This Document Contains Chapters 13 to 15 Chapter 13 Efficient Capital Markets and Behavioral Finance 1. To create value, firms should accept financing proposals with positive net present values. Firms can create valuable financing opportunities in three ways: 1) Fool investors. A firm can issue a complex security to receive more than the fair market value. Financial managers attempt to package securities to receive the greatest value. 2) Reduce costs or increase subsidies. A firm can package securities to reduce taxes. Such a security will increase the value of the firm. In addition, financing techniques involve many costs, such as accountants, lawyers, and investment bankers. Packaging securities in a way to reduce these costs will also increase the value of the firm. 3) Create a new security. A previously unsatisfied investor may pay extra for a specialized security catering to his or her needs. Corporations gain from developing unique securities by issuing these securities at premium prices. 2. The three conditions that are necessary for efficient markets are a) Rationality, b) Independent deviations from rationality, and c) Arbitrage. A detailed description of each condition together with an example is given in Section 13.2 of the textbook. 3. The three forms of the efficient markets hypothesis are: 1) Weak form. Market prices reflect information contained in historical prices. Investors are unable to earn abnormal returns using historical prices to predict future price movements. 2) Semi-strong form. In addition to historical data, market prices reflect all publicly-available information. Investors with insider, or private information, are able to earn abnormal returns. 3) Strong form. Market prices reflect all information, public or private. Investors are unable to earn abnormal returns using insider information or historical prices to predict future price movements. On average, the only return that is earned is the required return—investors buy assets with returns in excess of the required return (positive NPV), bidding up the price and thus causing the return to fall to the required return (zero NPV); investors sell assets with returns less than the required return (negative NPV), driving the price lower and thus causing the return to rise to the required return (zero NPV). 4. The market is not weak form efficient. 5. Behavioural finance argues that the three conditions that underpin efficient market theory are so often violated that they are not valid for all intents and purposes. The theory argues that investors are not rational, that investors can act irrationally for long periods of time and that arbitrage is not possible because no trader has infinite wealth to take infinite bets on mispricing. 6. There have been many deviations from market efficiency recorded in recent history. These are detailed in section 13.6 of the textbook. However, the main ones are a) the continued existence of arbitrage possibilities, b) post earnings announcement drift, c) the size anomaly, d) the book to market anomaly, and most recently, e) irrational stock market bubbles and crashes. This Document Contains Chapters 13 to 15 7. This question gets the student to develop their own viewpoint and argue for a particular theory. As such, there is no correct solution to this question. 8. There is a detailed discussion in Section 13.8 of the textbook. The main issues that need to be considered in this context are a) using discretion in financial reporting, b) how managers time information and corporate events, c) should corporations speculate on market conditions and make decisions on this basis? And d) should decisions be made on the basis of market prices and their recent changes? 9. a. False. Market efficiency implies that prices reflect all available information, but it does not imply certain knowledge. Many pieces of information that are available and reflected in prices are fairly uncertain. Efficiency of markets does not eliminate that uncertainty and therefore does not imply perfect forecasting ability. b. True. Market efficiency exists when prices reflect all available information. To be efficient in the weak form, the market must incorporate all historical data into prices. Under the semi-strong form of the hypothesis, the market incorporates all publicly-available information in addition to the historical data. In strong form efficient markets, prices reflect all publicly and privately available information. c. False. Market efficiency implies that market participants are rational. Rational people will immediately act upon new information and will bid prices up or down to reflect that information. d. False. In efficient markets, prices reflect all available information. Thus, prices will fluctuate whenever new information becomes available. e. True. Competition among investors results in the rapid transmission of new market information. In efficient markets, prices immediately reflect new information as investors bid the stock price up or down. 10. The efficient markets hypothesis would say that, if the market is not weak form efficient, such a strategy could be effective. However, if it was weak form efficient (and consequently, semi- strong and strong form efficient), such a strategy would not earn abnormal returns. Behavioural finance would argue that such a strategy could be effective. Given the breadth of anomalies that behavioural finance captures, there could be any reason given. For example, one could argue that if enough investors follow this strategy, they would create a space for themselves and actually cause prices to change. This would reinforce the power of the strategy. 11. The EMH only says, within the bounds of increasingly strong assumptions about the information processing of investors, that assets are fairly priced. An implication of this is that, on average, the typical market participant cannot earn excessive profits from a particular trading strategy. However, that does not mean that a few particular investors cannot outperform the market over a particular investment horizon. Certain investors who do well for a period of time get a lot of attention from the financial press, but the scores of investors who do not do well over the same period of time generally get considerably less attention from the financial press. Behavioural finance would argue that Buffett’s performance is easily explained using a number of different anomalies. However, the main one is that being an investment guru, his investments gain a lot of media attention. Investors, who have little time to carry out detailed research on investment, would rather free load on his decisions. If enough people do this, their combined investment decisions may actually change prices and force managers to change their behaviour. 12. A technical analyst would argue that the market is not efficient. Since a technical analyst examines past prices, the market cannot be weak form efficient for technical analysis to work. If the market is not weak form efficient, it cannot be efficient under stronger assumptions about the information available. The technical analyst would argue that investors do not have time to analyse all information and so they must follow rules or heuristics to make decisions. This leads to patterns in prices that can be exploited by a technical analyst. 13. There are several behavioural explanations to the pattern. One relates to investor attention. Most investors don’t have time to analyse all information and so they may follow the trading behavior of investors who do have information (i.e. company insiders). If enough people do this, price could change as a result. Alternatively, investors may simply see insider trades as a signal to the market and trade on them without analyzing them fully. 14. A consumer confidence index is used to capture market sentiment. If investors feel good about the economy, it can give investors a signal of where the future market movements may go (i.e. up). If consumer confidence is low, then it may predict market falls. This index can be used as an additional factor in predicting price patterns, just like any other series. Students should choose a country and compare it to the index. You should get students to focus on lead effects and potential lag effects. 15. It is likely the market has a better estimate of the share price, assuming it is semi-strong form efficient. However, semi-strong form efficiency only states that you cannot easily profit from publicly available information. If financial statements are not available, the market can still price shares based upon the available public information, limited though it may be. Therefore, it may have been as difficult to examine the limited public information and make an extra return. 16. a. Kasetsart’s share price should rise immediately after the announcement of the positive news. b. Only scenario (ii) indicates market efficiency. In that case, the share price rises immediately to the level that reflects the new information, eliminating all possibility of abnormal returns. In the other two scenarios, there are periods of time during which an investor could trade on the information and earn abnormal returns. 17. Because there is less trading volume and financial sophistication in emerging markets, it would be expected that they are less efficient and more sensitive to market sentiment. 18. False. The share price would have adjusted before the founder’s death only if investors had perfect forecasting ability. The 12.5 per cent increase in the share price after the founder’s death indicates that either the market did not anticipate the death or that the market had anticipated it imperfectly. However, the market reacted immediately to the new information, implying efficiency. It is interesting that the share price rose after the announcement of the founder’s death. This price behavior indicates that the market felt he was a liability to the firm. 19. The market is often considered to be relatively efficient up to the semi-strong form. If so, no systematic profit can be made by trading on publicly-available information. Although illegal, the lead engineer of the device can profit from purchasing the firm’s equity before the news release on the implementation of the new technology. The price should immediately and fully adjust to the new information in the article. Thus, no abnormal return can be expected from purchasing after the publication of the article. 20. Under the semi-strong form of market efficiency, the share price should stay the same. The accounting system changes are publicly available information. Investors would identify no changes in either the firm’s current or its future cash flows. Thus, the share price will not change after the announcement of increased earnings. 21. Because the number of subscribers has increased dramatically, the time it takes for information in the newsletter to be reflected in prices has shortened. With shorter adjustment periods, it becomes impossible to earn abnormal returns with the information provided by Durkin. If Durkin is using only publicly-available information in its newsletter, its ability to pick equities is inconsistent with the efficient markets hypothesis. Under the semi-strong form of market efficiency, all publicly-available information should be reflected in share prices. The use of private information for trading purposes is illegal. 22. You should not agree with your broker. The performance ratings of the small manufacturing firms were published and became public information. Prices should adjust immediately to the information, thus preventing future abnormal returns. 23. Assuming market efficiency, share prices should immediately and fully rise to reflect the announcement. Thus, one cannot expect abnormal returns following the announcement. Assuming behavioural finance is true, it is possible that enough investors will believe the financial economist and buy equities en masse. This would result in price increases, reinforcing the financial economist’s statement. 24. a. No. Earnings information is in the public domain and reflected in the current share price. b. No. If the rumours were publicly disseminated, the prices would have already adjusted for the possibility of a merger. If the rumour is information, insiders would have already traded on the information and prices would have adjusted (this is illegal). c. No. The information is already public, and thus, already reflected in the share price. 25. Serial correlation occurs when the current value of a variable is related to the future value of the variable. If the market is efficient, the information about the serial correlation in the macroeconomic variable and its relationship to net earnings should already be reflected in the stock price. In other words, although there is serial correlation in the variable, there will not be serial correlation in equity returns. Therefore, knowledge of the correlation in the macroeconomic variable will not lead to abnormal returns for investors. 26. The statement is false because every investor has a different risk preference. Although the expected return from every well-diversified portfolio is the same after adjusting for risk, investors still need to choose funds that are consistent with their particular risk level. 27. The share price will decrease immediately to reflect the new information. At the time of the announcement, the share price should immediately decrease to reflect the negative information. 28. In an efficient market, the cumulative abnormal return (CAR) for Prospectors would rise substantially at the announcement of a new discovery. The CAR falls slightly on any day when no discovery is announced. There is a small positive probability that there will be a discovery on any given day. If there is no discovery on a particular day, the price should fall slightly because the good event did not occur. The substantial price increases on the rare days of discovery should balance the small declines on the other days, leaving CARs that are horizontal over time. 29. Behavioral finance attempts to explain both these events by changes in investor sentiment and psychology. These changes can lead to non-random price behaviour. 30. It is evidence of both. If financial institutions believe that share prices are low because of managerial performance or decisions, they can use a media strategy to get investors to force the managers to change their behaviour and decisions. Prices will then increase in response to changes in managerial decisions. However, it also means that financial institutions believe that investors read newspapers and the media can change their views. This will only happen if investors have limited attention and focus only on headlines stories such as an activism event. 31. A number of explanations can be given and students should be encourage to discuss these. However, it probably means that the management of the new firm is responding to the collective intelligence of the market and changing their behaviour as a result. 32. Both. It may mean that prices have changed as a result of new information (the insider transaction) or they have traded because investors are simply following the insider without analysing the information based on the trade. 33. To find the cumulative abnormal returns, we chart the abnormal returns for each of the three airlines for the days preceding and following the announcement. . The abnormal return is calculated by subtracting the market return from an equity’s return on a particular day, Ri – RM. Group the returns by the number of days before or after the announcement for each respective airline. Calculate the cumulative average abnormal return by adding each abnormal return to the previous day’s cumulative abnormal return. Abnormal returns (Ri – RM) Days from announcement National Airlines Group Air France- KLM Lufthansa Sum Average abnormal return Cumulative average return –4 –0.2 –0.2 –0.2 –0.6 –0.2 –0.2 –3 0.2 –0.1 0.2 0.3 0.1 –0.1 –2 0.2 –0.2 0.0 0.0 0.0 –0.1 –1 0.2 0.2 –0.4 0.0 0.0 –0.1 0 3.3 0.2 1.9 5.4 1.8 1.7 1 0.2 0.1 0.0 0.3 0.1 1.8 2 –0.1 0.0 0.1 0.0 0.0 1.8 3 –0.2 0.1 –0.2 –0.3 –0.1 1.7 4 –0.1 –0.1 –0.1 –0.3 –0.1 1.6 The market reacts favourably to the announcements. Moreover, the market reacts only on the day of the announcement. Before and after the event, the cumulative abnormal returns are relatively flat. This behaviour is consistent with market efficiency. 34. The diagram does not support the efficient markets hypothesis. The CAR should remain relatively flat following the announcements. The diagram reveals that the CAR rose in the first month, only to drift down to lower levels during later months. Such movement violates the semi-strong form of the efficient markets hypothesis because an investor could earn abnormal profits while the stock price gradually decreased. 35. a. Supports. The CAR remained constant after the event at time 0. This result is consistent with market efficiency, because prices adjust immediately to reflect the new information. Drops in CAR prior to an event can easily occur in an efficient capital market. For example, consider a sample of forced removals of the CEO. Since any CEO is more likely to be fired following bad rather than good share price performance, CARs are likely to be negative prior to removal. Because the firing of the CEO is announced at time 0, one cannot use this information to trade profitably before the announcement. Thus, price drops prior to an event are neither consistent nor inconsistent with the efficient markets hypothesis. Cumulative Abnormal Returns -0.2 -0.1 -0.1 -0.1 1.7 1.8 1.8 1.7 1.6 -0.5 0 0.5 1 1.5 2 -4 -3 -2 -1 0 1 2 3 4 Days from announcement CAR b. Rejects. Because the CAR increases after the event date, one can profit by buying after the event. This possibility is inconsistent with the efficient markets hypothesis. c. Supports. The CAR does not fluctuate after the announcement at time 0. While the CAR was rising before the event, insider information would be needed for profitable trading. Thus, the graph is consistent with the semi-strong form of efficient markets. d. Supports. The diagram indicates that the information announced at time 0 was of no value. There appears to be a slight drop in the CAR prior to the event day. Similar to part a, such movement is neither consistent nor inconsistent with the efficient markets hypothesis (EMH). Movements at the event date are neither consistent nor inconsistent with the efficient markets hypothesis. 36. Once the verdict is reached, the diagram shows that the CAR continues to decline after the court decision, allowing investors to earn abnormal returns. The CAR should remain constant on average, even if an appeal is in progress, because no new information about the company is being revealed. Thus, the diagram is not consistent with the efficient markets hypothesis (EMH). Chapter 13 case study Your Retirement Account at West Coast Yachts 1. Before the fact, you would expect that mutual funds managers would be able to outperform the market. This is due, in part, to the Darwinian nature of the business. Good performing fund managers are richly rewarded, and poor performing fund managers are fired, often very quickly. In reality, we should expect that less than 50 percent of all equity mutual funds would outperform the market. This does not depend on the level of market efficiency. Consider the following question: What percentage of investors will outperform the market in a given year? Answer: Fifty percent. While there could be one really poor investor who takes all of the losses in a given year, in general, to get the market average we would expect one-half of investors would outperform the market, and one-half would underperform the market. After all, the market average return has to be the average return of all investors’ average return. This is definitely true if we consider the weighted average return, that is, the average return of investors weighted by the dollar amount of the investment. We would expect more than 50 percent of mutual funds would underperform the market because of the expenses charged by the mutual funds. Consider the large-cap stock fund, with and expense ratio of 1.50 percent. The fund must exceed the market return by 1.50 percent before fees in order to achieve a return after fees equal to the market return. Whether the market is efficient or inefficient is irrelevant unless mutual funds managers are the best investors in the market, and all other investors, including private money managers, pension fund managers, individuals, etc. are the bad investors in the market. We should also consider that mutual funds managers may be able to outperform the market before expenses. Whether they can outperform the market on an after-expense basis becomes a question of whether mutual fund managers can extract economic rents from the stock market. The evidence tends to support the idea that they cannot. In general, research has found that mutual fund managers underperform the market after expenses by the average expense ratio. This means that mutual funds as a whole tend to have the market average return before expenses, so they do not appear to be able to outperform the market. 2. The results in the graph tend to support the idea of market efficiency. Consider the case of the Fidelity Magellan Fund, one of the largest actively managed equity mutual funds at the time this was written. The total assets of the fund at the time this was written was about $55 billion. So the question is this: What would Fidelity pay for one year to increase the return of the Magellan Fund by 0.01 percent? If we multiply the fund assets by 0.01 percent, we get: $55,000,000,000(.0001) = $5,500,000. So, if Fidelity can increase the return of this one fund by only 0.01 percent per year, it should be willing to pay up to $5.5 million for that year. Given the amount mutual fund companies would be willing to spend for research, and the Darwinian nature of the industry, we would expect that mutual fund managers should be able to outperform the market. While there have been notable exceptions, such as Peter Lynch’s tenure at Magellan, as a whole, mutual fund managers do not seem to be able to outperform the market. As a result, if the “best” and definitely best-financed investors cannot outperform the market, the results support the concept of market efficiency. 3. Given that the evidence presented tends to support market efficiency, you should invest in the Market index fund. However, this is not the entire answer. By investing the entire equity portion of your account in the Market index, your portfolio is not diversified since the Market index includes only large-cap stocks. Therefore, part of your equity investment should probably be in the small cap fund for diversification purposes. Note that a small cap index fund may be the best option, but there is no small cap fund available in the Retirement account. Chapter 14 Long-Term Financing 1. Cash flow rights refer to the cash claim on each share. So, for example, if a company pays a £.06 dividend per share, a share holder with 10,000 shares will receive £600 in dividends. Voting rights refer to the number of votes the shareholder receives at an AGM. If the shareholder in the previous example had 1 vote for every two shares, she would have 5,000 votes. In this example, the cash flow rights are greater than the voting rights. 2. Bonds have different characteristics because of different risk. In addition, companies may wish to issue a bond overseas in a different currency because the appetite for purchasing the bond is greater overseas. 3. Some firms can benefit from issuing preference shares. The reasons can be: a. Firms reporting losses to the tax authorities already don’t have positive income for any tax deductions, so they are not affected by the tax disadvantage of dividends versus interest payments. They may be willing to issue preference shares. b. Firms that issue preference shares can avoid the threat of bankruptcy that exists with debt financing because preference shares are not a legal obligation like interest payments on corporate debt. 4. International differences in long-term financing may relate to how dominant banks or financial markets are in the country, as well as the appetite for different forms of capital in various countries. In addition, religious differences may lead to different patterns of financing. 5. Hierarchies exist in long-term financing because it is necessary to ensure that debt holders have first claim over the assets of a distressed firm. Given that firms have several debt issues; these have to be prioritised in terms of seniority. 6. Islamic financing shies away from the charge or receipt of interest on money. 7. The return on non-convertible preference shares is lower than the return on corporate bonds for one main reason: Issuing corporations are willing and able to offer higher returns on debt since the interest on the debt reduces their tax liabilities. Preferred dividends are paid out of net income; hence they provide no tax shield. 8. The following table summarizes the main difference between debt and equity: Debt Equity Repayment is an obligation of the firm Yes No Grants ownership of the firm No Yes Provides a tax shield Yes No Liquidation will result if not paid Yes No Companies often issue hybrid securities because of the potential tax shield and the bankruptcy advantage. If the tax authority accepts the security as debt, the firm can use it as a tax shield. If the security maintains the bankruptcy and ownership advantages of equity, the firm has the best of both worlds. Preference shares are the most common hybrid security. Their fixed dividend is just like a bond coupon and so it has debt features. The fact that non-payment of the fixed dividend does not lead to bankruptcy and it gives ownership in the firm means it is also like equity. 9. The equity value of International Energy plc before the share issue is: Ordinary Shares (100,000 @ £1 par value) £100,000 Retained Earnings £213,000 Equity Value £313,000 After the Issue: Ordinary Shares (125,000 @ £1 par value) £125,000 Additional Paid in Capital (25,000 x (£9 - £1)) £200,000 Retained Earnings £213,000 Equity Value £538,000 So the total par value is £125,000; the additional paid in capital is £200,000; and the Book value per share is (£538,000 / 125,000=) £4.304. 10. The trends in long-term financing in the United Kingdom were presented in the text. If Cable Company follows the trends, it will probably use about 90 percent internal financing – net income of the project plus depreciation less dividends – and 10 percent external financing, long-term debt and equity. 11. Preference shares are similar to both debt and equity. Preference shareholders receive a stated dividend only, and if the corporation is liquidated, preference shareholders get a stated value. However, unpaid preferred dividends are not debts of a company and preferred dividends are not a tax deductible business expense. 12. Leasing is consistent with the principles of Islamic financing because it does not involve making money out of money (interest) and the transaction is directly linked to the underlying asset. 13. A company has to issue more debt to replace the old debt that comes due if the company wants to maintain its capital structure. There is also the possibility that the market value of a company continues to increase (we hope). This also means that to maintain a specific capital structure on a market value basis the company has to issue new debt, since the market value of existing debt generally does not increase as the value of the company increases (at least by not as much). 14. Internal financing comes from internally generated cash flows and does not require issuing securities. In contrast, external financing requires the firm to issue new securities. The three basic factors that affect the decision to raise external financing are: 1) The general economic environment, specifically, business cycles. 2) The level of share prices, and 3) The availability of positive NPV projects. 15. The priority ladder for corporate funding is: 1. Secured debt; 2. Unsecured debt; 3. Preference shares; 4. Equity. If only €50 million can go to the funders of the firm, the €15 million of secured bonds are paid off, the €34 million of unsecured bonds are paid off, and only €1 million of the preference shares are paid off. This will be distributed pro-rata among all the preference shareholders. 16. The best methods would be a Bai’al-inah (sale and buyback) or Ijarah Thumma Al Bai’ (hire purchase). 17. a. The retained earnings is simply the difference between the Total equity value and the sum of par value and additional paid in capital. This is £6,421,830 – (120,000 + 4,526,123) = £1,775,707 b. Since the ordinary shares entry in the balance sheet represents the total par value of the shares, simply divide that by the par per share: Shares outstanding = £120,000 / £0.12 Shares outstanding = 1,000,000 c. Additional Paid in Capital is the amount received over par, so Additional Paid in Capital plus par gives you the £ received. In aggregate, the solution is: Net capital from the sale of shares =Ordinary Shares + Additional Paid in Capital Net capital from the sale of shares = £120,000 + £4,526,123 Net capital from the sale of shares = £4,646,123 Therefore, the average price is: Average price = £4,646,123 / 1,000,000 Average price = £4.65 per share d. The book value per share is the total book value of equity divided by the shares outstanding, or: Book value per share = £6,421,830 / 1,000,000 Book value per share = £6.42 18. a. The ordinary shares outstanding account is the shares outstanding times the par value per share, or: Ordinary shares value = 290,000(Nkr2) Ordinary shares value = Nkr580,000 So, the total equity account is: Total equity = £580,000 + £1,150,000 + £750,000 Total equity = £2,480,000 b. The Additional Paid in Capital on the sale of the new shares is the price per share above par times the shares sold, or: Additional Paid in Capital on sale = (Nkr20 – Nkr2)(50,000) Additional Paid in Capital on sale = Nkr900,000 So, the new equity accounts will be: Ordinary Shares, Nkr2 par value 340,000 shares outstanding Nkr680,000 Additional Paid in Capital 2,050,000 Retained earnings 750,000 Total Nkr3,480,000 19. a. First, we will find the Ordinary Share account value, which is the shares outstanding times the par value, or: Ordinary Shares = 410,000(£5) Ordinary Shares = £2,050,000 The Additional Paid in Capital account is the amount paid for the shares over par value. Since the equity was sold at an average premium of 30 percent to par value, the average share price when sold was: Average share price when sold = £5(1.30) Average share price = £6.50 So, the Additional Paid in Capital is: Additional Paid in Capital = (Average sale price – Par)(Number of shares) Additional Paid in Capital = (£6.50 – £5)(410,000) Additional Paid in Capital = £615,000 And the new retained earnings balance will be: Retained earnings = Previous retained earnings + Net income – Dividends Retained earnings = £3,545,000 + £650,000 – (£650,000)(0.30) Retained earnings = £4,000,000 So, the equity accounts will be: Ordinary Shares, £5 par value £2,050,000 Additional Paid in Capital 615,000 Retained earnings 4,000,000 Total £6,665,000 b. The accounts that will change are the Ordinary Shares account and Additional Paid in Capital account. The new Ordinary Share account is: Ordinary Shares, £5 par value = 435,000 shares x £5 = £2,175,000 The new Additional Paid in Capital will be: Additional Paid in Capital = Previous Additional Paid in Capital, + Additional Capital from sale of new issues Additional Paid in Capital = £615,000 + (Sales price – Par value)(Number of shares sold) Additional Paid in Capital = £615,000 + (£4 – £5)(25,000) Additional Paid in Capital = £590,000 Note that because the equity was sold for less than par value, the additional paid in capital from the sale of the equity is negative. So, the new equity accounts will be: Ordinary Shares, £5 par value £2,175,000 Additional Paid in Capital 590,000 Retained earnings 4,000,000 Total £6,765,000 20. If the company uses straight voting, the board of directors is elected one at a time. You will need to own one-half of the shares, plus one share, in order to guarantee enough votes to win the election. So, the number of shares needed to guarantee election under straight voting will be: Shares needed = (500,000 shares / 2) + 1 Shares needed = 250,001 And the total cost to you will be the shares needed times the price per share, or: Total cost = 250,001 £34 Total cost = £8,500,034 If the company uses cumulative voting, the board of directors are all elected at once. You will need 1/(N + 1) percent of the shares (plus one share) to guarantee election, where N is the number of seats up for election. So, the percentage of the company’s equity you need is: Per cent of shares needed = 1/(N + 1) Per cent of shares needed = 1 / (7 + 1) Per cent of shares needed = .1250 or 12.50% So, the number of shares you need to purchase is: Number of shares to purchase = (500,000 × .1250) + 1 Number of shares to purchase = 62,501 And the total cost to you will be the shares needed times the price per share, or: Total cost = 62,501 £34 Total cost = £2,125,034 21. The Murabaha contract requires an asset on which to frame the funding. In this example, your division would require such an asset before it could enter the Murabaha contract. If the company needs £6 billion Bahrain Dinari to buy the warehouse, then your division would buy it from the seller and then sell the asset for an amount that is competitive with Western loans. In this example, the company wishes to pay for the asset in 10 equal instalments. So, your company would first compare the rates with Western rates. r = 8% T = 10 years PV = 6 billion Bahrain Dinari C = PV/PVIFA8%,10 = BHD894,176,932.18 The total payments are BHD894,176,932.18 x 10 = BHD8,941,769,321.8 This would be the amount for which your division would sell the warehouse to the company and require annual payments of BHD894,176,932.18. 22. First you must determine what a Western bank would request in payments. The quoted rate is 12%, so this means that the monthly rate of interest is 1%. The term is 60 months and the financing amount is 40,000 BHD. C = PV/PVIFA1%,60 = BHD889.78 Total amount paid is 889.78 x 60 = BHD53,386.8 The customer can pay BHD1,000 a month but given that this is more than BHD889.78, your company requests that she pays this amount instead. 23. First estimate what would be paid in a Western loan. PV = €20 billion T = 10 years r = 8% C = PV/PVIFA8%,10 = €2,980,589,773.94 Total payment required is €2,980,589,773.94 x 10 = €29,805,897,739.40 So your division would sell a building to the company for €29,805,897,739.40 to be paid up in ten annual instalments of €2,980,589,773.94. In return, your division would buy the building back and pay €20 billion immediately. 24. The share capital is the original par value times the number of ordinary shares. The share premium and other paid in capital amounts relate to subsequent funding efforts. The two distinct classes of share premium reserve and other paid in capital are because of different share classes. Total paid in capital is the sum of Share Capital, Share Premium Reserve and Other Paid in Capital. 25. Being both shareholder and debt holder reduces the risk of the owner. If the company is successful, the owner can gain from the increase in value of the equity. If the company fails, the owner can protect their investment by owning debt secured on the assets of the company. This type of ownership structure is typical in financially risky companies that have a significant probability of being in financial distress in the future. 26. Clearly, firms wish to raise their profile among potential investors. It is consistent with market efficiency because the firm is using product market advertising to improve information quality relating to its operations and consequently value. If the new information is assessed rationally and valuations respond as a result, the market is efficient. 27. This is a complex question because both debt and equity could be justified. If the family wishes to retain control, they will opt for equity and sold to themselves. However, family capital isn’t available; they may opt for debt to ensure that they still retain control. 28. The funding choice depends on the cost of debt and equity capital, the confidence of the managers that the investment will be successful, and whether the existing shareholders wish to maintain control of the firm. Higher levels of investment mean that the assets could be used as collateral and this could reduce the cost of debt. 29. It is probable that high R&D firms will not receive debt financing because of the risk of not being able to pay the interest and principal in the future. There may also be country differences. Chapter 15 Capital structure: Basic concepts 1. In a world with no taxes, distress costs, or transaction costs, the choice of debt or equity is irrelevant to the value of the firm. In this scenario, the firm is like a pizza. It doesn’t matter how you slice it, you still have a pizza – no more, no less. 2. Section 15.2 goes into this in detail. However, in a world with no taxes, transaction costs or distress costs, any change in capital structure that increases the value of the firm will have a direct impact on the shareholders. Similarly, when the value of the firm decreases, this will hurt both debt holders and shareholders. In a world with frictions (taxes, distress costs, transaction costs), this is not necessarily true. 3. False. A reduction in leverage will decrease both the risk of the equity and its expected return. Modigliani and Miller state that, in the absence of taxes, these two effects exactly cancel each other out and leave the share price and the overall value of the firm unchanged. 4. False. Modigliani-Miller Proposition II (No Taxes) states that the required return on a firm’s equity is positively related to the firm’s debt-equity ratio [RS = R0 + (B/S)(R0 – RB)]. Therefore, any increase in the amount of debt in a firm’s capital structure will increase the required return on the firm’s equity. 5. Section 15.5 covers this in detail. The main impact is that taxes make debt valuable because of the tax shield that comes with debt. In addition, the risk of equity increases as debt increases in the capital structure. These are Propositions I and II of Modigliani & Miller’s theorem. 6. This is covered in Section 15.6. A firm is indifferent between equity and debt when: (1−tC )(1−tS ) =1−tB 7. The question requires the student to develop their own example. The relevant sections in the chapter that this question refers to are 15.3 and 15.4. 8. If the total asset value is £120,000 before the restructuring, the debt and equity values after the restructuring are £60,000 each. The debt to equity ratio is 1 and the debt to assets ratio is 0.5. 9. The table below outlines the income statement for the three states: State 1 2 3 EBIT £8,000 £10,000 £12,000 Interest £6,000 £6,000 £6,000 NI £2,000 £4,000 £6,000 ROE 3.33% 6.67% 10.00% 10. a. A table outlining the income statement for the three possible states of the economy is shown below. The EPS is the net income divided by the 1 billion shares outstanding. The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy. Recession Normal Expansion EBIT 1.024 € 2.56 € 3.33 Interest € 0 € 0 € 0 Taxes € 0 € 0 € 0 NI € 1.024 € 2.560 € 3.328 EPS € 1.024 € 2.560 € 3.328 %EPS -60.00% ––– 30.00% b. If the company undergoes the proposed recapitalization, it will repurchase: Share price = Equity / Shares outstanding Share price = 12.68/1 Share price = €12.68 Shares repurchased = Debt issued / Share price Shares repurchased =€2 billion/€12.68 Shares repurchased = 157,728,707 The interest payment each year under all three scenarios will be: Interest payment = €2 billion(.05) = €100 million The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy under the proposed recapitalization. Recession Normal Expansion EBIT 1.024 2.560 3.328 Interest € 0.1 € 0.1 € 0.1 Taxes € 0 € 0 € 0 NI € 0.924 € 2.460 € 3.228 EPS € 1.097 € 2.921 € 3.832 %EPS -62.44% ––– 31.22% 11. a. A table outlining the income statement with taxes for the three possible states of the economy is shown below. The EPS is the net income divided by the 1 billion shares outstanding. The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy. Recession Normal Expansion EBIT 1.024 2.560 3.328 Interest Taxes € 0.154 € 0.384 € 0.499 NI € 0.87 € 2.18 € 2.83 EPS € 0.870 € 2.176 € 2.829 %EPS -60.00% ––– 30.00% b. A table outlining the income statement with taxes for the three possible states of the economy and assuming the company undertakes the proposed capitalization is shown below. The interest payment and shares repurchased are the same as in part b of Problem 1. Recession Normal Expansion EBIT 1.024 2.560 3.328 Interest € 0.100 € 0.100 € 0.100 Taxes € 0.139 € 0.369 € 0.484 NI € 0.79 € 2.09 € 2.74 EPS € 0.932 € 2.483 € 3.258 %EPS -62.44% ––– 31.22% Notice that the percentage change in EPS is the same both with and without taxes. 12. a. Since the company has a market-to-book ratio of 1.0, the total equity of the firm is equal to the market value of equity. Using the equation for ROE: ROE = NI/1 billion The ROE for each state of the economy under the current capital structure and no taxes is: NI € 1.024 € 2.560 € 3.328 ROE 8.08% 20.19% 26.25% %ROE -60.00% ––– 30.00% The second row shows the percentage change in ROE from the normal economy. b. If the company undertakes the proposed recapitalization, the new equity value will be: Equity = €12.68– 2 = €10.68 billion So, the ROE for each state of the economy is: ROE = NI/€10.68 billion NI € 0.924 € 2.460 € 3.228 ROE 8.65% 23.03% 30.22% %ROE -62.44% ––– 31.22% c. If there are corporate taxes and the company maintains its current capital structure, the ROE is: NI € 0.819 € 2.048 € 2.662 ROE 6.46% 16.15% 21.00% %ROE -60.00% ––– 30.00% If the company undertakes the proposed recapitalization, and there are corporate taxes, the ROE for each state of the economy is: NI € 0.739 € 1.968 € 2.582 ROE 6.92% 18.43% 24.18% %ROE -62.44% ––– 31.22% The percentage change in ROE is the same with or without taxes. 13. a. Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax. The EPS under this capitalization will be: EPS = £459/712 shares EPS = £0.647 Under Plan II, the levered company, EBIT will be reduced by the interest payment. The interest payment is the amount of debt times the interest rate, so: NI = £459 – .05(£1,000) NI = £409 million And the EPS will be: EPS = £409/475 shares EPS = £0.861 Plan II has the higher EPS when EBIT is £459 million. b. Under Plan I, the net income is £80 million and the EPS is: EPS = £80/712 shares EPS = £.112 Under Plan II, the net income is: NI = £80 – .05(£1000) NI = £30 million And the EPS is: EPS = £30/475 shares EPS = £0.063 Plan I has the higher EPS when EBIT is £800 million. c. To find the breakeven EBIT for two different capital structures, we simply set the equations for EPS equal to each other and solve for EBIT. The breakeven EBIT is: EBIT/712 = [EBIT – .05(£1,000)]/475 EBIT = £150.21 million 14. We can find the price per share by dividing the amount of debt used to repurchase shares by the number of shares repurchased. Doing so, we find the share price is: Share price = £1,000/(712 – 475) Share price = £4.219 per share The value of the company under the all-equity plan is: V = £4.219(712 shares) = £3.004 billion And the value of the company under the levered plan is: V = £4.219(475 shares) + £1,000 debt = £3.004 billion 15. a. The income statement for each capitalization plan is: I II All-equity EBIT 370 370 370 Interest 87.78 231 0 NI 282.22 139 370 EPS 0.174 € 0.139 € 0.185 The all-equity Plan has the highest EPS; Plan II has the lowest EPS. b. The breakeven level of EBIT occurs when the capitalization plans result in the same EPS. The EPS is calculated as: EPS = (EBIT – RDD)/Shares outstanding This equation calculates the interest payment (RDD) and subtracts it from the EBIT, which results in the net income. Dividing by the shares outstanding gives us the EPS. For the all- equity capital structure, the interest paid is zero. To find the breakeven EBIT for two different capital structures, we simply set the equations equal to each other and solve for EBIT. The breakeven EBIT between the all-equity capital structure and Plan I is: EBIT/2,000 = [EBIT – .11(798)]/1,620 EBIT = 462 million yuan And the breakeven EBIT between the all-equity capital structure and Plan II is: EBIT/2,000 = [EBIT – .11(2,100)]/1,000 EBIT = 462 million yuan The break-even levels of EBIT are the same because of M&M Proposition I. c. Setting the equations for EPS from Plan I and Plan II equal to each other and solving for EBIT, we get: [EBIT – .11(798)]/1,620 = [EBIT – .11(2,100)]/1,000 EBIT = 462 million yuan This break-even level of EBIT is the same as in part b again because of M&M Proposition I. d. The income statement for each capitalization plan with corporate income taxes is: I II All-equity EBIT 370 370 370 Interest 87.78 231 0 Taxes 70.56 34.75 92.5 NI 211.67 104.25 277.5 EPS 0.131 0.104 0.139 The All-Equity Plan still has the highest EPS; Plan II still has the lowest EPS. We can calculate the EPS as: EPS = [(EBIT – RDD)(1 – tC)]/Shares outstanding This is similar to the equation we used before, except that now we need to account for taxes. Again, the interest expense term is zero in the all-equity capital structure. So, the breakeven EBIT between the all-equity plan and Plan I is: EBIT(1 – .25)/2,000 = [EBIT – .11(798)](1 – .25)/1,620 EBIT = 616 million yuan The breakeven EBIT between the all-equity plan and Plan II is: EBIT(1 – .25)/2,000 = [EBIT – .11(2,100)](1 – .25)/1,000 EBIT = 616 million yuan And the breakeven between Plan I and Plan II is: [EBIT – .11(798)](1 – .25)/1,620 = [EBIT – .11(€2,100)](1 – .25)/1,000 EBIT = 616 million yuan The break-even levels of EBIT do not change because the addition of taxes reduces the income of all three plans by the same percentage; therefore, they do not change relative to one another. 16. To find the value per share under each capitalization plan, we can find the price per share by dividing the amount of debt used to repurchase shares by the number of shares repurchased. So, under Plan I, the value per share is: P = 798/380 shares P = 2.10 yuan per share And under Plan II, the value per share is: P = €2,100/1,000 shares P = 2.10 yuan per share This shows that when there are no corporate taxes, the shareholder does not care about the capital structure decision of the firm. This is M&M Proposition I without taxes. 17. a. The earnings per share are: EPS = £16,000/2,000 shares EPS = £8.00 So, the cash flow to the shareholder is: Cash flow = £8.00(100 shares) Cash flow = £800 b. To determine the cash flow to the shareholder, we need to determine the EPS of the firm under the proposed capital structure. The market value of the firm is: V = £70(2,000) V = £140,000 Under the proposed capital structure, the firm will raise new debt in the amount of: D = 0.40(£140,000) D = £56,000 This means the number of shares repurchased will be: Shares repurchased = £56,000/£70 Shares repurchased = 800 Under the new capital structure, the company will have to make an interest payment on the new debt. The net income with the interest payment will be: NI = £16,000 – .08(£56,000) NI = £11,520 This means the EPS under the new capital structure will be: EPS = £11,520/1,200 shares EPS = £9.60 Since all earnings are paid as dividends, the shareholder will receive: Shareholder cash flow = £9.60(100 shares) Shareholder cash flow = £960 c. To replicate the proposed capital structure, the shareholder should sell 40 percent of their shares, or 40 shares, and lend the proceeds at 8 percent. The shareholder will have an interest cash flow of: Interest cash flow = 40(£70)(.08) Interest cash flow = £224 The shareholder will receive dividend payments on the remaining 60 shares, so the dividends received will be: Dividends received = £9.60(60 shares) Dividends received = £576 The total cash flow for the shareholder under these assumptions will be: Total cash flow = £224 + £576 Total cash flow = £800 This is the same cash flow we calculated in part a. d. The capital structure is irrelevant because shareholders can create their own leverage or unlever the equity to create the payoff they desire, regardless of the capital structure the firm actually chooses. 18. a. The rate of return earned will be the dividend yield. The company has debt, so it must make an interest payment. The net income for the company is: NI = NKr73,000 – .10(NKr300,000) NI = NKr43,000 The investor will receive dividends in proportion to the percentage of the company’s equity they own. The total dividends received by the shareholder will be: Dividends received = NKr43,000(NKr30,000/NKr300,000) Dividends received = NKr4,300 So the return the shareholder expects is: R = NKr4,300/NKr30,000 R = .1433 or 14.33% b. To generate exactly the same cash flows in the other company, the shareholder needs to match the capital structure of ABC. The shareholder should sell all shares in XYZ. This will net NKr30,000. The shareholder should then borrow NKr30,000. This will create an interest cash flow of: Interest cash flow = .10(–NKr30,000) Interest cash flow = –NKr3,000 The investor should then use the proceeds of the equity sale and the loan to buy shares in ABC. The investor will receive dividends in proportion to the percentage of the company’s share they own. The total dividends received by the shareholder will be: Dividends received = NKr73,000(NKr60,000/NKr600,000) Dividends received = NKr7,300 The total cash flow for the shareholder will be: Total cash flow = NKr7,300 – NKr 3,000 Total cash flow = NKr4,300 The shareholders return in this case will be: R = NKr4,300/NKr30,000 R = .1433 or 14.33% c. ABC is an all equity company, so: RE = RA = NKr73,000/NKr600,000 RE = .1217 or 12.17% To find the cost of equity for XYZ, we need to use M&M Proposition II, so: RE = RA + (RA – RD)(D/E)(1 – tC) RE = .1217 + (.1217 – .10)(1)(1) RE = .1433 or 14.33% d. To find the WACC for each company, we need to use the WACC equation: WACC = (E/V)RE + (D/V)RD(1 – tC) So, for ABC, the WACC is: WACC = (1)(.1217) + (0)(.10) WACC = .1217 or 12.17% And for XYZ, the WACC is: WACC = (1/2)(.1433) + (1/2)(.10) WACC = .1217 or 12.17% When there are no corporate taxes, the cost of capital for the firm is unaffected by the capital structure; this is M&M Proposition II without taxes. 19. With no taxes, the value of an unlevered firm is the Net Income divided by the unlevered cost of equity, so: V = EBIT/WACC £35,000,000 = EBIT/.13 EBIT = .13(£35,000,000) EBIT = £4,550,000 20. If there are corporate taxes, the value of an unlevered firm is: VU = EBIT(1 – tC)/RU Using this relationship, we can find EBIT as: £35,000,000 = EBIT(1 – .28)/.13 EBIT = £6,319,444 The WACC remains at 13 percent. Due to taxes, EBIT for an all-equity firm would have to be higher for the firm to still be worth £35 million. 21. a. With the information provided, we can use the equation for calculating WACC to find the cost of equity. The equation for WACC is: WACC = (E/V)RE + (D/V)RD(1 – tC) The company has a debt-equity ratio of 1.5, which implies the weight of debt is 1.5/2.5, and the weight of equity is 1/2.5, so WACC = .12 = (1/2.5)RE + (1.5/2.5)(.12)(1 – .35) RE = .1830 or 18.30% b. To find the unlevered cost of equity, we need to use M&M Proposition II with taxes, so: RE = R0 + (R0 – RD)(D/E)(1 – tC) .1830 = R0 + (R0 – .12)(1.5)(1 – .35) RO = .1519 or 15.19% c. To find the cost of equity under different capital structures, we can again use M&M Proposition II with taxes. With a debt-equity ratio of 2, the cost of equity is: RE = R0 + (R0 – RD)(D/E)(1 – tC) RE = .1519 + (.1519 – .12)(2)(1 – .35) RE = .1934 or 19.34% With a debt-equity ratio of 1.0, the cost of equity is: RE = .1519 + (.1519 – .12)(1)(1 – .35) RE = .1726 or 17.26% And with a debt-equity ratio of 0, the cost of equity is: RE = .1519 + (.1519 – .12)(0)(1 – .35) RE = R0 = .1519 or 15.19% 22. a. For an all-equity financed company: WACC = R0 = RE = .12 or 12% b. To find the cost of equity for the company with leverage, we need to use M&M Proposition II with taxes, so: RE = R0 + (R0 – RD)(D/E)(1 – tC) RE = .12 + (.12 – .08)(.25/.75)(1 – .28) RE = .1296 or 12.96% c. Using M&M Proposition II with taxes again, we get: RE = R0 + (R0 – RD)(D/E)(1 – tC) RE = .12 + (.12 – .08)(.50/.50)(1 – .28) RE = .1488 or 14.88% d. The WACC with 25 percent debt is: WACC = (E/V)RE + (D/V)RD(1 – tC) WACC = .75(.1296) + .25(.08)(1 – .28) WACC = .1116 or 11.16% And the WACC with 50 percent debt is: WACC = (E/V)RE + (D/V)RD(1 – tC) WACC = .50(.1488) + .50(.08)(1 – .28) WACC = .1032 or 10.32% 23. a. The value of the unlevered firm is: V = EBIT(1 – tC)/R0 V = £95,000(1 – .28)/.22 V = £310,909.1 b. The value of the levered firm is: V = VU + tCB V = £310,909.1 + .28(£60,000) V = £327,709.1 24. We can find the cost of equity using M&M Proposition II with taxes. First, we need to find the market value of equity, which is: V = D + E £327,709.1 = £60,000 + E E = £267,709.1 Now we can find the cost of equity, which is: RE = R0 + (R0 – RD)(D/E)(1 – t) RE = .22 + (.22 – .11)(£60,000/£267,709.1)(1 – .28) RE = .2378 or 23.78% Using this cost of equity, the WACC for the firm after recapitalization is: WACC = (E/V)RE + (D/V)RD(1 – tC) WACC = (£267,709.1/£327,709.1)(.2378) + (£60,000/£327,709.1).11(1 – .28) WACC = .2087 or 20.87% When there are corporate taxes, the overall cost of capital for the firm declines the more highly leveraged is the firm’s capital structure. This is M&M Proposition I with taxes. 25. Since Unlevered is an all-equity firm, its value is equal to the market value of its outstanding shares. Unlevered has 10 million shares outstanding, worth £80 per share. Therefore, the value of Unlevered: VU = 10,000,000(£80) = £800,000,000 Modigliani-Miller Proposition I states that, in the absence of taxes, the value of a levered firm equals the value of an otherwise identical unlevered firm. Since Levered is identical to Unlevered in every way except its capital structure and neither firm pays taxes, the value of the two firms should be equal. Therefore, the market value of Levered plc should be £800 million also. Since Levered has 4.5 million outstanding shares, worth £100 per share, the market value of Levered’s equity is: EL = 4,500,000(£100) = £450,000,000 The market value of Levered’s debt is £275 million. The value of a levered firm equals the market value of its debt plus the market value of its equity. Therefore, the current market value of Levered is: VL = B + S VL = £275,000,000 + 450,000,000 VL = £725,000,000 The market value of Levered’s equity needs to be £525 million, £75 million higher than its current market value of £450 million, for MM Proposition I to hold. Since Levered’s market value is less than Unlevered’s market value, Levered is relatively underpriced and an investor should buy shares in the firm. 26. To find the value of the levered firm, we first need to find the value of an unlevered firm. So, the value of the unlevered firm is: VU = EBIT(1 – tC)/R0 VU = (£35,000)(1 – .28)/.14 VU = £180,000 Now we can find the value of the levered firm as: VL = VU + tCB VL = £180,000 + .28(£70,000) VL = £199,600 Applying M&M Proposition I with taxes, the firm has increased its value by issuing debt. As long as M&M Proposition I holds, that is, there are no bankruptcy costs and so forth, then the company should continue to increase its debt/equity ratio to maximize the value of the firm. 27. With no debt, we are finding the value of an unlevered firm, so: V = EBIT(1 – tC)/R0 V = £9,000(1 – .28)/.17 V = £38,117.65 With debt, we simply need to use the equation for the value of a levered firm. With 50 percent debt, one-half of the firm value is debt, so the value of the levered firm is: V = VU + tCB V = £38,117.65+ .28(£38,117.65/2) V = £43,454.12 And with 100 percent debt, the value of the firm is: V = VU + tCB V = £38,117.65+ .28(£38,117.65) V = £48,790.59 28. According to M&M Proposition I with taxes, the increase in the value of the company will be the present value of the interest tax shield. Since the loan will be repaid in equal installments, we need to find the loan interest and the interest tax shield each year. The loan schedule will be: Year Loan Balance Interest Tax Shield 0 €1,000,000 1 €500,000 €80,000 .35(€80,000) = €28,000 2 0 €40,000 .35(€40,000) = €14,000 So, the increase in the value of the company is: Value increase = €28,000/1.08 + €14,000/(1.08)2 Value increase = €37,928.67 29. a. Since Alpha NV is an all-equity firm, its value is equal to the market value of its outstanding shares. Alpha has 5,000 shares of equity outstanding, worth €20 per share, so the value of Alpha NV is: VAlpha = 5,000(€20) = €100,000 b. Modigliani-Miller Proposition I states that in the absence of taxes, the value of a levered firm equals the value of an otherwise identical unlevered firm. Since Beta NV is identical to Alpha NV in every way except its capital structure and neither firm pays taxes, the value of the two firms should be equal. So, the value of Beta NV is €100,000 as well. c. The value of a levered firm equals the market value of its debt plus the market value of its equity. So, the value of Beta’s equity is: VL = B + S €100,000 = €25,000 + S S = €75,000 d. The investor would need to invest 20 percent of the total market value of Alpha’s equity, which is: Amount to invest in Alpha = .20(€100,000) = €20,000 Beta has less equity outstanding, so to purchase 20 percent of Beta’s equity, the investor would need: Amount to invest in Beta = .20(€75,000) = €15,000 e. Alpha has no interest payments, so the euro return to an investor who owns 20 percent of the company’s equity would be: Euro return on Alpha investment = .20(€35,000) = €7,000 Beta NV has an interest payment due on its debt in the amount of: Interest on Beta’s debt = .12(€25,000) = €3,000 So, the investor who owns 20 percent of the company would receive 20 percent of EBIT minus the interest expense, or: Euro return on Beta investment = .20(€35,000 – €3,000) = €6,400 f. From part d, we know the initial cost of purchasing 20 percent of Alpha NV’s equity is €20,000, but the cost to an investor of purchasing 20 percent of Beta NV’s equity is only €15,000. In order to purchase €20,000 worth of Alpha’s equity using only €15,000 of his own money, the investor must borrow €5,000 to cover the difference. The investor will receive the same euro return from the Alpha investment, but will pay interest on the amount borrowed, so the net euro return to the investment is: Net euro return = €7,000 – .12(€5,000) = €6,400 Notice that this amount exactly matches the euro return to an investor who purchases 20 percent of Beta’s equity. g. The equity of Beta NV is riskier. Beta must pay off its debt holders before its equity holders receive any of the firm’s earnings. If the firm does not do particularly well, all of the firm’s earnings may be needed to repay its debt holders, and equity holders will receive nothing. 30. a. A firm’s debt-equity ratio is the market value of the firm’s debt divided by the market value of a firm’s equity. So, the debt-equity ratio of the company is: Debt-equity ratio = MV of debt / MV of equity Debt-equity ratio = €10,000,000 / €20,000,000 Debt-equity ratio = .50 b. We first need to calculate the cost of equity. To do this, we can use the CAPM, which gives us: RS = RF + [E(RM) – RF] RS = .08 + .90(.18 – .08) RS = .1700 or 17.00% We need to remember that an assumption of the Modigliani-Miller theorem is that the company debt is risk-free, so we can use the Treasury bill rate as the cost of debt for the company. In the absence of taxes, a firm’s weighted average cost of capital is equal to: RWACC = [B / (B + S)]RB + [S / (B + S)]RS RWACC = (€10,000,000/€30,000,000)(.08) + (€20,000,000/€30,000,000)(.17) RWACC = .1400 or 14.00% c. According to Modigliani-Miller Proposition II with no taxes: RS = R0 + (B/S)(R0 – RB) .17 = R0 + (.50)(R0 – .08) R0 = .1400 or 14.00% This is consistent with Modigliani-Miller’s proposition that, in the absence of taxes, the cost of capital for an all-equity firm is equal to the weighted average cost of capital of an otherwise identical levered firm. 31. a. To purchase 5 percent of Knight’s equity, the investor would need: Knight investment = .05(Skr1,714,000) = Skr85,700 And to purchase 5 percent of Veblen without borrowing would require: Veblen investment = .05(Skr2,400,000) = SKr120,000 In order to compare krona returns, the initial net cost of both positions should be the same. Therefore, the investor will need to borrow the difference between the two amounts, or: Amount to borrow = SKr120,000 – SKr 85,700 = Skr34,300 An investor who owns 5 percent of Knight’s equity will be entitled to 5 percent of the firm’s earnings available to ordinary share holders at the end of each year. While Knight’s expected operating income is Skr300,000, it must pay Skr60,000 to debt holders before distributing any of its earnings to shareholders. So, the amount available to this shareholder will be: Cash flow from Knight to shareholder = .05(SKr300,000 – SKr 60,000) = Skr12,000 Veblen will distribute all of its earnings to shareholders, so the shareholder will receive: Cash flow from Veblen to shareholder = .05(Skr300,000) = Skr15,000 However, to have the same initial cost, the investor has borrowed Skr34,300 to invest in Veblen, so interest must be paid on the borrowings. The net cash flow from the investment in Veblen will be: Net cash flow from Veblen investment = SKr15,000 – .06(SKr34,300) = SKr12,942 For the same initial cost, the investment in Veblen produces a higher krona return. b. Both of the two strategies have the same initial cost. Since the krona return to the investment in Veblen is higher, all investors will choose to invest in Veblen over Knight. The process of investors purchasing Veblen’s equity rather than Knight’s will cause the market value of Veblen’s equity to rise and/or the market value of Knight’s equity to fall. Any differences in the krona returns to the two strategies will be eliminated, and the process will cease when the total market values of the two firms are equal. 32. a. Before the announcement of the stock repurchase plan, the market value of the outstanding debt is £7,500,000. Using the debt-equity ratio, we can find that the value of the outstanding equity must be: Debt-equity ratio = B / S .40 = £7,500,000 / S S = £18,750,000 The value of a levered firm is equal to the sum of the market value of the firm’s debt and the market value of the firm’s equity, so: VL = B + S VL = £7,500,000 + £18,750,000 VL = £26,250,000 According to MM Proposition I without taxes, changes in a firm’s capital structure have no effect on the overall value of the firm. Therefore, the value of the firm will not change after the announcement of the share repurchase plan b. The expected return on a firm’s equity is the ratio of annual earnings to the market value of the firm’s equity, or return on equity. Before the restructuring, the company was expected to pay interest in the amount of: Interest payment = .10(£7,500,000) = £750,000 The return on equity, which is equal to RS, will be: ROE = RS = (£3,750,000 – £750,000) / £18,750,000 RS = .1600 or 16.00% c. According to Modigliani-Miller Proposition II with no taxes: RS = R0 + (B/S)(R0 – RB) .16 = R0 + (.40)(R0 – .10) R0 = .1429 or 14.29% This problem can also be solved in the following way: R0 = Earnings before interest / VU According to Modigliani-Miller Proposition I, in a world with no taxes, the value of a levered firm equals the value of an otherwise-identical unlevered firm. Since the value of the company as a levered firm is £26.25 million (= £7,500,000 + 18,750,000) and since the firm pays no taxes, the value of the company as an unlevered firm is also £26.25 million. So: R0 = £3,750,000 / £26,250,000 R0 = .1429 or 14.29% d. In part c, we calculated the cost of an all-equity firm. We can use Modigliani-Miller Proposition II with no taxes again to find the cost of equity for the firm with the new leverage ratio. The cost of equity under the share repurchase plan will be: RS = R0 + (B/S)(R0 – RB) RS = .1429 + (.50)(.1429 – .10) RS = .1643 or 16.43% 33. a. The expected return on a firm’s equity is the ratio of annual aftertax earnings to the market value of the firm’s equity. The amount the firm must pay each year in taxes will be: Taxes = .28(£1,500,000) = £420,000 So, the return on the unlevered equity will be: R0 = (£1,500,000 – £420,000) / £10,000,000 R0 = .1080 or 10.8% Notice that perpetual after-tax annual earnings of £1,080,000, discounted at 10.8 percent, yields the market value of the firm’s equity b. The company’s market value balance sheet before the announcement of the debt issue is: Debt – Assets £10,000,000 Equity £10,000,000 Total assets £10,000,000 Total D&E £10,000,000 The price per share is simply the total market value of the equity divided by the shares outstanding, or: Price per share = £10,000,000 / 500,000 = £20.00 c. Modigliani-Miller Proposition I states that in a world with corporate taxes: VL = VU + TCB When Green Manufacturing announces the debt issue, the value of the firm will increase by the present value of the tax shield on the debt. The present value of the tax shield is: PV(Tax Shield) = TCB PV(Tax Shield) = .28(£2,000,000) PV(Tax Shield) = £560,000 Therefore, the value of Green Manufacturing will increase by £560,000 as a result of the debt issue. The value of Gree Manufacturing after the repurchase announcement is: VL = VU + TCB VL = £10,000,000 + .28(£2,000,000) VL = £10,560,000 Since the firm has not yet issued any debt, Green’s equity is also worth £10,560,000. Green’s market value balance sheet after the announcement of the debt issue is: Old assets £10,000,000 Debt – PV(tax shield) 560,000 Equity £10,560,000 Total assets £10,560,000 Total D&E £10,560,000 d. The share price immediately after the announcement of the debt issue will be: New share price = £10,560,000 / 500,000 = £21.12 e. The number of shares repurchase will be the amount of the debt issue divided by the new share price, or: Shares repurchased = £2,000,000 / £21.12 = 94,696.97 The number of shares outstanding will be the current number of shares minus the number of shares repurchased, or: New shares outstanding = 500,000 – 94,696.97 = 405,303 f. The share price will remain the same after restructuring takes place. The total market value of the outstanding equity in the company will be: Market value of equity = £21.12(405,303) = £8,560,000 The market-value balance sheet after the restructuring is: Old assets £10,000,000 Debt £2,000,000 PV(tax shield) 560,000 Equity 8,560,000 Total assets £10,560,000 Total D&E £10,560,000 g. According to Modigliani-Miller Proposition II with corporate taxes RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .108 + (£2,000,000 / £8,560,000)(.108 – .06)(1 – .28) RS = .1161 or 11.61% 34. a. In a world with corporate taxes, a firm’s weighted average cost of capital is equal to: RWACC = [B / (B+S)](1 – tC)RB + [S / (B+S)]RS We do not have the company’s debt-to-value ratio or the equity-to-value ratio, but we can calculate either from the debt-to-equity ratio. With the given debt-equity ratio, we know the company has 2.5 euros of debt for every euro of equity. Since we only need the ratio of debt-to-value and equity-to-value, we can say: B / (B+S) = 2.5 / (2.5 + 1) = .7143 E / (B+S) = 1 / (2.5 + 1) = .2857 We can now use the weighted average cost of capital equation to find the cost of equity, which is: .15 = (.7143)(1 – 0.35)(.10) + (.2857)(RS) RS = .3625 or 36.25% b. We can use Modigliani-Miller Proposition II with corporate taxes to find the unlevered cost of equity. Doing so, we find: RS = R0 + (B/S)(R0 – RB)(1 – tC) .3625 = R0 + (2.5)(R0 – .10)(1 – .35) R0 = .2000 or 20.00% c. We first need to find the debt-to-value ratio and the equity-to-value ratio. We can then use the cost of levered equity equation with taxes, and finally the weighted average cost of capital equation. So: If debt-equity = .75 B / (B+S) = .75 / (.75 + 1) = .4286 S / (B+S) = 1 / (.75 + 1) = .5714 The cost of levered equity will be: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .20 + (.75)(.20 – .10)(1 – .35) RS = .2488 or 24.88% And the weighted average cost of capital will be: RWACC = [B / (B+S)](1 – tC)RB + [S / (B+S)]RS RWACC = (.4286)(1 – .35)(.10) + (.5714)(.2488) RWACC = .17 If debt-equity =1.50 B / (B+S) = 1.50 / (1.50 + 1) = .6000 E / (B+S) = 1 / (1.50 + 1) = .4000 The cost of levered equity will be: RS = R0 + (B/S)(R0 – RB)(1 – tC) RS = .20 + (1.50)(.20 – .10)(1 – .35) RS = .2975 or 29.75% And the weighted average cost of capital will be: RWACC = [B / (B+S)](1 – tC)RB + [S / (B+S)]RS RWACC = (.6000)(1 – .35)(.10) + (.4000)(.2975) RWACC = .1580 or 15.80% 35. M&M Proposition II states: RE = R0 + (R0 – RD)(D/E)(1 – tC) And the equation for WACC is: WACC = (E/V)RE + (D/V)RD(1 – tC) Substituting the M&M Proposition II equation into the equation for WACC, we get: WACC = (E/V)[R0 + (R0 – RD)(D/E)(1 – tC)] + (D/V)RD(1 – tC) Rearranging and reducing the equation, we get: WACC = R0[(E/V) + (E/V)(D/E)(1 – tC)] + RD(1 – tC)[(D/V) – (E/V)(D/E)] WACC = R0[(E/V) + (D/V)(1 – tC)] WACC = R0[{(E+D)/V} – tC(D/V)] WACC = R0[1 – tC(D/V)] 36. The return on equity is net income divided by equity. Net income can be expressed as: NI = (EBIT – RDD)(1 – tC) So, ROE is: RE = (EBIT – RDD)(1 – tC)/E Now we can rearrange and substitute as follows to arrive at M&M Proposition II with taxes: RE = [EBIT(1 – tC)/E] – [RD(D/E)(1 – tC)] RE = RAVU/E – [RD(D/E)(1 – tC)] RE = RA(VL – tCD)/E – [RD(D/E)(1 – tC)] RE = RA(E + D – tCD)/E – [RD(D/E)(1 – tC)] RE = RA + (RA – RD)(D/E)(1 – tC) 37. M&M Proposition II, with no taxes is: RE = RA + (RA – Rf)(B/S) Note that we use the risk-free rate as the return on debt. This is an important assumption of M&M Proposition II. The CAPM to calculate the cost of equity is expressed as: RE = E(RM – Rf) + Rf We can rewrite the CAPM to express the return on an unlevered company as: RA = A(RM – Rf) + Rf We can now substitute the CAPM for an unlevered company into M&M Proposition II. Doing so and rearranging the terms we get: RE = A(RM – Rf) + Rf + [A(RM – Rf) + Rf – Rf](B/S) RE = A(RM – Rf) + Rf + [A(RM – Rf)](B/S) RE = (1 + B/S)A(RM – Rf) + Rf Now we set this equation equal to the CAPM equation to calculate the cost of equity and reduce: E(RM – Rf) + Rf = (1 + B/S)A(RM – Rf) + Rf E(RM – Rf) = (1 + B/S)A(RM – Rf) E = A(1 + B/S) 38. Using the equation we derived in Problem 37: E = A(1 + D/E) The equity beta for the respective asset betas is: Debt-equity ratio Equity beta 0 1(1 + 0) = 1 1 1(1 + 1) = 2 5 1(1 + 5) = 6 20 1(1 + 20) = 21 The equity risk to the shareholder is composed of both business and financial risk. Even if the assets of the firm are not very risky, the risk to the shareholder can still be large if the financial leverage is high. These higher levels of risk will be reflected in the shareholder’s required rate of return RE, which will increase with higher debt/equity ratios. 39. We first need to set the cost of capital equation equal to the cost of capital for an all-equity firm, so: B S B + RB + B S S + RS = R0 Multiplying both sides by (B + S)/S yield: S B R B + RS = S B +S R 0 We can rewrite the right-hand side as: S B R B + RS = S B R 0 + R0 Moving (B/S)RB to the right-hand side and rearranging gives us: RS = R0 + S B (R0 – RB) Chapter 15 Case Study Stephenson Real Estate Recapitalization 1. If Stephenson wishes to maximize the overall value of the firm, it should use debt to finance the £100 million purchase. Since interest payments are tax deductible, debt in the firm’s capital structure will decrease the firm’s taxable income, creating a tax shield that will increase the overall value of the firm. 2. Since Stephenson is an all-equity firm with 15 million shares outstanding, worth £32.50 per share, the market value of the firm is: Market value of equity = £32.50(15,000,000) Market value of equity = £487,500,000 So, the market value balance sheet before the land purchase is: Market value balance sheet Assets £487,500,000 Equity £487,500,000 Total assets £487,500,000 Debt & Equity £487,500,000 3. a. As a result of the purchase, the firm’s pre-tax earnings will increase by £25 million per year in perpetuity. These earnings are taxed at a rate of 28 percent. Therefore, after taxes, the purchase increases the annual expected earnings of the firm by: Earnings increase = £25,000,000(1 – .40) Earnings increase = £18,000,000 Since Stephenson is an all-equity firm, the appropriate discount rate is the firm’s unlevered cost of equity, so the NPV of the purchase is: NPV = –£100,000,000 + (£18,000,000 / .125) NPV = £44,000,000 b. After the announcement, the value of Stephenson will increase by £44 million, the net present value of the purchase. Under the efficient-market hypothesis, the market value of the firm’s equity will immediately rise to reflect the NPV of the project. Therefore, the market value of Stephenson’s equity after the announcement will be: Equity value = £487,500,000 + £44,000,000 Equity value = £531,500,000 Market value balance sheet Old assets £487,500,000 NPV of project 44,000,000 Equity £531,500,000 Total assets £531,500,000 Debt & Equity £531,500,000 Since the market value of the firm’s equity is £531,500,000 and the firm has 15 million shares outstanding, Stephenson’s share price after the announcement will be: New share price = £531,500,000 / 15,000,000 New share price = £35.43 Since Stephenson must raise £100 million to finance the purchase and the firm’s equity is worth £35.43 per share, Stephenson must issue: Shares to issue = £100,000,000 / £35.43 Shares to issue = 2,822,201 c. Stephenson will receive £100 million in cash as a result of the equity issue. This will increase the firm’s assets and equity by £100 million. So, the new market value balance sheet after the equity issue will be: Market value balance sheet Cash £100,000,000 Old assets 487,500,000 NPV of project 44,000,000 Equity £631,500,000 Total assets £631,500,000 Debt & Equity £631,500,000 The share price will remain unchanged. To show this, Stephenson will now have: Total shares outstanding = 15,000,000 + 2,822,201 Total shares outstanding = 17,822,201 So, the share price is: Share price = £631,500,000 / 17,822,201 Share price = £35.43 d. The project will generate £25 million of additional annual pretax earnings forever. These earnings will be taxed at a rate of 28 percent. Therefore, after taxes, the project increases the annual earnings of the firm by £18 million. So, the after-tax present value of the earnings increase is: PVProject = £18,000,000 / .125 PVProject = £144,000,000 So, the market value balance sheet of the company will be: Market value balance sheet Old assets £487,500,000 PV of project 144,000,000 Equity £631,500,000 Total assets £631,500,000 Debt & Equity £631,500,000 4. a. Modigliani-Miller Proposition I states that in a world with corporate taxes: VL = VU + tCB As was shown in Question 3, Stephenson will be worth £631.5 million if it finances the purchase with equity. If it were to finance the initial outlay of the project with debt, the firm would have £100 million worth of 8 percent debt outstanding. So, the value of the company if it financed with debt is: VL = £631,500,000 + .28 (£100,000,000) VL = £659,500,000 b. After the announcement, the value of Stephenson will immediately rise by the present value of the project. Since the market value of the firm’s debt is £100 million and the value of the firm is £659.5 million, we can calculate the market value of Stephenson’s equity. Stephenson’s market-value balance sheet after the debt issue will be: Market value balance sheet Value unlevered £631,500,000 Debt £100,000,000 Tax shield 28,000,000 Equity 559,500,000 Total assets £659,500,000 Debt & Equity £659,500,000 Since the market value of the Stephenson’s equity is £559.5 million and the firm has 15 million shares of common stock outstanding, Stephenson’s share price after the debt issue will be: Share price = £559,500,000 / 15,000,000 Share price = £37.30 5. If Stephenson uses equity in order to finance the project, the firm’s share price will remain at £35.43 per share. If the firm uses debt in order to finance the project, the firm’s sharek price will rise to £37.30 per share. Therefore, debt financing maximizes the per share value of a firm’s equity. Solution Manual for Corporate Finance David Hillier, Stephen Ross, Randolph Westerfield, Jeffrey Jaffe, Bradford Jordan 9780077139148
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