Supply the missing words: “There are three forms of the

Supply the missing words: “There are three forms of the efficient-market hypothesis. Tests of randomness in stock returns provide evidence for the form of the hypothesis. Tests of stock price reaction to well-publicized news provide evidence for the form, and tests of the performance of professionally managed funds provide evidence for the form. Market efficiency results from competition between investors. Many investors search for new information about the company’s business that would help them to value the stock more accurately. Such research helps to ensure that prices reflect all available information; in other words, it helps to keep the market efficient in the form. Other investors study past stock prices for recurrent patterns that would allow them to make superior profits.

Such research helps to ensure that prices reflect all the information contained in past stock prices; in other words, it helps to keep the market efficient in the form.”

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Suppose that Sudbury Mechanical Drifters is proposing to invest $10

Suppose that Sudbury Mechanical Drifters is proposing to invest $10 million in a new factory. It can depreciate this investment straight-line over 10 years. The tax rate is 40%, and the is 10%.

a. What is the present value of Sudbury’s depreciation tax shields?

b. Suppose that the government allows companies to use double-declining-balance depreciation with the option to switch at any point to straight-line. Now what is the present value of the depreciation tax shields?

c. What would be the present value of the tax shield if the government allowed Sudbury to write-off the factory immediately?

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1. Calculate the NPV of the proposed investment, using the

1. Calculate the NPV of the proposed investment, using the inputs suggested in this case. How sensitive is this NPV to future sales volume?

2. What are the pros and cons of waiting for a year before deciding whether to invest? What happens if demand turns out high and Sparky-Cola also invests? What if Ecsy-Cola invests right away and gains a one-year head start on Sparky-Cola?

Libby Flannery, the regional manager of Ecsy-Cola, the international soft drinks empire, was reviewing her investment plans for Central Asia. She had contemplated launching Ecsy-Cola in the ex-Soviet republic of Inglistan in 2022. This would involve a capital outlay of $20 million in 2021 to build a bottling plant and set up a system there. Fixed costs (for manufacturing, and marketing) would then be $3 million per year from 2021 onward. This would be sufficient to make and sell 200 million liters per year—enough for every man, woman, and child in Inglistan to drink four bottles per week! But there would be few savings from building a smaller plant, and import tariffs and transport costs in the region would keep all production within national borders.

The variable costs of production and would be 12 cents per liter. Company policy requires a rate of return of 25% in nominal dollar terms, after local taxes but before deducting any costs of financing. The sales revenue is forecasted to be 35 cents per liter.

Bottling plants last almost forever, and all unit costs and revenues were expected to remain constant in nominal terms. Tax would be payable at a rate of 30%, and under the Inglistan corporate tax code, capital expenditures can be written off on a straight-line basis over four years.

All these inputs were reasonably clear. But Ms. Flannery racked her brain trying to forecast sales. Ecsy-Cola found that the “1–2–4” rule works in most new markets. Sales typically double in the second year, double again in the third year, and after that remain roughly constant. Libby’s best guess was that, if she went ahead immediately, initial sales in Inglistan would be 12.5 million liters in 2023, ramping up to 50 million in 2025 and onward.

Ms. Flannery also worried whether it would be better to wait a year. The soft drink market was developing rapidly in neighboring countries, and in a year’s time she should have a much better idea whether Ecsy-Cola would be likely to catch on in Inglistan. If it didn’t catch on and sales stalled below 20 million liters, a large investment probably would not be justified.

Ms. Flannery had assumed that Ecsy-Cola’s keen rival, Sparky-Cola, would not also enter the market. But last week she received a shock when in the lobby of the Kapitaliste Hotel she bumped into her opposite number at Sparky-Cola. Sparky-Cola would face costs similar to Ecsy-Cola.

How would Sparky-Cola respond if Ecsy-Cola entered the market? Would it decide to enter also?

If so, how would that affect the profitability of Ecsy-Cola’s project?

Ms. Flannery thought again about postponing investment for a year. Suppose Sparky-Cola were interested in the Inglistan market. Would that favor delay or immediate action?

Maybe Ecsy-Cola should announce its plans before Sparky-Cola has a chance to develop its own proposals. It seemed that the Inglistan project was becoming more complicated by the day.

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The scene: John and Marsha hold hands in a cozy

The scene: John and Marsha hold hands in a cozy French restaurant in downtown Manhattan, several years before the mini-case in Chapter 9. Marsha is a futures-market trader. John manages a $250 million common-stock for a large pension fund. They have just ordered tournedos financiere for the main course and flan financiere for dessert. John reads the financial pages of The Wall Street Journal by candlelight.

John: Wow! Potato futures hit their daily limit. Let’s add an order of gratin dauphinoise. Did you manage to hedge the forward interest rate on that euro loan?
Marsha: John, please fold up that paper. (He does so reluctantly.) John, I love you. Will you marry me?
John: Oh, Marsha, I love you too, but . . . there’s something you must know about me—something I’ve never told anyone.
Marsha: (concerned) John, what is it?
John: I think I’m a closet indexer.
Marsha: What? Why?
John: My returns always seem to track the S&P 500 market index. Sometimes I do a little better, occasionally a little worse. But the correlation between my returns and the market returns is over 90%.

Marsha: What’s wrong with that? Your client wants a diversified of large-cap Of course your will follow the market.

John: Why doesn’t my client just buy an index fund? Why is he paying me? Am I really adding value by active management? I try, but I guess I’m just an . . . indexer.

Marsha: Oh, John, I know you’re adding value. You were a star security analyst. John: It’s not easy to find that are truly over- or undervalued. I have firm opinions about a few, of course.

Marsha: You were explaining why Pioneer Gypsum is a good buy. And you’re bullish on Global Mining.

John: Right, Pioneer. (Pulls handwritten notes from his coat pocket.) Stock price $87.50. I estimate the expected return as 11% with an annual standard deviation of 32%. That’s twice the market standard deviation of 16%.

Marsha: Only 11%? You’re forecasting a market return of 12.5%.

John: Yes, I’m using a market risk premium of 7.5% and the risk-free interest rate is about 5%. That gives 12.5%. But Pioneer’s beta is only .65. I was going to buy 30,000 shares this morning, but I lost my nerve. I’ve got to stay diversified.

Marsha: Have you tried modern theory?
John: MPT? Not practical. Looks great in textbooks, where they show efficient frontiers with 5 or 10 But I choose from hundreds, maybe thousands, of Where do I get the inputs for 1,000 That’s a million variances and covariances!

Marsha: Actually only about 500,000, dear. The covariances above the diagonal are the same as the covariances below. But you’re right, most of the estimates would be out-of-date or just garbage.

John: To say nothing about the expected returns. Garbage in, garbage out.

Marsha: But John, you don’t need to solve for 1,000 weights. You only need a handful. Here’s the trick: Take your benchmark, the S&P 500, as security 1. That’s what you would end up with as an indexer. Then consider a few securities you really know something about. Pioneer could be security 2, for example. Global, security 3. And so on. Then you could put your wonderful financial mind to work.

John: I get it: Active management means selling off some of the benchmark and investing the proceeds in specific like Pioneer. But how do I decide whether Pioneer really improves the Even if it does, how much should I buy?

Marsha: Just maximize the Sharpe ratio, dear.

John: I’ve got it! The answer is yes!

Marsha: What’s the question?

John: You asked me to marry you. The answer is yes. Where should we go on our honeymoon?

Marsha: How about Australia? I’d love to visit the Sydney Futures Exchange.

1. Table 8.4 reproduces John’s notes on Pioneer Gypsum and Global Mining. Calculate the expected return, risk premium, and standard deviation of a invested partly in the market and partly in Pioneer. (You can calculate the necessary inputs from the betas and standard deviations given in the table. Hint: A beta equals its covariance with the market return divided by the variance of the market return.) Does adding Pioneer to the market benchmark improve the Sharpe ratio? How much should John invest in Pioneer and how much in the market?

2. Repeat the analysis for Global Mining. What should John do in this case? Assume that Global accounts for .75% of the S&P index.

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1. Calculate the NPV of the wildcat oil well, taking

1. Calculate the NPV of the wildcat oil well, taking account of the probability of a dry hole, the shipping costs, the decline in production, and the forecasted increase in oil prices. How long does production have to continue for the well to be a positive-NPV investment? Ignore taxes and other possible complications.

2. Now consider operating leverage. How should the shipping costs be valued, assuming that output is known and the costs are fixed? How would your answer change if the shipping costs were proportional to output? Assume that unexpected fluctuations in output are zero-beta and diversifiable. (Hint: The Jones’s oil company has an excellent credit rating. Its long-term borrowing rate is only 7%.)

The Scene: It is early evening in the summer of 2018, in an ordinary family room in Manhattan. Modern furniture, with old copies of The Wall Street Journal and the Financial Times scattered around. Autographed photos of Jerome Powell and George Soros are prominently displayed.

A picture window reveals a distant view of lights on the Hudson River. John Jones sits at a computer terminal, glumly sipping a glass of chardonnay and putting on a carry trade in Japanese yen over the Internet. His wife Marsha enters.

Marsha: Hi, honey. Glad to be home. Lousy day on the trading floor, though. Dullsville. No volume. But I did manage to hedge next year’s production from our copper mine. I couldn’t get a good quote on the right package of futures contracts, so I arranged a commodity swap.

John doesn’t reply.

Marsha: John, what’s wrong? Have you been selling yen again? That’s been a losing trade for weeks.

John: Well, yes. I shouldn’t have gone to Goldman Sachs’s foreign exchange brunch. But I’ve got to get out of the house somehow. I’m cooped up here all day calculating covariances and efficient risk-return trade-offs while you’re out trading commodity futures. You get all the glamour and excitement.

Marsha: Don’t worry, dear, it will be over soon. We only recalculate our most efficient once a quarter. Then you can go back to leveraged leases.

John: You trade, and I do all the worrying. Now there’s a rumor that our leasing company is going to get a hostile takeover bid. I knew the debt ratio was too low, and you forgot to put on the poison pill. And now you’ve made a negative-NPV investment!

Marsha: What investment?

John: That wildcat oil well. Another well in that old Sourdough field. It’s going to cost $5 million! Is there any oil down there?

Marsha: That Sourdough field has been good to us, John. Where do you think we got the capital for your yen trades? I bet we’ll find oil. Our geologists say there’s only a 30% chance of a dry hole.

John: Even if we hit oil, I bet we’ll only get 75 barrels of crude oil per day.

Marsha: That’s 75 barrels day in, day out. There are 365 days in a year, dear.

John and Marsha’s teenage son Johnny bursts into the room.

Johnny: Hi, Dad! Hi, Mom! Guess what? I’ve made the junior varsity derivatives team! That means I can go on the field trip to the Chicago Board Options Exchange. (Pauses.) What’s wrong?

John: Your mother has made another negative-NPV investment. A wildcat oil well, way up on the North Slope of Alaska.

Johnny: That’s OK, Dad. Mom told me about it. I was going to do an NPV calculation yesterday, but I had to finish calculating the junk-bond default probabilities for my corporate finance homework. (Grabs a financial calculator from his backpack.) Let’s see: 75 barrels a day times 365 days per year times $100 per barrel when delivered in Los Angeles . . . that’s $2.7 million per year.

John: That’s $2.7 million next year, assuming that we find any oil at all. The production will start declining by 5% every year. And we still have to pay $20 per barrel in pipeline and tanker charges to ship the oil from the North Slope to Los Angeles. We’ve got some serious operating leverage here.

Marsha: On the other hand, our energy consultants project increasing oil prices. If they increase with inflation, price per barrel should increase by roughly 2.5% per year. The wells ought to be able to keep pumping for at least 15 years.

Johnny: I’ll calculate NPV after I finish with the default probabilities. The interest rate is 6%.

Is it OK if I work with the beta of .8 and our usual figure of 7% for the market risk premium?

Marsha: I guess so, Johnny. But I am concerned about the fixed shipping costs.

John: (Takes a deep breath and stands up.) Anyway, how about a nice family dinner? I’ve reserved our usual table at the Four Seasons.

Everyone exits.

Announcer: Is the wildcat well really negative-NPV? Will John and Marsha have to fight a hostile takeover? Will Johnny’s derivatives team use Black–Scholes or the binomial method? Find out in the next episode of The Jones Family Incorporated.

You may not aspire to the Jones family’s way of life, but you will learn about all their activities, from futures contracts to binomial option pricing, later in this book. Meanwhile, you may wish to replicate Johnny’s NPV analysis.

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Suppose that in year 2030, investors become much more willing

Suppose that in year 2030, investors become much more willing than before to bear risk. As a result, they require a return of 8% to invest in common rather than the 10% that they had required in the past. This shift in risk aversion causes a 15% change in the value of the market portfolio.

a. Do stock prices rise by 15% or fall?

b. If you now use past returns to estimate the expected risk premium, will the inclusion of data for 2030 cause you to underestimate or overestimate the return that investors required in the past?

c. Will the inclusion of data for 2030 cause you to underestimate or overestimate the return that investors require in the future?

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The Cambridge Opera Association has come up with a unique

The Cambridge Opera Association has come up with a unique door prize for its December 2019 fund-raising ball: Twenty door prizes will be distributed, each one a ticket entitling the bearer to receive a cash award from the association on December 31, 2020.

The cash award is to be determined by calculating the ratio of the level of the Standard and Poor’s Composite Index of stock prices on December 31, 2020, to its level on June 30, 2020, and multiplying by $100. Thus, if the index turns out to be 1,000 on June 30, 2020, and 1,200 on December 31, 2020, the payoff will be 100 × (1,200/1,000) = $120.

After the ball, a black market springs up in which the tickets are traded. What will the tickets sell for on January 1, 2020? On June 30, 2020? Assume the risk-free interest rate is 10% per year. Also assume the Cambridge Opera Association will be solvent at year-end 2020 and will, in fact, pay off on the tickets. Make other assumptions as necessary.

Would ticket values be different if the tickets’ payoffs depended on the Dow Jones Industrial Index rather than the Standard and Poor’s Composite?

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Integrated Potato Chips (IPC) does not pay a dividend. Its

Integrated Potato Chips (IPC) does not pay a dividend. Its current stock price is $150 and there is an equal probability that the return over the coming year will be –10%, +20%, or +50%.

a. What is the expected price at year-end?

b. If the probabilities of future returns remain unchanged and you could observe the returns of IPC over a large number of years, what would be the (arithmetic) average return?

c. If you were to discount IPC’s expected price at year-end from part (a) by this number, would you underestimate, overestimate, or correctly estimate the stock’s present value?

d. If you could observe the returns of IPC over a large number of years, what would be the compound (geometric average) rate of return?

e. If you were to discount IPC’s expected price at year-end from part (a) by this number, would you underestimate, overestimate, or correctly estimate the stock’s present value?

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Consider the following two projects:a. If the opportunity cost of

Consider the following two projects:

a. If the opportunity is 11%, which of these two projects would you accept (A, B, or both)?

b. Suppose that you can choose only one of these two projects. Which would you choose? The is still 11%.

c. Which one would you choose if the is 16%?

d. What is the of each project?

e. Is the project with the shortest also the one with the highest NPV?

f. What are the internal rates of return on the two projects?

g. Does the IRR rule in this case give the same answer as NPV?

h. If the opportunity is 11%, what is the profitability index for each project? Is the project with the highest profitability index also the one with the highest NPV? Which measure should you use to choose between the projects?

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Phoenix Corp. faltered in the recent recession but is recovering.

Phoenix Corp. faltered in the recent recession but is recovering. Free cash flow has grown rapidly. Forecasts made in 2019 are as follows:

Phoenix’s recovery will be complete by 2024, and there will be no further growth in net income or free cash flow.

a. Calculate the PV of free cash flow, assuming a of 9%.

b. Assume that Phoenix has 12 million shares outstanding. What is the price per share?

c. Confirm that the expected rate of return on Phoenix stock is exactly 9% in each of the years from 2020 to 2024.

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