In a particular bond market, thetwo - year par yield at time t = 0is 4.15% and the issue price attime t = 0 of a two - year fixedinterest stock, paying coupons of8% annually in arrears and redeemed at 98, is $105.40 per$100 nominal. Calculate: (a) theone - year spot rate (b) the two -year spot rate
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In a particular bond market, thetwo - year par yield at time t = 0is 4.15% and the issue price attime t = 0 of a two - year fixedinterest stock, paying coupons of8% annually in arrears and redeemed at 98, is $105.40 per$100 nominal. Calculate: (a) theone - year spot rate (b) the two -year spot rate
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.Suppose you are borrowing 25,000 and making monthly payments with 1% interest. Show that the monthly payments should equal 556.11. The key relationships are that for any month t (Ending month t balance) = (Ending month t 1 balance) ((Monthly payment) (Month t interest)) (Month t interest) = (Beginning month t balance) (Monthly interest rate) Of course, the ending month 60 balance must equal 0.You are considering a 10-year investment project. At present, the expected cash flow each year is 10,000. Suppose, however, that each years cash flow is normally distributed with mean equal to last years actual cash flow and standard deviation 1000. For example, suppose that the actual cash flow in year 1 is 12,000. Then year 2 cash flow is normal with mean 12,000 and standard deviation 1000. Also, at the end of year 1, your best guess is that each later years expected cash flow will be 12,000. a. Estimate the mean and standard deviation of the NPV of this project. Assume that cash flows are discounted at a rate of 10% per year. b. Now assume that the project has an abandonment option. At the end of each year you can abandon the project for the value given in the file P11_60.xlsx. For example, suppose that year 1 cash flow is 4000. Then at the end of year 1, you expect cash flow for each remaining year to be 4000. This has an NPV of less than 62,000, so you should abandon the project and collect 62,000 at the end of year 1. Estimate the mean and standard deviation of the project with the abandonment option. How much would you pay for the abandonment option? (Hint: You can abandon a project at most once. So in year 5, for example, you abandon only if the sum of future expected NPVs is less than the year 5 abandonment value and the project has not yet been abandoned. Also, once you abandon the project, the actual cash flows for future years are zero. So in this case the future cash flows after abandonment should be zero in your model.)
- A European put option allows an investor to sell a share of stock at the exercise price on the exercise data. For example, if the exercise price is 48, and the stock price is 45 on the exercise date, the investor can sell the stock for 48 and then immediately buy it back (that is, cover his position) for 45, making 3 profit. But if the stock price on the exercise date is greater than the exercise price, the option is worthless at that date. So for a put, the investor is hoping that the price of the stock decreases. Using the same parameters as in Example 11.7, find a fair price for a European put option. (Note: As discussed in the text, an actual put option is usually for 100 shares.)The IRR is the discount rate r that makes a project have an NPV of 0. You can find IRR in Excel with the built-in IRR function, using the syntax =IRR(range of cash flows). However, it can be tricky. In fact, if the IRR is not near 10%, this function might not find an answer, and you would get an error message. Then you must try the syntax =IRR(range of cash flows, guess), where guess" is your best guess for the IRR. It is best to try a range of guesses (say, 90% to 100%). Find the IRR of the project described in Problem 34. 34. Consider a project with the following cash flows: year 1, 400; year 2, 200; year 3, 600; year 4, 900; year 5, 1000; year 6, 250; year 7, 230. Assume a discount rate of 15% per year. a. Find the projects NPV if cash flows occur at the ends of the respective years. b. Find the projects NPV if cash flows occur at the beginnings of the respective years. c. Find the projects NPV if cash flows occur at the middles of the respective years.Referring to Example 11.1, if the average bid for each competitor stays the same, but their bids exhibit less variability, does Millers optimal bid increase or decrease? To study this question, assume that each competitors bid, expressed as a multiple of Millers cost to complete the project, follows each of the following distributions. a. Triangular with parameters 1.0, 1.3, and 2.4 b. Triangular with parameters 1.2, 1.3, and 2.2 c. Use @RISKs Define Distributions window to check that the distributions in parts a and b have the same mean as the original triangular distribution in the example, but smaller standard deviations. What is the common mean? Why is it not the same as the most likely value, 1.3?
- In Example 11.1, the possible profits vary from negative to positive for each of the 10 possible bids examined. a. For each of these, use @RISKs RISKTARGET function to find the probability that Millers profit is positive. Do you believe these results should have any bearing on Millers choice of bid? b. Use @RISKs RISKPERCENTILE function to find the 10th percentile for each of these bids. Can you explain why the percentiles have the values you obtain?In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?A company manufacturers a product in the United States and sells it in England. The unit cost of manufacturing is 50. The current exchange rate (dollars per pound) is 1.221. The demand function, which indicates how many units the company can sell in England as a function of price (in pounds) is of the power type, with constant 27556759 and exponent 2.4. a. Develop a model for the companys profit (in dollars) as a function of the price it charges (in pounds). Then use a data table to find the profit-maximizing price to the nearest pound. b. If the exchange rate varies from its current value, does the profit-maximizing price increase or decrease? Does the maximum profit increase or decrease?
- Amanda has 30 years to save for her retirement. At the beginning of each year, she puts 5000 into her retirement account. At any point in time, all of Amandas retirement funds are tied up in the stock market. Suppose the annual return on stocks follows a normal distribution with mean 12% and standard deviation 25%. What is the probability that at the end of 30 years, Amanda will have reached her goal of having 1,000,000 for retirement? Assume that if Amanda reaches her goal before 30 years, she will stop investing. (Hint: Each year you should keep track of Amandas beginning cash positionfor year 1, this is 5000and Amandas ending cash position. Of course, Amandas ending cash position for a given year is a function of her beginning cash position and the return on stocks for that year. To estimate the probability that Amanda meets her goal, use an IF statement that returns 1 if she meets her goal and 0 otherwise.)Referring to the retirement example in Example 11.6, rerun the model for a planning horizon of 10 years; 15 years; 25 years. For each, which set of investment weights maximizes the VAR 5% (the 5th percentile) of final cash in todays dollars? Does it appear that a portfolio heavy in stocks is better for long horizons but not for shorter horizons?Let Xi be the price (in dollars) of stock i one year fromnow. X1 is N(15, 100) and X2 is N(20, 2025). Today I buythree shares of stock 1 for $12/share and two shares of stock2 for $17/share. Assume that X1 and X2 are independentrandom variables.a Find the mean and variance of the value of my stocksone year from now.b What is the probability that one year from now I willhave earned at least a 30% return on my investment?c If X1 and X2 were not independent, why would it bedifficult to answer parts (a) and (b)?