Returns risk premiums and volatility would all be

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Unformatted text preview: ue from the learning curve, which will increase at 5 percent. All earnings are paid out as dividends, so we find the earnings per share are: EPS = Earnings/total number of outstanding shares EPS = ($15,000,000 × 1.05) / 10,000,000 EPS = $1.58 254 From the NPVGO mode: P = E/(R – g) + NPVGO P = $1.58/(0.10 – 0.05) + NPVGO P = $31.50 + NPVGO Now we can compute the NPVGO of the new project to be launched two years from now. The earnings per share two years from now will be: EPS2 = $1.58(1 + .05)2 EPS2 = $1.6538 Therefore, the initial investment in the new project will be: Initial investment = .30($1.6538) Initial investment = $0.50 The earnings per share of the new project is a perpetuity, with an annual cash flow of: Increased EPS from project = $6,500,000 / 10,000,000 shares Increased EPS from project = $0.65 So, the value of all future earnings in year 2, one year before the company realizes the earnings, is: PV = $0.65 / .10 PV = $6.50 Now, we can find the NPVGO per share of the investment opportunity in year 2, which will be: NPVGO2 = –$0.50 + 6.50 NPVGO2 = $6.00 The value of the NPVGO today will be: NPVGO = $6.00 / (1 + .10)2 NPVGO = $4.96 Plugging in the NPVGO model we get; P = $31.50 + 4.96 P = $36.46 Note that you could also value the company and the project with the values given, and then divide the final answer by the shares outstanding. The final answer would be the same. 255 CHAPTER 10 RISK AND RETURN: LESSONS FROM MARKET HISTORY Answers to Concepts Review and Critical Thinking Questions 1. 2. 3. 4. 5. 6. They all wish they had! Since they didn’t, it must have been the case that the stellar performance was not foreseeable, at least not by most. As in the previous question, it’s easy to see after the fact that the investment was terrible, but it probably wasn’t so easy ahead of time. No, stocks are riskier. Some investors are highly risk averse, and the extra possible return doesn’t attract them relative to the extra risk. Unlike gambling, the stock market is a positive sum game; everybody can win. Also, speculators provide liquidity to markets and thus help to promote efficiency. T-bill rates were highest in the early eighties. This was during a period of high inflation and is consistent with the Fisher effect. Before the fact, for most assets, the risk premium will be positive; investors demand compensation over and above the risk-free return to invest their money in the risky asset. After the fact, the observed risk premium can be negative if the asset’s nominal return is unexpectedly low, the riskfree return is unexpectedly high, or if some combination of these two events occurs. Yes, the stock prices are currently the same. Below is a diagram that depicts the stocks’ price movements. Two years ago, each stock had the same price, P0. Over the first year, General Materials’ stock price increased by 10 percent, or (1.1) × P0. Standard Fixtures’ stock price declined by 10 percent, or (0.9) × P0. Over the second year, General Materials’ stock price decreased by 10 percent, or (0.9)(1.1) × P0, while Standard Fixtures’ stock price increased by 10 percent, or (1.1) (0.9) × P0. Today, each of the stocks is worth 99 percent of its original value. 2 years ago P0 P0 1 year ago (1.1)P0 (0.9)P0 Today (1.1)(0.9)P0 = (0.99)P0 (0.9)(1.1)P0 = (0.99)P0 7. General Materials Standard Fixtures 8. The stock prices are not the same. The return quoted for each stock is the arithmetic return, not the geometric return. The geometric return tells you the wealth increase from the beginning of the period to the end of the period, assuming the asset had the same return each year. As such, it is a better measure of ending wealth. To see this, assuming each stock had a beginning price of $100 per share, the ending price for each stock would be: Lake Minerals ending price = $100(1.10)(1.10) = $121.00 Small Town Furniture ending price = $100(1.25)(.95) = $118.75 Whenever there is any variance in returns, the asset with the larger variance will always have the greater difference between the arithmetic and geometric return. 9. To calculate an arithmetic return, you simply sum the returns and divide by the number of returns. As such, arithmetic returns do not account for the effects of compounding. Geometric returns do account for the effects of compounding. As an investor, the more important return of an asset is the geometric return. 10. Risk premiums are about the same whether or not we account for inflation. The reason is that risk premiums are the difference between two returns, so inflation essentially nets out. Returns, risk premiums, and volatility would all be lower than we estimated because aftertax returns are smaller than pretax returns. Solutions to Questions and Problems NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the fi...
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