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# Finance 1. Problem Set 3 Spring 2010 You are considering a new project that will cost \$945,000 to launch, has a three year life, and no re-sale value...

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Finance Problem Set 3 Spring 2010 1. You are considering a new project that will cost \$945,000 to launch, has a three year life, and no re-sale value at the end of project. Depreciation is straight-line to a zero-salvage value. The opportunity cost of capital for this project is 20 percent, and the tax rate is 34 percent. Sales are projected at 80 units per year. The price per unit is expected to be \$35,000, variable costs are projected at \$21,900 per unit, and fixed costs are anticipated to be \$500,000 per year. (a) What is the NPV based on this information? (b) The accept/reject decision for this project could be affected by acquiring better information about the project characteristics. Conduct a sensitivity analysis with respect to sales volume and selling price projections (only!). In each instance, assume that, in addition to the base-case scenario, there is a pessimistic case and an optimistic case corresponding to plus/minus 10% of the base-case. Under what conditions would your decision change? (c) What are the accounting and economic break-even levels of sales? 2. A financial claim will pay \$24,000 in real terms five years from today. How much would you be willing to pay in nominal dollars two years from today for this asset? The real rate is 4% per year and expected inflation is 5% per year. 3. You own 500 acres of timberland, with young timber worth \$40,000 if logged now. This represents 1,000 cords of wood worth \$40 per cord net of costs of cutting and hauling. You expect the price per cord to increase at 4 percent per year indefinitely. The market value of your land would be \$100 per cord if you cut and removed the timber this year. The value of cut-over land is also expected to grow at 4% per year indefinitely. A paper company has offered to purchase your tract for \$100,000. If the cost of capital is 9% per year, should you accept the offer? You also have the following information on the expected increase in the number of cords per acre in subsequent years if the timber is not harvested and sold. Years Yearly growth rate of cords per acre 1-4 16% 5-8 11% 9-13 4% 14 and subsequent years 1% 4. Calamity Mining Company's reserves of ore are being depleted, and its costs of recovering a declining quantity of ore are rising each year. As a result, the company’s dividends are declining at the rate of 10% per year. If the dividend, which is about to be paid (and that you will receive) is \$5 and the required rate of return is 14%, what is the value of the firm's stock? 5. (a) Draw the profit diagram that would result from buying one call option and one put option on the same underlying stock (assuming that you do not own the stock) if the options have the same exercise price and sell for the same premium. Based on the resulting payoff pattern, when would you recommend that someone adopt this strategy? When will
it be most profitable? Explain. (b) Draw the profit diagram that would result from buying one call option with an exercise price of \$100, selling two calls with an exercise price of \$110, and buying one call with an exercise price of \$120 if the options all sell for the same premium. Based on the resulting payoff pattern, when would you recommend that someone adopt this strategy? When will it be most profitable? Explain. 6. This question illustrates the impact of changes in the exercise price, the underlying stock price, the risk-free rate of interest, and the volatility of the underlying stock on option values. Recall our in-class example of an option with an exercise price of \$100, the current stock price of \$100, and a risk-free interest rate of 5%. Next period, the stock price was expected to take one of two values, P L = \$90, or P H = \$110. Under these conditions, we found that the option value was \$7.14. (a) What will be the value of the option if the exercise price is \$105, all other values equal to the original parameters? What is the relation between option values and changes in the exercise price? (b) What will be the value of the option if the distribution of stock prices next period is P L = \$90 and P H = \$120, all other values equal to the original parameters? What is the relation between option values and changes in the expected stock price at expiration? (c) What will be the value of the option if the distribution of stock prices next period is P L = \$80 and P H = \$120, all other values equal to the original parameters? What is the relation between option values and changes in the volatility of the underlying stock price? (d) What will be the value of the option if the risk-free interest rate is 7% per year, all other values equal to the original parameters? What is the relation between option values and changes in the risk-free rate of interest? 7. If I deposit money in an account and anticipate tripling my money in eight years, what is the annual rate of return?

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