GESTÃO FINANCEIRA II PROBLEM SET 1 - SOLUTIONS (FROM BERK AND DEMARZO S CORPORATE FINANCE ) LICENCIATURA UNDERGRADUATE COURSE 1 ST SEMESTER 2010-2011
Chapte 1 The Copoation 1-13. What is the diffeence between a public and pivate copoation? The shaes of a public copoation ae taded on an exchange (o "ove the counte" in an electonic tading system) while the shaes of a pivate copoation ae not taded on a public exchange. 1-14. Explain why the bid-ask spead is a tansaction cost. Investos always buy at the ask and sell at the bid. Since ask pices always exceed bid pices, investos lose this diffeence. It is one of the costs of tansacting. Since the maket makes take the othe side of the tade, they make this diffeence. 1-15. The following quote on Yahoo! Stock appeaed on Febuay 11, 2009, on Yahoo! Finance: If you wanted to buy Yahoo!, what pice would you pay? How much would you eceive if you wanted to sell Yahoo!? You would buy at $12.54 and sell fo $12.5 Chapte 2 Intoduction to Financial Statement Analysis [Type text]
2-3. Find the most ecent financial statements fo Stabucks copoation (SBUX) using the following souces: a. Fom the company s Web site www.stabucks.com (Hint : Seach fo investo elations. ) b. Fom the SEC Web site www.sec.gov. (Hint : Seach fo company filings in the EDGAR database.) c. Fom the Yahoo! Finance Web site http://finance.yahoo.com. d. Fom at least one othe souce. (Hint : Ente SBUX 10K at www.google.com.) Each method will help find the same SEC filings. Yahoo! Finance also povides some analysis such as chats and key statistics. 2-8. In Mach 2005, Geneal Electic (GE) had a book value of equity of $113 billion, 10.6 billion shaes outstanding, and a maket pice of $36 pe shae. GE also had cash of $13 billion, and total debt of $370 billion. Fou yeas late, in ealy 2009, GE had a book value of equity of $105 billion, 10.5 billion shaes outstanding with a maket pice of $10.80 pe shae, cash of $48 billion, and total debt of $524 billion. Ove this peiod, what was the change in GE s a. maket capitalization? b. maket-to-book atio? c. book debt-equity atio? d. maket debt-equity atio? e. entepise value? a. 2005 Maket Capitalization: 10.6 billion shaes x $36.00/shae = $381.6 billion. 2009 Maket Capitalization: 10.5 billion shaes x $10.80/shae = $113.4. The change ove the peiod is $113.4 - $381.6 = -$268.2 billion. 381.6 b. 2005 Maket-to-Book 113 peiod is: 1.08 3.38 = -2.3. 3.38. 2009 Maket-to-Book 113.4 105 370 c. 2005 Book Debt-to-Equity 3.27. 2009 Book Debt-to-Equity 113 ove the peiod is: 4.99 3.27 = 1.72. 370 d. 2005 Maket Debt-to-Equity 0.97. 2009 Maket Debt-to-Equity 381.6 change ove the peiod is: 4.62 0.97 = 3.65. 1.08. The change ove the 524 105 4.99. The change 524 113.4 4.62. The e. 2005 Entepise Value = $381.6-13 + 370 = $738.6 billion. 2009 Entepise Value = $113.4-48 + 524 = $589.4 billion. The change ove the peiod is: $589.4 738.6 = - $149.2 billion Chapte 3 Abitage and Financial Decision Making 3-12. Suppose Bank One offes a isk-fee inteest ate of 5.5% on both savings and loans, and Bank Enn offes a isk-fee inteest ate of 6% on both savings and loans. a. What abitage oppotunity is available?
b. Which bank would expeience a suge in the demand fo loans? Which bank would eceive a suge in deposits? c. What would you expect to happen to the inteest ates the two banks ae offeing? a. Take a loan fom Bank One at 5.5% and save the money in Bank Enn at 6%. b. Bank One would expeience a suge in the demand fo loans, while Bank Enn would eceive a suge in deposits. c. Bank One would incease the inteest ate, and/o Bank Enn would decease its ate. 3-13. Thoughout the 1990s, inteest ates in Japan wee lowe than inteest ates in the United States. As a esult, many Japanese investos wee tempted to boow in Japan and invest the poceeds in the United States. Explain why this stategy does not epesent an abitage oppotunity. Thee is exchange ate isk. Engaging in such tansactions may incu a loss if the value of the dolla falls elative to the yen. Because a pofit is not guaanteed, this stategy is not an abitage oppotunity. 3-14. An Ameican Depositay Receipt (ADR) is secuity issued by a U.S. bank and taded on a U.S. stock exchange that epesents a specific numbe of shaes of a foeign stock. Fo example, Nokia Copoation tades as an ADR with symbol NOK on the NYSE. Each ADR epesents one shae of Nokia Copoation stock, which tades with symbol NOK1V on the Helsinki stock exchange. If the U.S. ADR fo Nokia is tading fo $17.96 pe shae, and Nokia stock is tading on the Helsinki exchange fo 14.78 pe shae, use the Law of One Pice to detemine the cuent $/ exchange ate. We can tade one shae of Nokia stock fo $17.96 pe shae in the U.S. and 14.78 pe shae in Helsinki. By the Law of One Pice, these two competitive pices must be the same at the cuent exchange ate. Theefoe, the exchange ate must be: $17.96 / shae of Nokia $1.215 / today. 14.78 / shae of Nokia 3-18. Suppose a secuity with a isk-fee cash flow of $150 in one yea tades fo $140 today. If thee ae no abitage oppotunities, what is the cuent isk-fee inteest ate? The PV of the secuity s cash flow is ($150 in one yea)/(1 + ), whee is the one-yea isk-fee inteest ate. If thee ae no abitage oppotunities, this PV equals the secuity s pice of $140 today. Theefoe, $150 in one yea $140 today 1 Reaanging: $150 in one yea $140 today 1 $1.0714 in one yea / $ today, so 7.14% Chapte 4 The Time Value of Money 4-8. You daughte is cuently eight yeas old. You anticipate that she will be going to college in 10 yeas. You would like to have $100,000 in a savings account to fund he education at that time. If [Type text]
the account pomises to pay a fixed inteest ate of 3% pe yea, how much money do you need to put into the account today to ensue that you will have $100,000 in 10 yeas? 100, 000 PV= 74, 409.39 10 1.03 4-12. You have just eceived a windfall fom an investment you made in a fiend s business. He will be paying you $10,000 at the end of this yea, $20,000 at the end of the following yea, and $30,000 at the end of the yea afte that (thee yeas fom today). The inteest ate is 3.5% pe yea. a. What is the pesent value of you windfall? b. What is the futue value of you windfall in thee yeas (on the date of the last payment)? a. Timeline: 0 1 2 3 10,000 20,000 30,000 PV 10, 000 20, 000 30, 000 1.035 1.035 2 1.035 3 9, 662 18, 670 27, 058 55, 390 b. Timeline: 0 1 2 3 10,000 20,000 30,000 3 FV 55, 390 1.035 61, 412 4-19. What is the pesent value of $1000 paid at the end of each of the next 100 yeas if the inteest ate is 7% pe yea? Timeline: 0 1 2 3 100 1,000 1,000 1,000 1,000 The cash flows ae a 100 yea annuity, so by the annuity fomula: 1, 000 1 PV 1-14, 269.25. 100 0.07 1.07 4-20. You ae head of the Schwatz Family Endowment fo the Ats. You have decided to fund an ats school in the San Fancisco Bay aea in pepetuity. Evey five yeas, you will give the school $1 million. The fist payment will occu five yeas fom today. If the inteest ate is 8% pe yea, what is the pesent value of you gift? Timeline:
0 5 10 20 0 1 2 3 1,000,000 1,000,000 1,000,000 Fist we need the 5-yea inteest ate. If the annual inteest ate is 8% pe yea and you invest $1 fo 5 5 yeas you will have, by the 2nd ule of time tavel, (1.08) 1.4693 2808. So the 5 yea inteest ate is 46.93%. The cash flows ae a pepetuity, so: 1, 000, 000 PV 2,130, 833. 0.46932808 4-23. You gandmothe has been putting $1000 into a savings account on evey bithday since you fist (that is, when you tuned 1). The account pays an inteest ate of 3%. How much money will be in the account on you 18th bithday immediately afte you gandmothe makes the deposit on that bithday? Timeline: 0 1 2 3 18 1,000 1,000 1,000 1,000 We fist calculate the pesent value of the deposits at date 0. The deposits ae an 18-yea annuity: 1, 000 1 PV 1 13, 753.51 18 0.03 1.03 Now, we calculate the futue value of this amount: 18 FV 13, 753.51(1.03) 23, 414.43 4-24. A ich elative has bequeathed you a gowing pepetuity. The fist payment will occu in a yea and will be $1000. Each yea afte that, you will eceive a payment on the annivesay of the last payment that is 8% lage than the last payment. This patten of payments will go on foeve. If the inteest ate is 12% pe yea, a. What is today s value of the bequest? b. What is the value of the bequest immediately afte the fist payment is made? a. Timeline: 0 1 2 3 1,000 1,000(1.08) 1,000(1.08) 2 Using the fomula fo the PV of a gowing pepetuity gives: 1, 000 PV 25, 000. 0.12 0.08 [Type text]
b. Timeline: 1 2 3 4 0 1 2 3 1,000 1,000(1.08) 2 1,000(1.08) 3 Using the fomula fo the PV of a gowing pepetuity gives: 1, 000(1.08) PV 27, 000. 0.12 0.08 4-34. (includes 4.32) You ae thinking of puchasing a house. The house costs $350,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to boow the est of the puchase pice. The bank is offeing a 30-yea motgage that equies annual payments and has an inteest ate of 7% pe yea. (a) What will you annual payment be if you sign up fo this motgage? (b) You can affod to pay only $23,500 pe yea. The bank agees to allow you to pay this amount each yea, yet still boow $300,000. At the end of the motgage (in 30 yeas), you must make a balloon payment; that is, you must epay the emaining balance on the motgage. How much will this balloon payment be? (a) Timeline: (Fom the pespective of the bank) 0 1 2 3 30 300,0-300,000 C C C C 300, 000 C $24,176 1 1 1 30 0.07 1.07 (b)timeline: (whee X is the balloon payment.) 0 1 2 3 30 300,000 23,500 23,500 23,500 23,500 + X The pesent value of the loan payments must be equal to the amount boowed: 23, 500 1 X 300, 000 1. 30 30 0.07 1.07 1.07 Solving fo X: 23, 500 1 30 X 300, 000 1 1.07 $63, 848 30 0.07 1.07
Chapte 5 Inteest Rates 5-6. You bank account pays inteest with an EAR of 5%. What is the APR quote fo this account based on semiannual compounding? What is the APR with monthly compounding? Using the fomula fo conveting fom an EAR to an APR quote k APR 1 1.05 k Solving fo the APR 1 k APR 1.05 1 k With annual payments k = 1, so APR = 5% With semiannual payments k = 2, so APR = 4.939% With monthly payments k = 12, so APR = 4.889% 5-26. If the ate of inflation is 5%, what nominal inteest ate is necessay fo you to ean a 3% eal inteest ate on you investment? 1 1 implies 1 (1 )(1 i) (1.03)(1.05) 1.0815. 1 i Theefoe, a nominal ate of 8.15% is equied. 5-30. Suppose the tem stuctue of isk-fee inteest ates is as shown below: What is the pesent value of an investment that pays $100 at the end of each of yeas 1, 2, and 3? If you wanted to value this investment coectly using the annuity fomula, which discount ate should you use? PV = 100 / 1.0199 + 100 / 1.0241 2 + 100 / 1.0274 3 =$285.61. To detemine the single discount ate that would compute the value coectly, we solve the following fo : PV = 285.61 = 100/(1 + ) + 100 / (1 + ) 2 + 100/(1 + ) 3 = $285.61. This is just an IRR calculation. Using tial and eo o the annuity calculato, = 2.50%. Note that this ate is between the 1, 2, and 3-y ates given. Chapte 6 Investment Decision Rules [Type text]
6-5. Bill Clinton epotedly was paid $10 million to wite his book My Way. The book took thee yeas to wite. In the time he spent witing, Clinton could have been paid to make speeches. Given his populaity, assume that he could ean $8 million pe yea (paid at the end of the yea) speaking instead of witing. Assume his cost of capital is 10% pe yea. a. What is the NPV of ageeing to wite the book (ignoing any oyalty payments)? b. Assume that, once the book is finished, it is expected to geneate oyalties of $5 million in the fist yea (paid at the end of the yea) and these oyalties ae expected to decease at a ate of 30% pe yea in pepetuity. What is the NPV of the book with the oyalty payments? a. Timeline: 0 1 2 3 10 8 8 8 8 1 NPV 10 1 $9.895 million 3 0.1 1.1 0 1 2 3 4 5 6 10 8 8 8 5 5 5(1 0.3) 5 5(1-03) 2 b. Timeline: Fist calculate the PV of the oyalties at yea 3. The oyalties ae a declining pepetuity: 5 5 PV5 12.5 million 0.1 0.3 0.4 So the value today is 12.5 PV oyalties 9.391 1.1 3 Now add this to the NPV fom pat a), NPV 9.895 9.391 $503,381. 6-6. FastTack Bikes, Inc. is thinking of developing a new composite oad bike. Development will take six yeas and the cost is $200,000 pe yea. Once in poduction, the bike is expected to make $300,000 pe yea fo 10 yeas. Assume the cost of capital is 10%. a. Calculate the NPV of this investment oppotunity, assuming all cash flows occu at the end of each yea. Should the company make the investment? b. By how much must the cost of capital estimate deviate to change the decision? (Hint: Use Excel to calculate the IRR.) c. What is the NPV of the investment if the cost of capital is 14%? a. Timeline: 0 1 2 3 6 7 16 200,000 200,000 200,000 200,000 3 300,000 3 300,000
200,000 1 1 300,000 1 NPV= 1 + 1 1+ 1+ 1+ i. 6 6 10 200, 000 1 1 300, 000 1 = 1 1 0.1 1.1 1.1 0.1 1.1 =$169,482 6 6 10 NPV > 0, so the company should take the poject. ii. Setting the NPV = 0 and solving fo (using a speadsheet) the answe is IRR = 12.66%. So if the estimate is too low by 2.66%, the decision will change fom accept to eject. 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10-200 -200-200 -200-200 -200 300 300 300 300 300 300 300 300 300 300 IRR 12.66% NPV 10% $169.482 14% ($64.816) 200,000 1 1 300,000 1 NPV= 1 + 1 1+ 1+ 1+ iii. 6 6 10 200, 000 1 1 300, 000 1 1 1 0.14 1.14 1.14 0.14 1.14 $64.816 6 6 10 6-11. How many IRRs ae thee in pat (a) of Poblem 5? Does the IRR ule give the ight answe in this case? How many IRRs ae thee in pat (b) of Poblem 5? Does the IRR ule wok in this case? Timeline: 0 1 2 3 10 8 8 8 IRR is the that solves NPV 8 1 0 10 1 1 3 To detemine how many solutions this equation has, plot the NPV as a function of [Type text]
Fom the plot thee is one IRR of 60.74%. Since the IRR is much geate than the discount ate, the IRR ule says wite the book. Since this is a negative NPV poject (fom 6.5a), the IRR gives the wong answe. Timeline: 0 1 2 3 4 5 6 10 8 8 8 5 5 5(1 0.3) 5(1.03) 2 Fom 6.5(b) the NPV of these cash flows is 8 1 1 5 NPV 10 1 3 3 1 1 0.3 Plotting the NPV as a function of the discount ate gives The plot shows that thee ae 2 IRRs 7.165% and 41.568%. The IRR does give an answe in this case, so it does not wok 6-20. You ae consideing making a movie. The movie is expected to cost $10 million upfont and take a yea to make. Afte that, it is expected to make $5 million when it is eleased in one yea and $2 million pe yea fo the following fou yeas. What is the payback peiod of this investment? If you equie a payback peiod of two yeas, will you make the movie? Does the movie have positive NPV if the cost of capital is 10%? Timeline: 0 1 2 3 4 5 6 10 0 5 2 2 2 2 It will take 5 yeas to pay back the initial investment, so the payback peiod is 5 yeas. You will not make the movie. NPV 5 2 1 1 5 2 1 10 1 10 1 $628, 322 2 4 2 2 2 4 1 1 1 1.1 0.1 1.1 1.1 So the NPV agees with the payback ule in this case
0 1 2 3 4 5-10 5 2 2 2 2 Payback = 4 yeas NPV at 10% = $0.31 million 6-23. You ae deciding between two mutually exclusive investment oppotunities. Both equie the same initial investment of $10 million. Investment A will geneate $2 million pe yea (stating at the end of the fist yea) in pepetuity. Investment B will geneate $1.5 million at the end of the fist yea and its evenues will gow at 2% pe yea fo evey yea afte that. a. Which investment has the highe IRR? b. Which investment has the highe NPV when the cost of capital is 7%? c. In this case, fo what values of the cost of capital does picking the highe IRR give the coect answe as to which investment is the best oppotunity? d. Use the incemental IRR ule to coectly choose between the investments when the cost of capital is 7%. At what cost of capital would you decision change? a. Timeline: 0 1 2 3 A 10 2 2 2 B 10 1.5 1.5(1.02) 1.5(1.02) 2 NPV A 2 10 Setting NPV A = 0 and solving fo IRR A = 20% NPV B 1.5 0.02 10 Setting NPV B = 0 and solving fo 1.5 0.02 10 0.02 0.15 17%. So, IRR B 17% Based on the IRR, you always pick poject A. b. Substituting = 0.07 into the NPV fomulas deived in pat (a) gives NPV A = $18.5714 million, NPV B = $20 million. So the NPV says take B. c. Hee is a plot of NPV of both pojects as a function of the discount ate. The NPV ule selects A (and so agees with the IRR ule) fo all discount ates to the ight of the point whee the cuves coss. [Type text]
NPV A NPV 2 1.5 0.02 0.02 2 1.5 1.5 2 0.04 0.5 0.04 B 0.08 So the IRR ule will give the coect answe fo discount ates geate than 8% (d)timeline: 0 1 2 3 A 10 2 2 2 B 10 1.5 1.5(1.02) 1.5(1.02) 2 To calculate the incemental IRR subtact A fom B 0 1.5 2 1.5(1.02) 2 1.5(1.02) 2 2 NPV 1.5 2 0.02 0
2 1.5 0.02 0.02 2 1.5 1.5 2 0.04 0.5 0.04 0.08 So the incemental IRR is 8%. This ate is above the cost of capital, so we should take B. 6-24. You wok fo an outdoo play stuctue manufactuing company and ae tying to decide between two pojects: You can undetake only one poject. If you cost of capital is 8%, use the incemental IRR ule to make the coect decision. Timeline: 0 1 2 Playhouse 30 15 20 Fot 80 39 52 Subtact the Playhouse cash flows fom the Fot 50 24 32 NPV Solving fo 50 24 32 1 1 2 2 50 24 24 4 50 32 2 50 2 7.522% Since the incemental IRR of 7.522% is less than the cost of capital of 8%, you should take the Playhouse. [Type text]
6-31. Kaimalino Popeties (KP) is evaluating six eal estate investments. Management plans to buy the popeties today and sell them five yeas fom today. The following table summaizes the initial cost and the expected sale pice fo each popety, as well as the appopiate discount ate based on the isk of each ventue. KP has a total capital budget of $18,000,000 to invest in popeties. a. What is the IRR of each investment? b. What is the NPV of each investment? c. Given its budget of $18,000,000, which popeties should KP choose? d. Explain why the pofitably index method could not be used if KP s budget wee $12,000,000 instead. Which popeties should KP choose in this case? a. We can compute the IRR fo each as IRR = (Sale Pice/Cost) 1/5 1. See speadsheet below. b. We can compute the NPV fo each as NPV = Sale Pice/(1+) 5 Cost. See speadsheet below. Poject Cost Today Discount Rate Expected Sale Pice in Yea 5 IRR NPV Pofitability Index Mountain Ridge $ 3,000,000 15% $ 18,000,000 43.1% $ 5,949,181 1.98 Ocean Pak Estates 15,000,000 15% $ 75,500,000 38.2% 22,536,844 1.50 Lakeview 9,000,000 15% $ 50,000,000 40.9% 15,858,837 1.76 Seabeeze 6,000,000 8% $ 35,500,000 42.7% 18,160,703 3.03 Geen Hills 3,000,000 8% $ 10,000,000 27.2% 3,805,832 1.27 West Ranch 9,000,000 8% $ 46,500,000 38.9% 22,647,119 2.52 c. We can ank pojects accoding to thei pofitability index = NPV/Cost, as shown below. Thus, KP should invest in Seabeeze, West Ranch, and Mountain Ridge. (Note that anking pojects accoding to thei IRR would not maximize KP s total NPV, and so would not lead to the coect selection.) d. The pofitability index fails because the top-anked pojects do not completely use up the budget. In this case, you should take Mountain Ridge and West Ranch. Chapte 7 Fundamentals of Capital Budgeting 7-2. Kokomochi is consideing the launch of an advetising campaign fo its latest desset poduct, the Mini Mochi Munch. Kokomochi plans to spend $5 million on TV, adio, and pint
1 2 3 4 5 6 7 8 9 10 11 advetising this yea fo the campaign. The ads ae expected to boost sales of the Mini Mochi Munch by $9 million this yea and by $7 million next yea. In addition, the company expects that new consumes who ty the Mini Mochi Munch will be moe likely to ty Kokomochi s othe poducts. As a esult, sales of othe poducts ae expected to ise by $2 million each yea. Kokomochi s goss pofit magin fo the Mini Mochi Munch is 35%, and its goss pofit magin aveages 25% fo all othe poducts. The company s maginal copoate tax ate is 35% both this yea and next yea. What ae the incemental eanings associated with the advetising campaign? A B C D E Yea 1 2 Incemental Eanings Foecast ($000s) 1 Sales of Mini Mochi Munch 9,000 7,000 2 Othe Sales 2,000 2,000 3 Cost of Goods Sold (7,350) (6,050) 4 Goss Pofit 3,650 2,950 5 Selling, Geneal & Admin. (5,000) - 6 Depeciation - - 7 EBIT (1,350) 2,950 8 Income tax at 35% 473 (1,033) 9 Unleveed Net Income (878) 1,918 7-3. Home Builde Supply, a etaile in the home $300 impovement industy, cuently opeates seven $250 etail outlets in Geogia and South Caolina. Management is contemplating building an eighth $200 70 80 90 100 110 120 130 140 150 etail stoe acoss town fom its most successful etail outlet. The company aleady owns the land fo this stoe, which cuently has an abandoned waehouse located on it. Last month, the maketing depatment spent $10,000 on maket eseach to detemine the extent of custome demand fo the new stoe. Now Home Builde Supply must decide whethe to build and open the new stoe. Which of the following should be included as pat of the incemental eanings fo the poposed new etail stoe? a. The cost of the land whee the stoe will be located. b. The cost of demolishing the abandoned waehouse and cleaing the lot. c. The loss of sales in the existing etail outlet, if customes who peviously dove acoss town to shop at the existing outlet become customes of the new stoe instead. d. The $10,000 in maket eseach spent to evaluate custome demand. e. Constuction costs fo the new stoe. f. The value of the land if sold. g. Inteest expense on the debt boowed to pay the constuction costs. a. No, this is a sunk cost and will not be included diectly. (But see (f) below.) b. Yes, this is a cost of opening the new stoe. c. Yes, this loss of sales at the existing stoe should be deducted fom the sales at the new stoe to detemine the incemental incease in sales that opening the new stoe will geneate fo HBS. d. No, this is a sunk cost. e. This is a capital expenditue associated with opening the new stoe. These costs will, theefoe, incease HBS s depeciation expenses. f. Yes, this is an oppotunity cost of opening the new stoe. (By opening the new stoe, HBS fogoes the afte-tax poceeds it could have eaned by selling the popety. This loss is equal to the sale [Type text]
pice less the taxes owed on the capital gain fom the sale, which is the diffeence between the sale pice and the book value of the popety. The book value equals the initial cost of the popety less accumulated depeciation.) g. While these financing costs will affect HBS s actual eanings, fo capital budgeting puposes we calculate the incemental eanings without including financing costs to detemine the poject s unleveed net income. 7-7. Castle View Games would like to invest in a division to develop softwae fo video games. To evaluate this decision, the fim fist attempts to poject the woking capital needs fo this opeation. Its chief financial office has developed the following estimates (in millions of dollas): Assuming that Castle View cuently does not have any woking capital invested in this division, calculate the cash flows associated with changes in woking capital fo the fist five yeas of this investment. Yea0 Yea1 Yea2 Yea3 Yea4 Yea5 1 Cash 6 12 15 15 15 2 Accounts Receivable 21 22 24 24 24 3 Inventoy 5 7 10 12 13 4 Accounts Payable 18 22 24 25 30 5 Net woking capital (1+2+3-4) 0 14 19 25 26 22 6 Incease in NWC 14 5 6 1-4 7-9. Elmdale Entepises is deciding whethe to expand its poduction facilities. Although long-tem cash flows ae difficult to estimate, management has pojected the following cash flows fo the fist two yeas (in millions of dollas): a. What ae the incemental eanings fo this poject fo yeas 1 and 2? b. What ae the fee cash flows fo this poject fo the fist two yeas?
7-17. Anold Inc. is consideing a poposal to manufactue high-end potein bas used as food supplements by body buildes. The poject equies use of an existing waehouse, which the fim acquied thee yeas ago fo $1m and which it cuently ents out fo $120,000. Rental ates ae not expected to change going fowad. In addition to using the waehouse, the poject equies an up-font investment into machines and othe equipment of $1.4m. This investment can be fully depeciated staight-line ove the next 10 yeas fo tax puposes. Howeve, Anold Inc. expects to teminate the poject at the end of eight yeas and to sell the machines and equipment fo $500,000. Finally, the poject equies an initial investment into net woking capital equal to 10% of pedicted fist-yea sales. Subsequently, net woking capital is 10% of the pedicted sales ove the following yea. Sales of potein bas ae expected to be $4.8m in the fist yea and to stay constant fo eight yeas. Total manufactuing costs and opeating expenses (excluding depeciation) ae 80% of sales, and pofits ae taxed at 30%. a. What ae the fee cash flows of the poject? b. If the cost of capital is 15%, what is the NPV of the poject? a. Assumptions: (1) The waehouse can be ented out again fo $120,000 afte 8 yeas. (2) The NWC is fully ecoveed at book value afte 8 yeas. FCF = EBIT (1 t) + Depeciation CAPX Change in NWC FCF in yea 0: 1.4m CAPX 0.48m Change in NWC = 1.88m FCF in yeas 1-7: $4.8m Sales $3.84m Cost (80%) $0.96m $0.12m $0.14m $0.70m =Goss Pofit Lost Rent Depeciation =EBIT $0.21m Tax (30%) $0.49m $0.14m $0.63m = (1 t) x EBIT +Depeciation = FCF [Type text]
Note that thee is no moe CAPX no investment into NWC in yeas 1 7. FCF in yea 8: $0.63m + [$0.5m 0.30 x ($0.5m $0.28m)] + $0.48m = $1.544m Note that the book value of the machiney is still $0.28m when sold, and only the diffeence between the sale pice ($0.5m) and the book value is taxed. The NWC ($0.48m) is ecoveed at book value and hence its sale is not taxed at all. b. The NPV is the pesent value of the FCFs in yeas 0 to 8: NPV= -$1.88m + an annuity of $0.63m fo 7 yeas $1.544m 1.15 + 8 $0.63m 1 $1.544m $1.88m 1 7 8 0.15 1.15 1.15 $1.2458m 7-23. Baue Industies is an automobile manufactue. Management is cuently evaluating a poposal to build a plant that will manufactue lightweight tucks. Baue plans to use a cost of capital of 12% to evaluate this poject. Based on extensive eseach, it has pepaed the following incemental fee cash flow pojections (in millions of dollas): a. Fo this base-case scenaio, what is the NPV of the plant to manufactue lightweight tucks? b. Based on input fom the maketing depatment, Baue is uncetain about its evenue foecast. In paticula, management would like to examine the sensitivity of the NPV to the evenue assumptions. What is the NPV of this poject if evenues ae 10% highe than foecast? What is the NPV if evenues ae 10% lowe than foecast? c. Rathe than assuming that cash flows fo this poject ae constant, management would like to exploe the sensitivity of its analysis to possible gowth in evenues and opeating expenses. Specifically, management would like to assume that evenues, manufactuing expenses, and maketing expenses ae as given in the table fo yea 1 and gow by 2% pe yea evey yea stating in yea 2. Management also plans to assume that the initial capital expenditues (and theefoe depeciation), additions to woking capital, and continuation value emain as initially specified in the table. What is the NPV of this poject unde these altenative assumptions? How does the NPV change if the evenues and opeating expenses gow by 5% pe yea athe than by 2%?
NPV ($ million) d. To examine the sensitivity of this poject to the discount ate, management would like to compute the NPV fo diffeent discount ates. Ceate a gaph, with the discount ate on the x-axis and the NPV on the y-axis, fo discount ates anging fom 5% to 30%. Fo what anges of discount ates does the poject have a positive NPV? Yea 0 1 2 3 4 5 6 7 8 9 10 Fee Cash Flow Foecast ($ millions) 1 Sales 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 2 Manufactuing (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) (35.0) 3 Maketing Expenses (10.0) (10.0) (10.0) (10.0) (10.0) (10.0) (10.0) (10.0) (10.0) (10.0) 4 Depeciation (15.0) (15.0) (15.0) (15.0) (15.0) (15.0) (15.0) (15.0) (15.0) (15.0) 5 EBIT 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 40.0 6 Income tax at 35% (14.0) (14.0) (14.0) (14.0) (14.0) (14.0) (14.0) (14.0) (14.0) (14.0) 7 Unleveed Net Income 26.0 26.0 26.0 26.0 26.0 26.0 26.0 26.0 26.0 26.0 8 Depeciation 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 15.0 9 Inc. in NWC (5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0) (5.0) 10 Capital Expenditues (150.0) 11 Continuation value 12.0 12 Fee Cash Flow (150.0) 36.0 36.0 36.0 36.0 36.0 36.0 36.0 36.0 36.0 48.0 13 NPV at 12% 57.3 160 140 120 100 80 a. The NPV of the estimate fee cash flow is 1 1 48 NPV 150 36 1 $57.3 million. 9 10 0.12 1.12 1.12 b. Initial Sales 90 100 110 NPV 20.5 57.3 94.0 c. Gowth Rate 0% 2% 5% NPV 57.3 72.5 98.1 d. NPV is positive fo discount ates below the IRR of 20.6%. 60 40 20 0 0% -20 5% 10% 15% 20% 25% 30% 35% -40-60 Discount Rate [Type text]