Solutions to Practice Problems – Chapters 11, 12, 13
1 a) The price of gold today is $330 per troy ounce and the required return for gold is 10%; if we expect to produce 200 troy ounces of gold one year from now, the PV of that future production is $60,000. F Today's price is the PV of the future price (at any point in the future); So the PV of this future production is simply 330*200 = 66,000.b) The reason that today's gold price represents the PV of gold produced on any future date is that gold is a risky asset that pays no dividends. T Whenever there are no dividends, the price is expected to appreciate at a rate equal to the required return [E(Pt) = P0(1+r)t]; this makes the PV today of any future price equal to today's price.
c) If a project really has a positive NPV for you, there must be an economic reason for you to be able to use the assets more efficiently than others. T You will have a positive NPV only if you can generate higher-valued cashflows than than others, which is what is meant by using assets more efficiently.
d) If you can use a given set of assets more efficiently than others, this means the assets have a lower cost to you than they have to others. F Cost is the same for everyone; more efficient use implies a higher value, not a lower cost.
e) Managers will not always make investment decisions the way stockholders want them to; sometimes they may reject positive NPV projects, and sometimes they may accept negative NPV projects. T They may reject positive NPV projects with high bankruptcy risk; they may accept large projects with slightly negative NPV.
f) The risk of a project going bankrupt is part of the project's systematic risk so it's accounted for in the NPV computation; if a project has positive NPV despite a high probability of bankruptcy, stockholders want the project to be accepted. F The risk of going bankrupt is related to total risk, not systematic risk. (The second part of the statement is true though.)
g) Stockholders and managers have different attitudes to the risk of bankruptcy, since stockholders can diversify away the risk but managers cannot. T For stockholders it is only one firm in their portfolio being affected, but managers do not hold a portfolio of jobs. Their entire market value as managers is negatively affected.
h) Between the threat of being fired and the incentives provided to managers to act in the interests of stockholders, the potential agency problems relating to the investment decision disappear. F These two mechanism may reduce the size and scope of the problem, but they don't solve the problem completely, they don't make it disappear.
i) The term "economic rent" means the amount that must be charged for use of an asset each year, such that the PV of the rents equals the cost of purchasing the asset today. F It means excess profits (in excess of the opportunity cost of capital). In other words, economic rents are the source of positive NPV. (See the top of page 293.)
j) One problem in capital budgeting is that some investments do not show up in the capital budget. T Expenditures on Information Technology or R&D and even some marketing expenses represent long-term investments that typically do not show up in capital budgets.
k) A firm with many divisions should circulate consensus forecasts of the economy so that different divisions do not make inconsistent forecasts of the same variables. T If all divisions do not operate on a level playing field in this way, the division with the most attractive projects will be the division that got away with making the most optimistic assumptions.
2 a) The statement that "prices follow a random walk" means that "today's price is uncorrelated with yesterday's price". F After all, yesterday's closing price is today's opening price, so today's price has to be related to yesterday's. "Prices follow a random walk" means that "today's price change is uncorrelated with yesterday's price change". A small but important difference.
b) If prices follow a random walk, the concepts of a bull market (one in which prices are expected to keep increasing) or a bear market (one in which they are expected to keep decreasing) make no sense. T Whether prices have been increasing in the recent past or decreasing tells us nothing about how they will behave in the future.
c) In practice, price changes are not totally random; positive price changes are more likely than negative price changes. T Because stocks have a positive expected return, prices will tend to increase over time. Increases will be more frequent than decreases. That's why we say prices follow a random walk with drift.
d) It makes sense for prices to follow a random walk; any predictable patterns that might have existed have to automatically disappear they moment they are recognized and exploited. T If there is a predictable increase, investors will rush to buy, pushing up the price to the point where the expected return just equals the required return. There is no predictable pattern left, over and above the positive drift from the expected return. Actual return will be randomly higher or lower than the required return.
e) If investors can use information about past prices to predict future returns, this means the market is not semi-strong form efficient. T This is part of public information. In a semi-strong-form efficient market, investors should not be able to use it to predict future returns. (In this situation, the market is neither weak-form efficient nor semi-strong-form efficient.)
f) Only a perfectly functioning market can be strong-form efficient. F The best a perfectly functioning market can achieve is to have the price properly reflect all the information available to it. Inside information is not available to the market, so it cannot be reflected in the price even if the market is functioning with perfect efficiency.
g) In an event study, the key evidence of market efficiency is that there should be no systematic increase or decrease in CAR before the announcement. F Due to leakage of inside information, CAR will typically increase before a good news announcement and decrease before a bad news announcement. The key evidence of market efficiency is that there should be no systematic increase or decrease in CAR after the initial reaction to the announcement. In other words, investors buying or short-selling after the announcement (once the news has become public information) should not be able profit from a predictable pattern in the price.
h) Ultimately, at a pragmatic level, when we judge whether a market if efficient or not, what matters is not whether mis-pricing exists but whether it can be identified and exploited. T If investors cannot identify and exploit mis-pricing, it makes no difference to them whether it exists. As far as they are concerned, it is just as if mis-pricing does not exist. To them, returns seem to follow a random walk and cannot be predicted.
i) If a company wants to issue shares and its stock price has fallen over the last few days, it is better for them to wait rather than issue the shares right away. F Once the price has fallen, it's fallen. It's not more likely to increase than decrease from today's level, so there is no sense in which waiting is better than issuing right away.
j) Although stock splits should have no impact of the wealth of stockholders, event studies find that when firms announce stock splits the market treats the announcements as good news. T Announcements of splits do result in positive abnormal returns, but it turns out that the market is reacting not to the split itself but to the accompanying news about future dividends.
k) Even though investors desire diversification, they will still not pay more for firms that provide diversification by merging. T Since they can easily diversify on their own, there is no reason why they'll be willing to pay a higher price for two firms that merge to offer diversification.
l) If a market is semi-strong form efficient, it must also be weak form efficient. T: If it is semi-strong form efficient, then all public information is fully reflected in prices. Since past price information is part of public information, past price information is also fully reflected in prices. Hence markets are also weak form efficient.