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SHOW-YOUR-WORK Homework Assignment I 1. Consider the following two mutually exclusive projects, X and Y, and their cash flows information, Project Year 0 Year 1 Year 2 Year 3 Year 4 X ($1,400) $350 $750 $650 $650 Y ($1,000) $300 $400 $500 $600 (a) Assume that the discount rate is 12%, calculate the payback period, the IRR, NPV and PI of project X.<2.46 years;="" …;="" …;="" 1.276=""> (b) Calculate the Modified IRR (MIRR) for project X using the McKinsey’s approach. (c) Apply the incremental project analysis to calculate the cross-over rate (i.e., incremental IRR) for projects X and Y, and select between these two mutually exclusive projects. 2. Lee plans to retire in 22 years with a nest egg of $8M. He has already saved $500,000 in an investment account that generates a nominal rate of return of 12%, compounded quarterly. However, he needs to withdraw $150,000 from this account in 10 years to finance his son’s college education. (a) Numerically show that whether Lee’s investment account balance will reach $8M in 22 years, based on the information provided above. (b) The correct answer for part (a) indicates that Lee’s investment account will fall short of his retirement goal of $8M in 22 years. Thus, he continues his pursuit by making additional fixed contributions at the end of every quarter to the same investment account until he retires 22 years later. How big should be his quarterly contribution in order to achieve his goal? <$4,522.18> (c) Assume now that Lee retires and has $8M in his investment account. If he wants to leave $10M to each of his two children upon his death after enjoying 25 years of retirement. What is the maximum annual withdrawal from the investment account Lee can make at the beginning of every year during his retirement? <$818,587.57> 3. You have been asked by the president of your firm to evaluate the proposed acquisition of new special-purpose equipment. The equipment's base price is $500,000, and another $50,000 modification cost to tailor it for the project. The equipment falls into the MACRS 3-year class, and it will be sold at the end of the project’s 2-year life for $250,000. Use of the equipment will require net working capital investment equivalent to 20% of the following year’s incremental revenues. The equipment will increase annual revenues by $100,000, and save the firm $200,000 in annual operating costs. The annual revenues and operating costs are expected to grow at an annual rate of 10% during the 2nd-year of the project. This equipment will be placed in an unoccupied site, which can otherwise be sold for $100,000 today. This site will be sold for the same price at the termination of the project. The depreciation of this site that your firm owns can be ignored. The firm's tax rate is 30 percent and the discount rate for the project is 12%.
(a) Calculate the initial outlay of the project. (b) Calculate the operating cash flows (OCF) in Years 1 and 2.<$264,995; …=""> (c) Calculate the non-operating cash flows (i.e., capital spending and change in NWC) at the end of Year 2.<$333,679> (d) What is your recommendation on this project according to the conceptually most correct capital budgeting method? Explain your recommendation numerically! 4. You plan to buy a $25,000 car. A simplified leasing contract includes the following: (i) up- front cost of $3,000, (ii) $400 monthly lease payment over a 36-month period, and (iii) purchase cost of $12,000 at the end of the lease. Calculate the “implied” APR and EAR of the lease? Should you finance your purchase with the lease or a bank loan at 8%? <8.45%; …=""> 5. Chapter 4 Problem #59 on page 128 of the assigned text (12ed.) 6. Consider the following abbreviated financial statements for Parrothead Enterprises: 1. Calculate owners’ equity for 2018 and 2019. 2. Calculate the change in net working capital for 2019. <$35> 3. Calculate the cash flow from assets for the year, assume 35% tax rate. <$2,917> 4. During 2019, Parrothead Enterprises raised $420 in new long-term debt. How much long- term debt must Parrothead Enterprises have paid off during the year? Calculate the cash flow to creditors. And calculate the cash flow to stockholders for the year. <…; $2,733=""> 7. Maryanne, a baby boomer who turns 50 today, begins to save for retirement with $200,000 that she just receives from a trust fund. She immediately invests this $200,000 in a stock fund. In addition, she plans to contribute $10,000, $15,000, and $20,000, respectively, at the end of the next 3 years to the same stock fund. The stock fund generates a nominal rate of return of 10%, compounded annually. (a) What will be the value of her stock fund when she retires at the age of 67? <$1,195,452.48> (b) Right after her retirement, she transfers her nest egg into a conservative investment that compounds monthly. If Maryanne wants to withdraw a fixed monthly payment of $7,000 from this investment indefinitely, what should be the annual rate of return of this conservative investment? 8. Calculate LEE Corp.’s external funds needed (EFN) for the fiscal year of 2019 using the pro forma statement approach. Assume that the percentages of sales for cost of goods sold, current assets and current liabilities remain unchanged at their respective values in 2018. In addition, the dividend payout ratio is assumed to remain unchanged. It is also assumed that the plant capacity of LEE Corporation was underutilized in 2018 such that existing fixed assets can support the 10% projected growth rate in the sales level for 2019. Note: This problem is part of this homework assignment! Although Chapter 3 will not be on the Midterm Examination, it is still part of the course curriculum. 2019 and 2018 Partial Balance Sheets Assets Liabilities and Owners’ Equity 2018 2019 2018 2019 Current assets $1,005 $1,089 Current liabilities $ 402 $ 451 Net fixed assets 4,144 4,990 Long-term debt 2,190 2,329 2019 Income Statement Sales $12,751 Costs 5,946 Depreciation 1,136 Interest paid 323 LEE Corp. Income Statement (in millions) 2018 Net Sales $ 1,800 Cost of Goods Sold $ 1,200 Depreciation Expenses $ 180 Earnings Before Interest and Taxes $ 420 Interest Expenses $ 20 Taxable Income $ 400 Taxes (21%) $ 84 Net Income $ 316 Dividends Paid $ 190 Balance Sheet (in millions) 2017 2018 Current Assets $ 536 $ 520 Net Fixed Assets $ 2,164 $ 2,100 Total Assets $ 2,700 $ 2,620 Current Liabilities $ 980 $ 900 Long-term Debt $ 278 $ 218 Common Stock & Paid-in Capital $ 700 $ 634 Retained Earnings $ 742 $ 868 Total Liabilities and Equity $ 2,700 $ 2,620 NOTE: This homework assignment is composed of a SAMPLE of past examination problems that are pertaining to the midterm examination. Since this is just a sample, actual examination may include other numerical problems that are not included in this homework assignment, e.g., numerical problems from Chapters 2, 4, 5, and 6 such as taxation, other TVM applications, other capital budgeting decision rules, EAC, etc. As such, while you find this homework assignment a valuable tool for your preparation for the midterm examination, it is by no mean inclusive of all topics that are covered in the midterm examination! Besides, I need to explicitly remind you that it takes much practice to master the course materials. Students who only work on the homework problem sets (without investing needed time on learning/studying course materials and working through many practice problems with posted solutions) may find themselves underprepared for the examinations. The answers to selected problems are given for your reference. Due to the degree of similarity between homework problems and actual examination problems, detailed solutions will NOT be posted. Please note that numerical illustrations similar (but not identical) to these homework, and hence examination, problems can be found in the lecture notes (and lecture slides) for the respective chapters/topics!