01 -$1,000 2 $450 $450 3 $450
d. 17.55% e. 18.00%
Payback (nonconstant cash flows; 5 years)
xx
.
Tapley Dental Associates is considering a project that has the following cash flow data. What is the project's payback? Year: Cash flows: a. b. c. d. e. 2.11 years 2.50 years 2.71 years 3.05 years 3.21 years 01 -$1,000 2 $300 $310 3 $320 4 $330 5 $340
Discounted payback (constant cash flows; 3 years)
xxi
.
Blanchford Enterprises is considering a project that has the following cash flow and WACC data. What is the project's discounted payback? WACC = 10% Year: Cash flows: a. b. c. d. e. 2.01 years 2.35 years 2.65 years 2.84 years 3.17 years 01 -$1,000 2 $500 $500 3 $500
MIRR (uneven cash flows; 3 years)
xxii
.
Edison Electric Systems is considering a project that has the following cash flow and WACC data. What is the project's MIRR? Note that a project's projected MIRR can be less than the WACC (and even negative), in which case it will be rejected. WACC = 10% Year: Cash flows: a. b. c. d. 4.90% 5.18% 5.72% 6.23% 01 -$1,000 2 $350 $370 3 $390
e. 6.87% NPV vs IRR (constant cash flows; 3 years)
xxiii
.
Last month, Wong Systems Inc. decided to accept the project whose cash flows are shown below. However, before actually starting the project, the Federal Reserve took actions that changed interest rates and Wong's WACC. By how much did the change in the WACC affect the project's forecasted NPV? Assume that the Fed action will not affect the cash flows, and note that a project's projected NPV can be negative, in which case it should be rejected. Old WACC = 10% New WACC = 5% Year: 01 2 3 Cash flows: -$1,000 $500 $500 a. b. c. d. e. $ 88.67 $ 92.16 $104.93 $118.19 $124.18
$500
NPV vs payback
xxiv
.
Pettway Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the shorter payback, some value may be forgone. How much value will be lost in this instance? Note that under some conditions choosing projects on the basis of the shorter payback will not cause value to be lost. WACC = 13% Year: CFS: CFL: a. b. c. d. e. $55.16 $66.42 $78.79 $89.79 $96.16 01 -$1,000 -$2,100 2 $400 $800 $400 $800 3 $400 $800 4 $400 $800
NPV vs IRR
xxv
.
Ross Inc.'s CFO thinks the company should rely primarily on the NPV method, but the president prefers the IRR, so decisions are based on the IRR. The CFO wants you to show the president that at times decisions based on the IRR result in a reduction in the company's value relative to its value if the NPV criterion were used. The CFO then asked you to analyze two projects that the company is now considering, S and L, whose cash
flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will Ross be forgoing? Note that at times the project with the higher IRR will also have the higher NPV, and in these cases no value will by lost by relying on the IRR. WACC = 10% Year: CFS: CFL: a. b. c. d. e. $ 0.00 $125.47 $139.85 $143.96 $157.01 01 -$1,025 -$1,025 2 $650 $400 $650 $400 3 $400 4 $400
Ranking methods
xxvi
.
Assume a project has normal cash flows. All else equal, which of the following statements is CORRECT? a. b. c. d. e. The projects IRR increases as the WACC declines. The projects NPV increases as the WACC declines. The projects MIRR is unaffected by changes in the WACC. The projects regular payback increases as the WACC declines. The projects discounted payback increases as the WACC declines.
Normal vs. nonnormal cash flows
xxvii
.
Which of the following statements is CORRECT? a. b. c. d. If a project has normal cash flows, then its IRR must be positive. If a project has normal cash flows, then its MIRR must be positive. If a project has normal cash flows, then it will have exactly two real IRRs. The definition of normal cash flows is that the cash flow stream has one or more negative cash flows followed by a stream of positive cash flows and then one negative cash flow at the end of the projects life. e. If a project has normal cash flows, then it can have only one real IRR, whereas a project with nonnormal cash flows might have more than one real IRR.
NPV Answer:
xxviii
.
Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows.
a. A projects NPV is found by compounding the cash inflows at the IRR to find the terminal value (TV), then discounting the TV at the WACC. b. The lower the WACC used to calculate it, the lower the calculated NPV will be. c. If a projects NPV is less than zero, then its IRR must be less than the WACC. d. If a projects NPV is greater than zero, then its IRR must be less than zero. e. The NPV of a relatively low risk project should be found using a relatively high WACC.
Payback
xxix
.
Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows. a. The longer a projects payback period, the more desirable the project is normally considered to be by this criterion. b. One drawback of the payback criterion for evaluating projects is that this method does not properly account for the time value of money. c. If a projects payback is positive, then the project should be rejected because it must have a negative NPV. d. The regular payback ignores cash flows beyond the payback period, but the discounted payback method overcomes this problem. e. If a company uses the same requirement to evaluate all projects, say it requires a payback of 4 years or less, then the company will tend to reject projects with relatively short lives and accept long-lived projects, and this will cause its risk to increase over time.
NPV xxx . As the capital budgeting director for Denver Corporation, you are evaluating two mutually exclusive projects with the following net cash flows: Project X Project Z Year Cash Flow Cash Flow 0 -$100,000 -$100,000 1 50,000 10,000 2 40,000 30,000 3 30,000 40,000 4 10,000 60,000 If Denvers WACC is 15%, which project would you choose? a. b. c. d. e. Neither project. Project X, since it has the higher IRR. Project Z, since it has the higher NPV. Project X, since it has the higher NPV. Project Z, since it has the higher IRR.
IRR and mutually exclusive projects xxxi . A company is analyzing two mutually exclusive projects, S and L, whose cash flows are shown below: Years S L 0 |
r = 12%
1 | 1,000 0
2 | 350 300
3 | 50 1,500
-1,100 -1,100
The companys WACC is 12%. What is the regular IRR of the better project, that is, the project that maximizes the firms stock price? a. b. c. d. e. 12.00% 15.53% 18.62% 19.08% 20.46%
NPV and IRR
xxxii
.
A firm is analyzing two mutually exclusive projects with the following cash flows: Year 0 1 2 3 4 Project A Cash Flow -$50,000 10,000 15,000 40,000 20,000 Project B Cash Flow -$30,000 6,000 12,000 18,000 12,000
If the companys WACC is 10%, what is the NPV of the project with the highest IRR? a. b. c. d. e. $ 7,090 $ 8,360 $11,450 $12,510 $15,200
Annual operating cash flows, depr'n given
xxxiii
.
You work for Alpha Inc., and you must estimate the Year 1 operating net cash flow for a proposed project with the following data. What is the Year 1 operating cash flow? Sales $11,000 Depreciation $4,000
Other operating costs Tax rate a. $4,650 b. $4,800 c. $4,950 d. $5,100 e. $5,250
$6,000 35%
Annual operating cash flows: straight line depreciation
xxxiv
.
Delta Software is considering a new project whose data are shown below. The equipment that would be used has a 3-year tax life, after which it will be worthless, and it will be depreciated by the straight line method over 3 years. Revenues and other operating costs are expected to be constant over the project's 3-year life. What is the project's operating cash flow during Year 1? Equipment cost (depreciable basis) Straight line depreciation rate Sales $60,000 Operating costs excl. deprn Tax rate a. b. c. d. e. $27,000 $28,500 $30,000 $31,500 $33,000 $75,000 33.33% $25,000 35%
Ann. op. cash flows, depr'n given, interest given
xxxv
.
You work for the Delta Company, which is considering a new project whose data are shown below. What is the project's operating cash flow during Year 1? Sales $60,000 Depreciation Other operating costs Interest expense Tax rate a. b. c. d. e. $23,850 $25,550 $26,650 $27,950 $29,050 $8,000 $25,000 $8,000 35%
Annual operating cash flows. MACRS depr'n. year 4 CF
xxxvi
.
Your company, Acme Computer, is considering a new project whose data are shown below. The equipment that would be used has a 3-year tax life, and the MACRS rates for such property are 33%, 45%, 15%, and 7% for Years 1 through 4. Revenues and other operating costs are expected to be constant over the project's 10-year life. What is the project's operating cash flow during Year 4? Equipment cost (depreciable basis) MACRS rates, years 1-4 Sales $60,000 Operating costs excl. deprn Tax rate a. $22,577 b. $23,591 c. $24,588 d. $25,897 e. $26,167 $75,000 33% $25,000 35% 45% 15% 7%
Salvage value calculations
xxxvii
.
Big Air Services is now in the final year of a project. The equipment originally cost $20 million, of which 75% has been depreciated. Big Air can sell the used equipment today for $6 million, and its tax rate is 40%. What is the equipments after-tax net salvage value? a. b. c. d. e. $5,500,000 $5,600,000 $5,700,000 $5,800,000 $5,900,000
NPV, straight line, constant CFs, cannibalization
xxxviii
.
Yummy Foods is considering a new salsa product whose data are shown below. The equipment that would be used has a 3-year tax life, would be depreciated by the straight line method over the project's 3-year life, would have zero salvage value, and no new working capital would be required. Revenues and other operating costs are expected to be constant over the project's 3-year life. However, this project would compete with other Yummy products and would reduce their pre-tax annual cash flows. What is the project's NPV? (Hint: Cash flows are constant in Years 1-3.) WACC Annual pre-tax cannibalization cost 10% $5,000
Net investment cost (depreciable basis) Straight line deprn rate Sales revenues Operating costs excl. deprn Tax rate a. b. c. d. e. $17,455.87 $18,516.78 $19,892.34 $20,118.78 $21,214.55
$65,000 33.33% $70,000 $25,000 35%
NPV, constant CFs, working capital, salvage value
xxxix
.
The Movie Place is considering a new investment whose data are shown below. The required equipment has a 3-year tax life and would be fully depreciated by the straight line method over the 3 years, but it would have a positive salvage value at the end of Year 3, when the project would be closed down. Also, some new working capital would be required, but it would be recovered at the end of the project's life. Revenues and other operating costs are expected to be constant over the project's 3-year life. What is the project's NPV? WACC Net equipment cost (depreciable basis) Required new working capital Straight line deprn rate Sales revenues Operating costs excl. deprn Expected pretax salvage value Tax rate a. b. c. d. e. $24,971.86 $25,538.17 $26,553.97 $27,356.82 $28,879.81 10% $65,000 $10,000 33.33% $70,000 $25,000 $5,000 35%
Risk adjustment
xl
.
The relative risk of a proposed project is best accounted for by a. Adjusting the discount rate upward if the project is judged to have above average risk. b. Adjusting the discount rate downward if the project is judged to have above average risk. c. Reducing the NPV by 10% for risky projects. d. Picking a risk factor equal to the average discount rate.
e. Ignoring it because project risk cannot be measured accurately.
Relevant cash flows
xli
.
Which of the following is NOT a cash flow that should be included in the analysis of a project? a. b. c. d. e. Changes in net operating working capital. Shipping and installation costs. Cannibalization effects. Opportunity costs. Sunk costs that have been expensed for tax purposes.
Externalities
xlii
.
Which of the following statements is CORRECT?
a. An
b. c. d. e.
externality is a situation where a project would have an adverse effect on some other part of the firms overall operations. If the project would have a favorable effect on other operations, then this is not an externality. An example of an externality is a situation where a bank opens a new office, and that new office causes deposits of the banks other offices to decline. The NPV method automatically deals correctly with externalities, even if the externalities are not specifically identified, but the IRR method does not. This is another reason to favor the NPV. Both the NPV and IRR methods deal correctly with externalities, even if the externalities are not specifically identified. However, the payback method does not. The identification of an externality can never lead to an increase in the calculated NPV.
Relevant cash flows
xliii
.
A company is considering a new project. The CFO plans to calculate the projects NPV by first estimating the relevant cash flows for each year of the projects life (the initial investment cost, the annual operating cash flows, and the terminal cash flow), then discounting those cash flows at the companys WACC. Which of the following factors should the CFO INCLUDE IN THE CASH FLOWS when estimating the relevant cash flows? a. All sunk costs that have been incurred relating to the project. b. All interest expenses on debt used to help finance the project. c. The investment in working capital required to operate the project, even if that investment will be recovered at the end of the projects life. d. Sunk costs that have been incurred relating to the project, but only if those costs were incurred prior to the current year.
e. Effects of the project on other divisions of the firm, but only if those effects lower the projects own direct cash flows.
NPV with externalities
xliv
.
Ellison Products is considering a new project that develops a new laundry detergent, WOW. The company has estimated that the projects NPV is $3 million, but this does not consider that the new laundry detergent will reduce the revenues received on its existing laundry detergent products. Specifically, the company estimates that if it develops the WOW company will lose $500,000 in after-tax cash flows during each of the next 10 years because of the cannibalization of its existing products. Ellisons WACC is 10%. What is the net present value (NPV) of undertaking WOW after considering externalities? a. $2,927,716.00 b. $3,000,000.00 c. -$ 72,283.55 d. $2,807,228.00 e. -$3,072,283.55
You have been asked by the president of your company to evaluate the proposed acquisition of a new special-purpose truck. The trucks basic price is $50,000, and it will cost another $10,000 to modify it for special use by your firm. The truck falls in the MACRS 3-year class, and it will be sold after three years for $20,000. The applicable depreciation rates are 33%, 45%, 15%, and 7%. Use of the truck will require an increase in net operating working capital (spare parts inventory) of $2,000, which will be recovered in Year 3. The truck will have no effect on revenues, but it is expected to save the firm $20,000 per year in before-tax operating costs, mainly labor. The firms marginal tax rate is 40%.
New project investment
xlv
.
What is the net investment in the truck? (That is, what is the Year 0 net cash flow?) a. b. c. d. e. -$50,000 -$52,600 -$55,800 -$62,000 -$65,000
Operating cash flow
xlvi
.
What is the operating cash flow in Year 1? a. b. c. d. e. $17,820 $18,254 $19,920 $20,121 $21,737
Non-operating cash flows
xlvii
.
What is the total value of the terminal year non-operating cash flows at the end of Year 3? a. b. c. d. e. $10,000 $12,000 $15,680 $16,000 $18,000
New project NPV
xlviii
.
The trucks cost of capital is 10%. What is its NPV? a. -$1,547 b. -$ 562 c. $ 0 d. $ 562 e. $1,034
Breakeven analysis
xlix
.
A companys fixed operating costs are $500,000, its variable costs are $3.00 per unit, and the products sales price is $4.00. What is the companys breakeven point, i.e., at what unit sales volume would its income equal its costs? a. b. c. d. e. 500,000 600,000 700,000 800,000 900,000
l
.
Millman Electronics will produce 60,000 stereos next year. Variable costs will equal 50% of sales, while fixed costs will total $120,000. At what price must each stereo be sold for the company to achieve an EBIT of $95,000? a. b. c. d. e. $6.57 $6.87 $7.17 $7.47 $7.77
Business risk
li
.
An increase in the debt ratio will generally have no effect on . a. b. c. d. e. Business risk. Total risk. Financial risk. Market risk. It will not affect any measure of risk.
Optimal capital structure
lii
.
Which of the following statements is CORRECT? a. As a rule, the optimal capital structure is found by determining the debt-equity mix that maximizes expected EPS. b. The optimal capital structure simultaneously maximizes EPS and minimizes the WACC. c. The optimal capital structure minimizes the cost of equity, which is a necessary condition for maximizing the stock price. d. The optimal capital structure simultaneously minimizes the cost of debt, the cost of equity, and the WACC. e. The optimal capital structure simultaneously maximizes stock price and minimizes the WACC.
Inventory conversion period
liii
.
Kleck Corporation has $500,000 of inventory, and its annual sales are $3,000,000. Based on a 365 day year, what is Kleck's inventory conversion period? a. b. c. d. e. 56.49 days 57.04 days 60.83 days 62.81 days 65.27 days
Payables deferral period
liv
.
Plummer Products purchases $3,750,000 of materials each year, and it has an average accounts payable balance of $350,000. Assuming there are 365 days per year, what is Plummers payables deferral period? a. b. c. d. e. 25.91 days 27.83 days 30.38 days 32.52 days 34.07 days
Average collection period (or DSO)
lv
.
Carroll Construction has annual sales of $730,000, and it has $100,000 of accounts receivable. Based on a 365-day year, what is Carroll's average collection period (or DSO)? a. b. c. d. e. 50 days 52 days 54 days 56 days 58 days
Cash conversion cycle
lvi
.
Ashwell Corp has $1,600,000 of sales, $200,000 of inventories, $150,000 of receivables, and $100,000 of payables. Its cost of goods sold is 70% of sales. What is Ashwells cash conversion cycle (CCC)? a. b. c. d. e. 60.77 days 62.55 days 64.63 days 66.81 days 68.22 days
Cash conversion cycle
lvii
.
Which of the following statements is CORRECT? a. Other things held constant, it is better to have a relatively short than a relatively long cash conversion cycle. b. Other things held constant, it is better to have a relatively long than a relatively short cash conversion cycle.
c. Other things held constant, the length of the cash conversion cycle has no effect on a firms profitability. d. Other things held constant, the length of the cash conversion cycle might have an effect on a firms profitability, but it is impossible to state if that effect is positive or negative. e. Since firms have no control over their cash conversion cycles, there is little point in studying these cycles.
Working capital
lviii
.
Other things held constant, which of the following would lead to an increase in working capital? a. b. c. d. e. Cash is used to buy marketable securities. A cash dividend is declared and paid. Missing inventory is written off against retained earnings. Long-term bonds are retired from the proceeds of a preferred stock issue. Merchandise is sold on credit, but at a profit.
Additional funds needed -- positive AFN
lix
.
Bullock Inc's sales were $500,000 during 2005, and its year-end assets were $750,000. For 2006, sales are expected to grow by 30%, and since Bullock is operating at full capacity, its assets must grow in proportion to sales. Its 2005 current liabilities consisted of $40,000 of accounts payable, $50,000 of notes payable, and $30,000 of accruals. Its after-tax profit margin is forecasted to be 5%, and the firm plans to pay out 60% of its earnings. Based on the AFN equation, what is the firm's additional funds needed (AFN) for 2006? a. b. c. d. e. $177,000 $184,000 $191,000 $198,000 $205,000
Additional funds needed
lx
.
Jefferson City Computers has developed a forecasting model to estimate its AFN for the upcoming year. All else being equal, which of the following factors is most likely to increase its additional funds needed (AFN)? a. b. c. d. A sharp increase in its forecasted sales. A sharp reduction in its forecasted sales. The company reduces its dividend payout ratio. The company decides to switch its materials purchases to a supplier that sells on terms of 1/5, net 90, from a supplier whose terms are 3/15, net 35. e. The company discovers that it has excess capacity in its fixed assets.
Exchange rates
lxi
.
If one Canadian dollar can purchase $0.75 U.S. dollar, how many Canadian dollars can one U.S. dollar buy? a. b. c. d. e. 1.33 Canadian dollars/US dollar 1.44 Canadian dollars/US dollar 1.55 Canadian dollars/US dollar 1.66 Canadian dollars/US dollar 1.77 Canadian dollars/US dollar
Exchange rates
lxii
.
If U.S. dollars sell for 0.60 (British pounds) per dollar, what should pounds sell for in dollars per pound? a. b. c. d. e. $1.62/pound $1.67/pound $1.72/pound $1.77/pound $1.82/pound
Cross rates
lxiii
.
Currently, in the spot market $1 = 106.5 Japanese yen, 1 Japanese yen = 0.0096 euro, and 1 euro = 10.1 Mexican pesos. What is the exchange rate between the U.S. dollar and the Mexican peso? a. b. c. d. e. 10.326 pesos/$ 10.693 pesos/$ 10.910 pesos/$ 11.158 pesos/$ 11.448 pesos/$
Purchasing power parity
lxiv
.
A television set sells for $1,000 U.S. dollars. In the spot market, $1 = 110 Japanese yen. If purchasing power parity holds, what should be the price (in yen) of the same television set in Japan? a. 80,000 yen b. 90,000 yen c. 100,000 yen d. 110,000 yen e. 120,000 yen
Multinational financial management
lxv
.
Multinational financial management requires all of the following EXCEPT:
a. b. c. d.
The effects of changing currency values must be included in financial analyses. Legal and economic differences must be considered in financial decisions. Political risk should be excluded from multinational corporate financial analyses. Cultural differences must be accounted for when considering firm goals and employee management. e. The roles of different governments must be accounted for since they may vary greatly and usually affect the nature of competition.
i.
Expected dividend yield
D1 g P0 Dividend yield $2.00 6% $40.00 5.00%
i ii
.
Constant growth valuation
D1 rs g P0 $1.00 11% 5% $16.67
iii.
Preferred stock valuation
Preferred dividend Preferred par value Required return Preferred market price $2 $25 8% $25.00
iv.
Future price of a constant growth stock
Stock price Growth rate Years in the future Required return Stock price (in 4 years) $25.00 7% 4 10% $32.77
v.
Constant growth valuation; CAPM D1 b rRF RPM g rs P0 $1.00 1.20 3.0% 5.0% 5.0% 9.0% $25.00
v vi . Constant growth dividend
Stock price Required return Growth rate Dividend yield Expected dividend $40.00 10% 7.00% 3.00% $1.20
vii.
Constant growth stock
The required rate of return on the stock: 5% + (9% - 5%)1.3 = 10.2%. r1 DRF = $2.40 1.06 = $2.544. 5.50% The price of the stock today is $2.544/(0.102 - 0.06) = $60.57. RPM 6.00% b oupon rate 0.80 C viii. Component cost 8.00% of retained earnings: CAPM Answer: Periods/year 4 D1 $1.00 rs 10.30% Maturity (yr) 25 P0 $25.00 Bond price $900.90 g 6.00% Par value ix. Component cost $1,000 of retained earnings: DCF, D1 Answer: Tax rate 40% rs 10.00% Bond yield 6.50% Calculator inputs: Risk premium 4.00% Bond yield 6.50% x. Cost of retained 100 earnings: bond-yield-plus-risk premium Answer: N premium Risk 4.00% PV -$900.90 re 10.50% PMT $20 FV $1,000 rRF xi. Component cost of debt 5.50% D1 Answer: $1.25 I/YR 2.25% times 4 = 9.0% = Before-tax cost of debt RP P0 M 5.50% $40.00 = After-tax cost of debt (A-T r ) for use in WACC 5.40% d b g 6.00% 1.00 Weight of debt 80% Fs 5.00% r 11.00% xii. Component cost of new common stock, 20% based on DCF, D1 Answer: Weight of equity Expected Income 9.29% re D1 $1.20 $3,000,000 Dividend payout ratio 60% P0 $40.00 xiii. Retained earnings breakpoint Answer: g 7.00% $1,200,000 Retained earnings re Retained earnings breakpoint 10.00% $6,000,000 xiv. Max 11.00% Cost of retained earnings: risk premium, CAPM, and DCF Min 10.00% 1.00% Difference
d
c
e
a
a
b
xv.
Capital components
Statement c is true, because interest payments on debt are tax deductible. The other statements are false. xvi. Factors influencing WACC
xvii. WACC rs = D1/P0 + g = $3.00/$60.00 + 0.07 = 0.12 = 12%. WACC = wdrd(1 - T) + wcrs = (0.6)(0.08)(1 - 0.4) + (0.4)(0.12) = 0.0768 = 7.68%. xviii. WACC: Cash flows Answer: NPV = 10.00% 0 -$1,000 $137.24 1 $300 2 $300 WACC: Year 0: 3 $300 10.0% -$1,000 4 $300
NPV (constant cash flows; 5 years)
5 $300
xix.
IRR (constant cash flows; 3 years)
Cash flows Answer: IRR =
0 -$1,000 16.65%
1 $450
2 $450 Year 0:
3 $450 -$1,000
xx.
Payback (nonconstant cash flows; 5 years)
Cash flows Answer: Cumulative CF Payback = 0 -$1,000 -$1,000 1 $300 -$700 2 $310 -$390 3 $320 -$70 4 $330 $260 3.21
5 $340 $600 -
3.21
x xxi
.
Discounted payback (constant cash flows; 3 years)
WACC: Cash flows Answer: PV of CFs Cumulative CF Payback = 10.00% 0 -$1,000 -$1,000 -$1,000 1 $500 $455 -$545 2 $500 $413 -$132 3 $500 $376 $244 2.35
2.35
xxii. MIRR (uneven cash flows; 3 years) WACC: Cash flows 10.00% 0 -$1,000
1 $350
2 $370
3 $390
Answer: TV: Compounded values: $423.50 $407.00 $390.00 $1,220.50 6.87% found as discount rate that equates PV of TV to cost MIRR = 6.87% Alternative calculation, with Excel MIRR = x xxiii
.
NPV vs IRR (constant cash flows; 3 years)
Old WACC: Cash flows Answer: Old NPV = New NPV = Change x xxiv
10.00% 0 -$1,000 $243.43 $361.62 $118.19
1 $500
New WACC: 2 $500
5.00% 3 $500
.
NPV vs payback
WACC: CFS CFL
13.00% 0 -$1,000 -$2,100 1 $400 $800 2 $400 $800 3 $400 $800 4 $400 $800
Answer: Cumulative CF, S Cumulative CF, L Payback S 2.50 Payback L 2.63 NPV, L $279.58 NPV, S $189.79 $89.79 Value lost
-$1,000 -$2,100 -
-$600 -$1,300 -
-$200 -$500 -
$200 $300 2.50 2.63
$600 $1,100 -
Project S WACC: 13.0% Year 0: -$1,000 Year 1: $400 L 279.6 1,100.0 946.2 803.9 672.1 549.7 435.9 329.9 231.0 138.5 52.0 -29.0 -105.1 -176.6
Project L WACC: 13.0% Year 0: -$2,100 Year 1: $800
S 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 189.8 600.0 523.1 452.0 386.0 324.9 267.9 214.9 165.5 119.3 76.0 35.5 -2.5 -38.3
1,200 1,000 800 600 400 200 0 -200 0% 5% 10% 15% 20% 25%
S L
x xxv
.
NPV vs IRR
WACC: CFS CFL Answer: IRR, L IRR, S NPV, L NPV, S Value lost
700 600 500 400 300 200 100 0 -100 -200 0%
10.00% 0 -$1,025 -$1,025 20.5% 17.4% $242.95 $103.10 $0.00
1 $650 $400
2 $650 $400
3 $400
4 $400
S 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 103.1 275.0 237.0 201.0 166.7 134.1 103.1 73.5 45.3 18.4 -7.3 -31.9 -55.5 -78.1 -99.7 -120.5 -140.4
6%
12%
18%
24%
30%
L 242.9 575.0 498.1 427.0 361.0 299.9 242.9 189.9 140.5 94.3 51.0 10.5 -27.5 -63.3 -96.9 -128.6 -158.5
x xxvi
.
Ranking methods
Statement b is true, because a projects NPV increases as the WACC declines. xxvii.Normal vs. nonnormal cash flows xxviii.NPV xxix
Payback
.
xxx.
NPV
Financial calculator solution (in thousands): Project X: Inputs: CF0 = -100; CF1 = 50; CF2 = 40; CF3 = 30; CF4 = 10; I/YR = 15. Output: NPVX = -0.833 = -$833. Project Z: Inputs: CF0 = -100; CF1 = 10; CF2 = 30; CF3 = 40; CF4 = 60; I/YR = 15.
Output: NPVZ = -8.014 = -$8,014. At a WACC of 15%, both projects have negative NPVs and should be rejected.
xxxi. IRR and mutually exclusive projects
Because the two projects are mutually exclusive, the project with the higher positive NPV is the better project. Project S Inputs: CF0 = -1100; CF1 = 1000; CF2 = 350; CF3 = 50; I/YR = 12. Outputs: NPV = $107.46; IRR = 20.46%. Project L Inputs: CF0 = -1100; CF1 = 0; CF2 = 300; CF3 = 1500; I/YR = 12. Outputs: NPV = $206.83; IRR = 19.08%. Project L is the better project because it has the higher NPV; its IRR = 19.08%. x xxxii . NPV and IRR
Financial calculator solution: Project A: Inputs: CF0 = -50000; CF1 = 10000; CF2 = 15000; CF3 = 40000; CF4 = 20000; I/YR = 10. Outputs: NPV = $15,200.46 $15,200; IRR = 21.38%. Project B: Inputs: CF0 = -30000; CF1 = 6000; CF2 = 12000; CF3 = 18000; CF4 = 12000; I/YR = 10. Outputs: NPV = $7,091.73 $7,092; IRR = 19.28%.
Project A has the highest IRR, so the answer is $15,200. xxxiii.Annual
operating cash flows, depr'n given
Sales revenues - Operating costs (x-depr) - Depreciation expense Operating income (EBIT) - Taxes After-tax EBIT + Depreciation Operating cash flow $11,000 $6,000 $4,000 $1,000 -$350 $650 $4,000 $4,650
xxxiv.
Annual operating cash flows: straight line
depreciation
Sales revenues - Operating costs (x-depr) - Basis x rate = depreciation = Operating income (EBIT) - Taxes After-tax EBIT + Depreciation Operating cash flow, Year 1
$60,000 -$25,000 -$25,000 $10,000 -$3,500 $6,500 $25,000 $31,500
x xxxv
.
Ann. op. cash flows, depr'n given, interest given
Sales revenues - Operating costs (x-depr) - Depreciation expense Operating income (EBIT) - Taxes After-tax EBIT + Depreciation Operating cash flow $60,000 $25,000 $8,000 $27,000 -$9,450 $17,550 $8,000 $25,550 This is a bit harder because it provides information on interest, and some students might incorrectly include it as an input. We like this wrinkle because it's important that students know not to include financing costs in the cash flows.
xxxvi.Annual
operating cash flows. MACRS depr'n. year 4 CF
Sales revenues - Operating costs (x-depr) - Basis x rate = depreciation = Operating income (EBIT) - Taxes After-tax EBIT + Depreciation Operating cash flow, Year 4 $60,000 -$25,000 -$5,250 $29,750 -$10,413 $19,338 $5,250 $24,588
xxxvii.
Salvage value calculations
% depreciated on equip. Tax rate Equipment cost - Accumulated depr'n Current BV of equipment Market value Gain (loss) on sale of equip. Taxes paid (credited) After-tax net salvage value
75% 40% $20,000,000 $15,000,000 $5,000,000 $6,000,000 $1,000,000 -$400,000 $5,600,000
xxxviii.
NPV, straight line, constant CFs, cannibalization
Answer: Investment Sales revenues - Cannibalization cost - Operating costs (x-depr) - Basis x rate = depreciation = Operating income (EBIT) - Taxes After-tax EBIT + Depreciation Operating cash flow NPV t=0 -$65,000 t=1 $70,000 -$5,000 -$25,000 -$21,667 $18,333 -$6,417 $11,917 $21,667 $33,583 t=2 $70,000 -$5,000 -$25,000 -$21,667 $18,333 -$6,417 $11,917 $21,667 $33,583 t=3 $70,000 -$5,000 -$25,000 -$21,667 $18,333 -$6,417 $11,917 $21,667 $33,583
-$65,000 $18,516.78
xxxix.
NPV, constant CFs, working capital, salvage value
Answer: Investment in fixed assets Investment in net working capital Sales revenues - Operating costs (x-depr) - Basis x rate = depreciation = Operating income (EBIT) - Taxes After-tax EBIT + Depreciation Operating cash flow Recovery of working capital Salvage value, pre-tax Tax on salvage value Total cash flows NPV $26,553.97 t=0 -$65,000 -$10,000 t=1 t=2 t=3
-$75,000
$70,000 -$25,000 -$21,667 $23,333 -$8,167 $15,167 $21,667 $36,833
$70,000 -$25,000 -$21,667 $23,333 -$8,167 $15,167 $21,667 $36,833
-$75,000
$36,833
$36,833
$70,000 -$25,000 -$21,667 $23,333 -$8,167 $15,167 $21,667 $36,833 $10,000 $5,000 -$1,750 $50,083
xl. xli.
Risk adjustment Relevant cash flows
Relevant cash flows
xlii. Externalities xliii. xliv.
NPV with externalities
Step 1: Calculate the NPV of the negative externalities due to the cannibalization of existing projects: Enter the following input data in the calculator: CF0 = 0; CF1-10 = -500000; I/YR = 10; and then solve for NPV = $3,072,283.55. Recalculate the new projects NPV after considering externalities: +$3,000,000 $3,072,283.55 = -$72,283.55.
Step 2:
x xlv .
New project investment Initial investment: Cost Modification Change in NOWC Total net investment ($50,000) (10,000) (2,000) ($62,000)
x xlvi .
Operating cash flow Depreciation schedule: Year 1 2 3 4 MACRS Depreciation Rates 0.33 0.45 0.15 0.07
Depreciable Basis $60,000 60,000 60,000 60,000
Annual Depreciation $19,800 27,000 9,000 4,200 $60,000 2 $20,000 12,000 27,000 10,800 $22,800 3 $20,000 12,000 9,000 3,600 $15,600
Operating cash flows: Year 1) Before-tax cost reduction 2) After-tax cost reduction (line 1 0.6) 3) Depreciation 4) Deprec. tax savings (line 3 0.4) 5) Net operating CFs (lines 2 + 4) x xlvii .Non-operating cash flows Additional Year 3 cash flows: Salvage value Tax on salvage value
1 $20,000 12,000 19,800 7,920 $19,920
3 $20,000 (6,320)*
Recovery of NOWC Total terminal year CF
2,000 $15,680
*(Market value - Book value)(Tax rate) = ($20,000 - $4,200)(0.40) = $6,320.
xlviii.New project NPV
Time line: 0 k = 10% 1 | | -62,000 19,920 2 | 22,800 3 Years | 15,600 TV = 15,680 31,280
Numerical solution: NPV = -$62,000 + 1.10 + (1.10)2 + (1.10)3 = -$1,546.81 -$1,547. Financial calculator solution: Inputs: CF0 = -62000; CF1 = 19920; CF2 = 22800; CF3 = 31280; I/YR = 10.
Output: NPV = -$1,546.81 -$1,547. xlix. Breakeven analysis
Fixed operating costs Variable costs (per unit) Sales price Breakeven volume $500,000 $3.00 $4.00 500,000
$19, 920
$22 800 ,
$31, 280
l.
Setting the price
Units produced Variable costs (% of sales) Fixed costs Desired EBIT Required price 60,000 50% $120,000 $95,000 $7.17
li. lii.
Business risk
$500,000 $3,000,000 $8,219 60.83
$350,000 $3,750,000 $10,274 34.07
Optimal capital structure Inventory Annual sales liii. Inventory conversion period Sales/day Inventory conversion period (in days) = Accounts payable Annual purchases liv. Payables deferral period Purchases per day Inventory conversion period (in days) lv.
Average collection period (or DSO)
lvi.
$1,600,000 Sales $200,000 Inventories Annual sales $150,000 Receivables Accounts receivable $100,000 Payables day Sales per 70% Cost of goods sold (% of sales) / sales per day ACP (or DSO) = Accts receivable Inventory conversion period 65.18 Average collection period 34.22 Cash conversion cycle Payables deferral period 32.59 66.81 Cash conversion period
$730,000 $100,000 $2,000 50.00
lvii. Cash conversion cycle lviii.Working capital lix. Additional funds needed -- positive AFN $500,000 Old sales 30% Sales growth rate $650,000 New sales $750,000 Old total assets $975,000 New total assets $40,000 Old accounts payable $50,000 Old notes payable (has no effect on answer) $30,000 Old accruals 5% Profit margin 60% Payout ratio 40% Retention ratio Additional funds needed $191,000
lx.
Additional funds needed
Note that with purchase terms of 1/5 net 90, the cost of non-free credit is only 4.34%, whereas with 3/15, net 35, the cost of trade credit is 56.4%. Therefore, the firm should have been taking discounts originally, hence should have had few accounts payable, whereas it would probably not take discounts and thus have more accounts payable with the new supplier. That 0.75 Direct quotation ($/C$) change would lower its AFN. To find the indirect quotation, find the inverse (1/e0) of the direct quotation. Exchange rates 0.60 Indirect quotation (pounds/$) 1.33 Indirect quotation (C$/$) 106.5 Yen/dollar exchange rate 0.0096 Euro/yen exchange rate To find the direct quotation, find the inverse (1/e0) of the indirect quotation. lxii. Exchange rates rate 10.1 Peso/euro exchange lxi.
l lxiii .
1.67 Direct quotation ($/pound) To find the Dollar/peso exchange rate, cross multiplication of the available exchange rates must be used. x x Euro/yen 0.0096 x x Peso/euro 10.1
Peso/dollar = Yen/dollar Cross rates Peso/dollar = 106.5 10.326 Peso/dollar = $1,000 Television dollar price 110 Yen/$ exchange rate lxiv. Purchasing power parity
Television yen price lxv.
JPY 110,000
Multinational financial management

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1Lecture 1. Transformation of Random VariablesSuppose we are given a random variable X with density fX (x). We apply a function g to produce a random variable Y = g (X ). We can think of X as the input to a black box, and Y the output. We wish to nd the

GWU - APSC - 116

Transformations and Expectations of random variablesX FX (x): a random variable X distributed with CDF FX . Any function Y = g (X ) is also a random variable. If both X , and Y are continuous random variables, can we nd a simple way to characterize FY an

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Midterm Exam Solutions Ap.Sc. 116Problem 1. Suppose that a box contains ve coins, and that for each coin there is a dierent probability that a head will be obtained when the coin is tossed. Let pi denote the probability of a head when the ith coin is tos

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Functions of Random VariablesLecture 4Spring 2002Function of a Random VariableLet U be an random variable and V = g (U ). Then V is also a rv since, for any outcome e, V (e) = g (U (e). There are many applications in which we know FU (u) and we wish t

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Homework # 3 SolutionsThe George Washington UniversityApSc 1161 / 10Problem (Page 102, # 3)Suppose that two balanced dice are rolled, and let X denote the absolute value of the dierence between the two numbers that appear. Determine and sketch the p.

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Homework # 2 SolutionsThe George Washington UniversityApSc 1161/8Problem (Page 55 # 9)Suppose that a box contains one blue card and four red cards, which are labeled A, B, C, and D. Suppose also that two of these ve cards are selected at random, with

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Homework # 1 SolutionsApSc 116Problem Page 18 # 7We know Pr (AB ) = Pr (A) + Pr (B ) Pr (A B ) = 0.4 + 0.7 Pr (A B ) = 1.1 Pr (A B ) Since 0.7 Pr (A B ) 1 (the latter is true if A B ), we can conclude 0.1 Pr (AB ) 0.4.Problem Page 27 # 8There are 75

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Homework # 6 SolutionsEnrique Campos-Nnez aThe George Washington UniversityApSc 1161/9Problem (Page 175 # 1, Section 3.9)Suppose that X1 and X2 are i.i.d. random variables and that each of them has a uniform distribution on the interval [0, 1]. Find

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Homework # 5 SolutionsThe George Washington UniversityApSc 1161 / 11Problem (Page 157 # 1, Section 3.7)Suppose that three random variables X1 , X2 , and X3 have a continuous joint distribution with the following joint p.d.f.: ( c (x1 + 2x2 + 3x3 ) 0

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Homework # 4 SolutionsThe George Washington UniversityApSc 1161 / 11Problem (Page 136, # 7)Suppose that the joint p.d.f. of X and Y is as follows: f (x , y ) = 2xe y 0 for 0 x 1 and 0 < y < , otherwise.Are X and Y independent? Solution: Since f (x ,

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Discrete DistributionsEnrique Campos-Nnez aThe George Washington UniversityApSc 116Campos-Nnez (GWU) aDiscrete DistributionsApSc 1161 / 32Table of Contents1Bernoulli Binomial Hypergeometric Distribution Poisson Distribution Negative Binomial The

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ExpectationsEnrique Campos-Nnez aThe George Washington UniversityApSc 1161 / 41Table of ContentsThe Expectation of a Random Variable Expectations and Joint Distributions Properties of the Expectations Expectation of Non-negative r.v.s Variance Momen

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Functions of Random VariablesEnrique Campos-Nnez aThe George Washington UniversityApSc 1161 / 32Table of ContentsFunctions of a Single Random VariableFunctions of Several Random VariablesSum of Random Variables2 / 32Functions of a Single Random

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Multivariate DistributionsEnrique Campos-Nnez aThe George Washington UniversityApSc 116Multivariate Data: Height, Weight, and FatMotivating multivariate distributionsTable of ContentsBivariate DistributionsConditional DistributionsMultivariate Di

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Random Variables and Probability DistributionsEnrique Campos-Nnez aThe George Washington UniversityApSc 116Table of ContentsRandom VariablesCommon Discrete DistributionsContinuous Random Variables and DistributionsThe Distribution FunctionRandom

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Conditional ProbabilityEnrique Campos-Nnez aThe George Washington UniversityApSc 116Table of ContentsConditional ProbabilityEvent IndependenceIndependence and Conditional ProbabilitiesBayes TheoremThe Denition of Conditional ProbabilityThe quant

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Introduction to ProbabilityEnrique Campos-Nnez aThe George Washington UniversityApSc 116Table of ContentsInterpretations of ProbabilityProbability and Set TheoryThe Denition of ProbabilityCounting MethodsInterpretations of ProbabilityInterpretat

GWU - EMSE - 271

Student NameTotal Points Question 1 a b c d 5 5 10 20 40 Total Points 10 5 5 3 3 3 6 35 Total Points 5 5 5 5 10 30Subtracted 0 0 0 0Reason 5 5 10 20 40 Reason 0 0 0 0 0 0 0 10 5 5 3 3 3 6 35 Reason 0 0 0 0 0 5 5 5 5 10 30Question 2 a b c d e f g Quest

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Syllabus: EMSE 171/271Department of Engineering Management and Systems Engineering School of Engineering and Applied Science Semester: Fall 2008EMSE 171/271 Data Analysis for Engineers and ScientistsInstructor Information: Dr. J. Ren van Dorp - Profess

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ONE-WAY ANOVAHomework Set 8Question 1: Six samples of each of four types of cereal grain grown in a certain region were analyzed to determine thiamin content, resulting in the following data (.gg): Wheat Barley Maize Oats &# '& &) )$ %$ )! %( '" '! '" '

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X1 -1.52 -0.88 0.11 -0.59 -0.6 -0.44 -0.62 -0.31 1.27 -1.92 -0.69 0.65 -0.7 -0.77 0.05 -0.16 -1.08 0.86 0.33 0.39 -1.21 1.52 1.14 0.9 -0.29 1.09 0.49 -0.02 1.89 0.55 -0.5 0.09 -0.37 0.7 0.45 -1.22 -0.05 -0.24 -0.72 -0.96 1.27 2.29 -2.31 -1.33 -1.84 -1.14

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Original Variables X1 X2 -1.52 -1.29 -0.88 -0.22 0.11 -1.47 -0.59 -0.1 -0.6 -0.08 -0.44 -0.73 -0.62 0 -0.31 -0.49 1.27 2.39 -1.92 -1.4 -0.69 0.47 0.65 1.2 -0.7 -1.12 -0.77 -2.8 0.05 0.01 -0.16 -0.35 -1.08 -0.62 0.86 1.5 0.33 0.07 0.39 -0.18 -1.21 -0.27 1.

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EMSE 171/271: DATA ANALYSIS For Engineers and ScientistsSession 11: Principal Component Analysis (PCA), Introduction, How it works, MechanicsLecture Notes by: J. Ren van Dorp1www.seas.gwu.edu/~dorpjr1Department of Engineering Management and Systems E

GWU - EMSE - 271

EMSE 171/271: DATA ANALYSIS For Engineers and ScientistsSession 10: Multiple Regression, Residual Diagnostics, Outlier Detection, Comparing Imbedded Models, ForecastingLecture Notes by: J. Ren van Dorp1www.seas.gwu.edu/~dorpjr1Department of Engineeri

GWU - EMSE - 271

Question 1 a b c d e f gTotal Points 4 5 4 5 10 9 7 44 Total Points 8 8 8 8 32 Total PointsSubtracted 0 0 0 0 0 0 0Reason 4 5 4 5 10 9 7 44 Reason 0 0 0 0 8 8 8 8 32 Reason 0 0 0 8 8 8 24Total Points 44 32 24 100Question 2 a b c dSubtractedSubtract

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Original Individual 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Average St. Dev.X1 Sweat Rate 3.7 5.7 3.8 3.2 3.1 4.6 2.4 7.2 6.7 5.4 3.9 4.5 3.5 4.5 1.5 8.5 4.5 6.5 4.1 5.5X2 Sodium 48.5 65.1 47.2 53.2 55.5 36.1 24.8 33.1 47.4 54.1 36.9 58.8 27.

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EMSE 171/271: DATA ANALYSIS For Engineers and ScientistsSession 5: Vectors and Matrices, Matrix Algebra, Linear Combinations, Coordinate Systems, Geometric InterpretationLecture Notes by: J. Ren van Dorp1www.seas.gwu.edu/~dorpjr1Department of Enginee

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STATISTICAL REVIEWHomework Set 4_2Question 3: Low-Back Pain (LBP) is a serious health problem in many industrial settings. The article "Isodynamic Evaluation of Trunk Muscles and low-Back Pain Among Workers in a Steel Factory" (Ergonomics, 1995, 2107-21

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STATISTICAL REVIEWQuestion 1:Homework Set 4_1Let \ denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of \ is ) "B) 0 Bl) oe oe ! !YBY" otherwisewhere ) ". A random sample

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EMSE 171/271: DATA ANALYSIS For Engineers and ScientistsSession 2: Distribution Theory, Calculating Probabilities, Sums of Random Variables, Point-Estimation, Estimator DistributionsLecture Notes by: J. Ren van Dorp1www.seas.gwu.edu/~dorpjr1Departmen

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STATISTICAL REVIEWHomework Set 1Question 1: Recreate the exploratory analysis graphs in the lecture notes using MINITAB by appropriately organizing each dataset in columns, copying the data from EXCEL into MINITAB and using the graphical exploratory ana

Cal Poly - ME - ME 211

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of thi

Cal Poly - ME - ME212

Cal Poly - ME - ME212