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CHAPTER 12

LONG-TERM INVESTMENT DECISIONS

Gösterilen kısım, yapılan bir yatırımın yıllara göre bize olan getirisini göstermektedir. Proje A için her sene $14,000

iken, Proje B için yıllara göre farklılık göstermektedir. Başlangıçta yaptığımız yatırımlar ise $42,000 ve $45,000.

Net Present Value (NPV)

■ Bir projenin bugünkü değeri, kabaca açıklayacak olursak, kiracım ile 10 yıllık bir kira sözleşmem var, her ay

500 tl kira alacağım bu da 10 sene sonunda toplam 60,000 tl alacağımı gösterir. İşte bu 10 yıl boyunca

toplayacağım 60,000 tl’nin şu andaki değeridir.

Bir yatırım projesinin kabul edilebilmesi için projeden elde edilen gelirlerin masraflarından fazla olması gerekir ve

bunun için de tüm gelir giderlerin net şimdiki değerinin hesaplanması lazımdır. Bu bir yöntemdir ve proje

analizlerinde en çok kullanılan yöntemler arasındadır. Net şimdiki değer (NPV) yöntemiyle bir projenin iktisadi ömrü

boyunca sağlayacağı net nakit girişlerinin ve yatırım giderlerinin belli bir indirgeme oranı ile bugüne indirgenen

değerleri arasındaki fark bulunur. Bir projenin bu yönteme göre kabul edilebilmesi için net şimdiki değerin sıfıra eşit

veya büyük olması gerekmektedir. Daha anlaşılır olması için örnek vermemiz gerekirse;

ÖRNEK DEUcell tesislerinde kullanmayı düşündüğü bir makine için dönem başında 11.000 TL yatırım yapmayı

düşünmektedir. İskonto oranı %10 olarak kabul edilmiştir. Makinenin yıllar itibariyle sağlayacağı nakit girişleri

aşağıda gösterilmektedir.

Yıl Nakit Girişleri

1 2,500 2 2,600 3 4,000 4 6,000

ÇÖZÜM

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Yani bu projeye yapılacak 11,000 liralık bir yatırımın 4 yıllık süre sonucunda getireceği gelir, bugünkü değeriyle şirkete

524,83 liralık bir kar sağlayacak.

NPV’nin pozitif çıkması, yatırımın istenen getiri oranına eşit ya da onun üstünde bir getiri sağlayacağını ifade eder ve

projenin kabul edilebileceği anlamını taşır. NPV’si en yüksek olan projeler kabul edilir.

Tablo 12.1’e göre A ve B projelerinin NPV değerlerini bulalım;

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Yeni yatırım projelerinin değerlendirilmesinde, iskonto oranı olarak sermaye maliyeti kullanılmaktadır. Bu yüzden %10’luk cost of capital’ı kullanıyoruz. Sermaye maliyeti, bize istenen minimum yatırım getirisi oranını ifade etmektedir ve bu oran aynı zamanda bize alternatif yatırım projelerinin kabul edilebilirliğini belirlemekte yardımcı olur.

İlk önce 5 yıllık getirilerin sermaye maliyetine göre bugünkü değerini buluyoruz (mesela B projesi için ilk sene sonundaki $28,000’lık getirinin

bugünkü değeri $25,454 ) ve bunların toplamlarından ilk yatırımlarımızı çıkardığımızda net şimdiki değerleri elde etmiş oluyoruz.

EXAMPLE 12.4 Treadwell Tire Company, a tire retailer with a 10% cost of capital, is considering investing in either of two mutually exclusive projects, A and B. Each requires a $10,000 initial investment, and both are expected to provide constant annual cash inflows over their 15-year lives. For either project to be acceptable, its NPV must be greater than zero. Another way to say this is that the present value of the annuity (that is, the project’s cash inflows) must be greater than the initial cash outflow. If we let CF equal the annual cash inflow and let CF0 equal the initial investment, the following condition must be met for projects with annuity cash inflows, such as A and B, to be acceptable:

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Faiz oranı 10%, her bir projeye yapılan başlangıç yatırımı $10,000, projelerin yıllık getirileri “constant” yani sabit, 15 yıllık süresi var. CF = $1,314.74 -> breakeven cash flow NPV’nin 0 olduğu nokta, yani projenin yıllık getirisi $1,315’dan az ise bu yatırımdan zarar ederiz. Sonuç bize şunu gösteriyor; projenin kabul edilebilmesi için yıllık getirisinin en az $1,315 olması gerekiyor.

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SCENARIO ANALYSIS

Senaryo analizinde çeşitli olasılıklara göre projenin yıllık getiri miktarları değişmektedir. Yatırım tercihi için “range”leri karşılaştırırız. “Range”leri belirlemek için projedeki en yüksek değerden en düşük değeri çıkarırız. A projesinin yıllık getiri miktarları için range’imiz (2,500 - 1,500 = 1,000)dir. Riskten çekinen bir yatırımcı A projesini tercih edecektir çünkü range ne kadar düşükse risk de bir o kadar düşüktür. Hem de baktığımızda A projesinin NPV değerleri hep 0’ın üzerinde. Bu da gösteriyor ki A projesine yapılan yatırım hem daha az riskli hem de getirisi hep + yönde. RISK-ADJUSTED DISCOUNT RATES Her yatırımın riski farklı farklıdır. Bu yüzden farklı yatırımlara göre farklı risk oranları kullanırız. Talor Namtig is considering investing $1,000 in either of two stocks—A or B. She plans to hold the stock for exactly 5 years and expects both stocks to pay $80 in annual end-of-year cash dividends. At the end of year 5 she estimates that stock A can be sold to net $1,200 and stock B can be sold to net $1,500. Talor has carefully researched the two stocks and feels that although stock A has average risk, stock B is considerably riskier. Her research indicates that she should earn an annual return on an average-risk stock of 11%. Because stock B is considerably riskier, she will require a 14% return from it. Talor makes the following calculations to find the risk-adjusted net present values (NPVs) for the two stocks:

Although Talor’s calculations indicate that both stock investments are acceptable (NPVs > $0), on a risk-adjusted basis, she should invest in Stock B because it has a higher NPV. Yukarıdaki örnekte A ve B hisseleri var. Her biri için $1,000’lık yatırım yapılıyor. Ve bu hisseler 5 yıl boyunca elde tutuluyor. Konumuzla ilgili olan kısım ise yatırımların risklerinin farklı olması. Birinin %11 diğerinin ise %14. NPV hesabı yaptığımızda her iki yatırımın da kabul edilebilir olduğunu görüyoruz, fakat B hissesinin NPV değeri daha yüksek olduğundan yatırımcı B hissesini seçiyor. ------------------------------------------------------------------------------------------ CAPM hesabı yaparak yatırım için daha tutarlı kararlar alınabilir. ------------------------------------------------------------------------------------------

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EXAMPLE 12.5 Bennett Company wishes to use the risk-adjusted discount rate approach to determine, according to NPV, whether to implement project A or project B. In addition to the data presented in part A of Table 12.1, Bennett’s management after much analysis subjectively assigned “risk indexes” of 1.6 to project A and 1.0 to project B. The risk index is merely a numerical scale used to classify Project risk: Higher index values are assigned to higher-risk projects, and vice versa. The CAPM-type relationship used by the firm to link risk (measured by the risk index) and the required return (RADR) is shown in the following table. Management developed this relationship after analyzing CAPM and the risk– return relationships of the projects that they considered and implemented during the past few years.

Her yatırım farklı risk oranlarına sahip olduğunu daha önce belirtmiştik. Risk index, riskleri sınıflandırmak için kullanılan bir ölçektir. Risk index arttıkça risk oranı da artar. A ve B projelerini incelediğimizde A, B’den daha risklidir çünkü RADR’ı daha yüksek. Fakat her iki projenin NPV’lerini hesapladığımızda (Figure 12.3) B projesini seçeriz çünkü NPV’si A’nınkinden daha yüksek. Eğer RADR kullanmadan (yani proje risklerini aynı kabul ederek) hesaplamalarımızı yapsaydık A’yı seçerdik. Çünkü bu durumda da A’nın NPV’si daha yüksek. (bkz. Tablo 12.1)

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ANNUALIZED NET PRESENT VALUE (ANPV) APPROACH Uzunlukları farklı olan projeleri karşılaştırmak için bu yöntemi kullanırız.

EXAMPLE 12.7 The AT Company, a regional cable television company, is evaluating two projects, X and Y. The relevant cash flows for each project are given in the following table. The applicable cost of capital for use in evaluating these equally risky projects is 10%.

Adım 1. İlk önce projelerin NPV’leri bulunur.

Adım 2. Farklı uzunluklara sahip yatırımlar ANPV formülü ile karşılaştırılır.

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Adım 3. ANPV’si yüksek olan proje tercih edilir. √

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ANPV kullanarak farklı süreçlere sahip projelerin yıllık ortalama getirilerini hesaplayarak projeleri kıyaslayabildik. CAPITAL RATIONING Amaç kısıtlı olan bütçemizle NPV’si en yüksek projeleri seçmek. Örnekle açıklayacak olursak; Example 12.10 Tate Company, a fast-growing plastics company, is confronted with six projects competing for its fixed budget of $250,000. The initial investment and IRR for each project are shown in the following table:

B %20 $70,000

C %16 $100,000

E %15 $60,000

A %12 $80,000

F %11 $110,000

Şirketin “cost of capital”ı %10 bu yüzden IRR’si %10’un altındaki projeleri en başta eliyoruz. Sonra en yüksek IRR oranına sahip projeyi seçmekle başlıyoruz. Yani sırasıyla B, C ve E projelerini seçiyoruz. Bu projelerin tutarı $230,000. Bütçemiz kısıtlandığı için başka proje seçemiyoruz. Yeterli bütçe olsaydı sırasıyla A ve F projelerini de seçecektik. PROBLEMS AND SOLUTIONS E12-2 You wish to evaluate a project requiring an initial investment of $45,000 and having a useful life of 5 years. What minimum amount of annual cash inflow do you need if your firm has an 8% cost of capital? If the project is forecast to earn $12,500 per year over the 5 years, what is its IRR? Is the project acceptable?

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NPV formülünden yararlanarak soruyu çözüyoruz. $45,000’lık bir yatırımın %8’lik faiz oranına göre kabul edilebilir olması için yıllık minimum getirisi $11,270 olmalıdır. Eğer senelik getirisi $12,500 olsaydı faiz oranımız ne olurdu sorusunu da yine aynı formül ile çözüyoruz.

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Bu hesap ancak “financial calculator” ile yapılabilir. Sınavda böyle bir soru verilirse IRR tablosundan bakılarak çözülecek. İşlemin sonucu 3.6 çıkıyor.

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Time/IRR %1 %2 %3 ……. ….. %12

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5 3.6

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IRR = %12 o zaman %8 kabul edilebilir. E12-3 Like most firms in its industry, Yeastime Bakeries uses a subjective risk assessment tool of its own design. The tool is a simple index by which projects are ranked by level of perceived risk on a scale of 0–10. The scale is recreated in the following table.

The firm is analyzing two projects based on their RADRs. Project Sourdough requires an initial investment of $12,500 and is assigned a risk index of 6. Project Greek Salad requires an initial investment of $7,500 and is assigned a risk index of 8. The two projects have 7-year lives. Sourdough is projected to generate cash inflows of $5,500 per year. Greek Salad is projected to generate cash inflows of $4,000 per year. Use each project’s RADR to select the better project. SOLUTION

I II

Initial investment 12,500 7,500 Cash inflow 5,500 4,000 Year 7 years 7 years Risk index 6 8 RADR 7% 8% NPV $17,141 $13,325

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1. projenin NPV’si daha yüksek olduğu için tercih edilir.

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E12-4 Outcast, Inc., has hired you to advise the firm on a capital budgeting issue involving two unequal-lived, mutually exclusive projects, M and N. The cash flows for each project are presented in the following table. Calculate the NPV and the annualized net present value (ANPV) for each project using the firm’s cost of capital of 8%. Which project would you recommend?

SOLUTION İlk olarak projelerin net bugünkü değerlerini hesaplıyoruz.

Daha sonra da ANPV hesabı yapıp ANPV’si yüksek olan projeyi tercih ederiz.

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E12-5 Longchamps Electric is faced with a capital budget of $150,000 for the coming year. It is considering six investment projects and has a cost of capital of 7%. The six projects are listed in the following table, along with their initial investments and their IRRs. Using the data given, prepare an investment opportunities schedule (IOS). Which projects does the IOS suggest should be funded? Does this group of projects maximize NPV? Explain.

SOLUTION

4 11% $50,000

2 10% $40,000

5 9% $45,000

1 8% $75,000

Cost of capital %7 olduğu için %7 altı cost of capital’a sahip projeleri eliyoruz. Daha sonra en yüksek IRR’ye sahip projeden başlayarak bütçemizin izin verdiği kadar projeye yatırım yapıyoruz. 4, 2 ve 5 numaralı projelere yatırım yaptığımızda bu projelerin bize tutarı $135,000. Başlangıç bütçemiz $150,000 olduğu için bütçe kısıtından dolayı daha fazla projeye giremiyoruz. P12-11 Risk-adjusted rates of return using CAPM Centennial Catering, Inc., is considering two mutually exclusive investments. The company wishes to use a CAPM-type riskadjusted discount rate (RADR) in its analysis. Centennial’s managers believe that the appropriate market rate of return is 12%, and they observe that the current risk-free rate of return is 7%. Cash flows associated with the two projects are shown in the following table.

a. Use a risk-adjusted discount rate approach to calculate the net present value of each project, given that project X has an RADR factor of 1.20 and project Y has an RADR factor of 1.40. The RADR factors are similar to project betas. (Use Equation 12.5 to calculate the required project return for each.)

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b. Discuss your findings in part a, and recommend the preferred project. SOLUTION

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Daha yüksek NPV değerine sahip olduğundan X projesi tercih edilir. P12-16 NPV and ANPV decisions Richard and Linda Butler decide that it is time to purchase a high-definition (HD) television because the technology has improved and prices have fallen over the past 3 years. From their research, they narrow their choices to two sets, the Samsung 42-inch LCD with 1080p capability and the Sony 42-inch LCD with 1080p features. The price of the Samsung is $2,350 and the Sony will cost $2,700. They expect to keep the Samsung for 3 years; if they buy the more expensive Sony unit, they will keep the Sony for 4 years. They expect to be able to sell the Samsung for $400 by the end of 3 years; they expect they could sell the Sony for $350 at the end of year 4. Richard and Linda estimate the end-of-year entertainment benefits (that is, not going to movies or events and watching at home) from the Samsung to be $900 and for the Sony to be $1,000. Both sets can be viewed as quality units and are equally risky purchases. They estimate their opportunity cost to be 9%. The Butlers wish to choose the better alternative from a purely financial perspective. To perform this analysis they wish to do the following: a. Determine the NPV of the Samsung HD LCD. b. Determine the ANPV of the Samsung HD LCD. c. Determine the NPV of the Sony HD LCD. d. Determine the ANPV of the Sony HD LCD. e. Which set should the Butlers purchase and why? SOLUTIONS

a.

Samsung Sony

Cost ($2,350) ($2,700) Annual benefits $900 $1,000 Life 3 years 4 years Terminal value $400 $350 Required rate of return 9% 9%

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b.

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d.

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e.

Daha fazla ANPV değerine sahip olduğundan dolayı Sony tercih edilir. P12-19 Capital rationing—NPV approach A firm with a 13% cost of capital must select the optimal group of projects from those shown in the following table, given its capital budget of $1 million.

a. Calculate the present value of cash inflows associated with each project. b. Select the optimal group of projects, keeping in mind that unused funds are costly.

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SOLUTIONS

a.

Project Initial investment NPV PV of inflows Total investment

A $300,000 $84,000 $384,000 - B $200,000 $10,000 $210,000 - C $100,000 $25,000 $125,000 $100,000 D $900,000 $90,000 $990,000 E $500,000 $70,000 $570,000 F $100,000 $50,000 $150,000 $200,000 G $800,000 $160,000 $960,000 $1,000,000

Capital budget = $1,000,000

b. First accept Project G because it has the highest NPV. It’s initial investment is $800,000, so now you have $200,000 remained. You can choose B, C, or F. F has the highest NPV, so then choose F. You have remaining $100,000, with this money choose C. So, the optimal group of projects are C, F, and G.

INTEGRATIVE CASE 5

Lasting Impressions Company Lasting Impressions (LI) Company is a medium-sized commercial printer of promotional advertising brochures, booklets, and other direct-mail pieces. The firm’s major clients are ad agencies based in New York and Chicago. The typical job is characterized by high quality and production runs of more than 50,000 units. LI has not been able to compete effectively with larger printers because of its existing older, inefficient presses. The firm is currently having problems cost-effectively meeting run length requirements as well as meeting quality standards. The general manager has proposed the purchase of one of two large, six-color presses designed for long, high-quality runs. The purchase of a new press would enable LI to reduce its cost of labor and therefore the price to the client, putting the firm in a more competitive position. The key financial characteristics of the old press and of the two proposed presses are summarized in what follows. Old press Originally purchased 3 years ago at an installed cost of $400,000, it is being depreciated under MACRS using a 5-year recovery period. The old press has a remaining economic life of 5 years. It can be sold today to net $420,000 before taxes; if it is retained, it can be sold to net $150,000 before taxes at the end of 5 years. Press A This highly automated press can be purchased for $830,000 and will require $40,000 in installation costs. It will be depreciated under MACRS using a 5-year recovery period. At the end of the 5 years, the machine could be sold to net $400,000 before taxes. If this machine is acquired, it is anticipated that the current account changes shown in the following table would result.

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Press B This press is not as sophisticated as press A. It costs $640,000 and requires $20,000 in installation costs. It will be depreciated under MACRS using a 5-year recovery period. At the end of 5 years, it can be sold to net $330,000 before taxes. Acquisition of this press will have no effect on the firm’s net working capital investment. The firm estimates that its earnings before depreciation, interest, and taxes with the old press and with press A or press B for each of the 5 years would be as shown in Table 1 (see page 504). The firm is subject to a 40% tax rate. The firm’s cost of capital, r, applicable to the proposed replacement is 14%.

TO DO a. For each of the two proposed replacement presses, determine: (1) Initial investment. (2) Operating cash inflows. (Note: Be sure to consider the depreciation in year 6.) (3) Terminal cash flow. (Note: This is at the end of year 5.) b. Using the data developed in part a, find and depict on a time line the relevant cash flow stream associated with each of the two proposed replacement presses, assuming that each is terminated at the end of 5 years. c. Using the data developed in part b, apply each of the following decision techniques: (1) Payback period. (Note: For year 5, use only the operating cash inflows—that is, exclude terminal cash flow—when making this calculation.) (2) Net present value (NPV). (3) Internal rate of return (IRR). e. Recommend which, if either, of the presses the firm should acquire if the firm has (1) unlimited funds or (2) capital rationing.

SOLUTIONS

Old press: Purchased 3 years ago Installed cost = $400,000 MACRS – 5 year Remaining economic life = 5 years Selling price today = $420,000 At the end of 5 years = $150,000

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Press A: New equipment cost = $830,000 Installation cost = $40,000 MACRS 5 years Selling price at the end of 5 years = $400,000

Cash $25,400

A/R $120,000

Inventory ($20,000)

Increase in C.A. $125,400

Increase in C.L. ($35,000)

Increase in NWC $90,400

Press B: Cost = $640,000 Installation cost = $20,000 MACRS-5 years Selling price = $330,000 Tax rate = 40% r = 14% a.

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Press A Press B Installed cost of new press Cost of new press $830,000 $640,000 +Installation cost $40,000 $20,000 Total cost-new press $870,000 $660,000 -After tax proceed from sale of old Proceeds from sale of old $420,000 $420,000 -Tax on sale of old ($121,600) ($121,600) Total proceeds-sale of old ($298,400) ($298,400) + NWC $90,400 0 Initial Investment $662,000 $361,600 2- Operating cash inflows (Existing press)

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EBDIT $120,000 $120,000 $120,000 $120,000 $120,000 0 -Depreciation ($48,000) ($48,000) ($20,000) 0 0 0 EBIT $72,000 $72,000 $100,000 $120,000 $120,000 0 -Taxes ($28,800) ($28,800) ($40,000) ($48,000) ($48,000) 0 NOPAT $43,200 $43,200 $60,000 $72,000 $72,000 0

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+Depreciation $48,000 $48,000 $20,000 0 0 0 $91,200 $91,200 $80,000 $72,000 $72,000 0

MACRS-5 year (Depreciation) 20% 32% 19% 12% = $48,000 project’s 1st year 12% = $48,000 project’s 2nd year 5% = $20,000 projects 3rd year

Press A

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EBDIT $250,000 $270,000 $300,000 $330,000 $370,000 0 -Depreciation ($174,000) ($278,400) ($165,300) ($104,400) ($104,400) ($43,500) EBIT $76,000 $8,400 $134,700 $225,600 $265,600 ($43,500) -Taxes ($30,400) $3,360 ($53,880) ($90,240) ($106,240) $17,400 NOPAT $45,600 ($5,040) $80,820 $135,360 $159,360 ($26,100) +Depreciation $174,000 $278,400 $165,300 $104,400 $104,400 $43,500 $219,600 $273,360 $246,120 $239,760 $263,760 $17,400 $91,200 $91,200 $80,000 $72,000 $72,000 0 Inc. OCF $128,400 $182,160 $166,120 $167,760 $191,760 $17,400

MACRS-5 YEARS (PRESS A)

20% = $174,000 32% = $278,400 19% = $165,300 12% = $104,400 12% = $104,400

5% = $43,500

MACRS-5 YEARS (PRESS B) 20% = $132,000 32% = $211,200 19% = $125,400 12% = $79,200 12% = $79,200 5% = $33,000

Press B

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EBDIT $210,000 $210,000 $210,000 $210,000 $210,000 $210,000 -Depreciation ($132,000) ($211,200) ($125,400) ($79,200) ($79,200) ($33,000) EBIT $78,000 ($1,200) $84,600 $130,800 $130,800 $177,000 -Taxes ($31,200) $480 ($33,840) ($52,320) ($52,320) ($70,800) NOPAT $46,800 ($720) $50,760 $78,480 $78,480 $106,200 +Depreciation $132,000 $211,200 $125,400 $79,200 $79,200 $33,000 $178,800 $210,480 $176,160 $157,680 $157,680 $139,200 $91,200 $91,200 $80,000 $72,000 $72,000 0 Inc. OCF $87,600 $119,280 $96,160 $85,680 $85,680 $139,200

3- Terminal Cash Flow

Press A Press B

After-tax proceeds-sale of new Proceeds from sale of new $400,000 $330,000 Taxes ($142,600) ($118,800) Total proceeds-new press $257,400 $211,200

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-After-tax proceeds sale of old Proceeds from sale of old $150,000 $150,000 Taxes ($60,000) ($60,000) Total proceeds – old press $90,000 $90,000 NWC $90,400 0 Terminal cash flow $257,800 $121,200

MACRS 20% 32% 19% 12% 12% 5% BV b- Press A

-$662,000 $128,400 $182,160 $166,120 $167,760 $449,560

0 1 2 3 4 5 6

Press B

-$361,600 $87,600 $119,280 $96,160 $85,680 $206,880

0 1 2 3 4 5 6