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The excess return on an optimally allocated two asset portfolio is given as:
[ E ( R ) R f ] w E ( R ) (1 w ) E ( R )
P A A A B
Assume that RA rA r f and RB rB rf
Variance of this portfolio is:
, each representing excess returns on assets A
2 w 2 (1 w ) 2 2 2 Cov ( R , R )
p A A A A A B
The optimal allocation to asset A is derived by maximizing the Sharp Ratio:
S E ( R ) R w E ( R ) (1 w ) E ( R )
p f A A A B
p p w 2 (1 w ) 2 2 2 Cov ( R , R )
A A A B
a. Show that optimal weight wA is given by:
R 2 R Cov ( R , R )
A B B A B
A R 2 R 2 ( R R ) Cov ( R , R )
A B A
B A B A B
b. Verify your solution by using Solver in Excel. Use a simple 2 asset example, by making assumptions about expected returns and volatilities of assets A and B.
It is March 9th and you have just entered into a short position in Soybean meal futures. The contract matures on July 9th and calls for delivery on 100 tons of soybean meal. Further because this is a futures position, it requires the posting of a $3,000 initial margin and $1,500 maintenance margin. For simplicity assume that the account is market to market on a monthly basis. Assume the following represent the contract delivery prices that prevail on each settlement date:
Date Settlement Prices
March 9 (initiation) 173.00
April 9 179.75
May 9 189.00
June 9 182.50
July 9 174.25
a. Assuming that the underlying soybean meal investment pays no dividend and requires storage cost of 1.5% (of current value) estimate the current (theoretical) spot price of a ton of soybean meal (as of March 9th ) and implied May 9th price for the same ton. In your calculations assume an annual risk free rate of 8% during the entire contract life (Note that the storage cost is proportional to the price of the soybean)
b. Suppose that on March 9 you also entered into a long forward contract for the purchase of 100 tons of soybean meal on July 9. Assume further that the July forward and futures contract prices always are identical to one another at any point in time. Calculate the cash amount of your gain or loss if you unwind both positions in respective markets on May 9 and June 9 taking into account the prevailing settlement conditions in the two markets.
Hint: You need to calculate the value of the forward contracts on May 9th and June 9th.
Consider a two period binomial model in which stock currently trades at a price of $65. The stock price can go up 20% or down 17 percent each period. The risk free rate is 5% per period. Assume that each period is one year.
a. Calculate the price of a European put option expiring in two periods with exercises price of $60.
b. Based on your answer in Part a, calculate the number of units of the underlying stock that would be needed at each point in the binomial tree in order to construct the risk free hedge. Use 10,000 puts.
Consider a stock, CVN, with a price of $50 and a standard deviation of 0.3. The current risk-free rate of interest is 10 percent. A European call option with an exercise price of $55 expiring in 3 months (0.25 years) is traded in the market. If the option delta N(d1) = 0.3469, what should be the Black and Scholes Price of the put option with $55 srike and 3 months to expiration.
Hint: You can use excel functions Normsdist(x)
In October 2018 global equity markets collectively lost $5tr of their market valuation. Briefly discuss the factors behind decline. Why did market bounced back later on; what are the explanations for high equity prices during at present time.
Please read the following short case and answer the questions A through E. Submit you analysis in an Excel sheet, but provide answers in written form with references to the Excel sheet. You can copy and paste excel cells, but I would like to see your excel file for the solution. You can create a tab in the main Excel sheet:
Foster, Inc. is a leading producer of fresh, frozen, and made-from-concentrate orange drinks. The firm was founded in 1949 by Geoffrey Foester, who inherited several orange fields from his family. When Foester returned to the family town Dogville, the family business consisted primarily of harvesting and selling oranges to wholesalers for distribution to grocery stores. The business and its cash flows were necessarily seasonal. Based on his conviction that there was a growing market for orange juices and cocktails, Foester decided to expand the scope of the business. Accordingly, he joined several other growers to form Foster, Inc., which processes its own juices. The company purchases concentrates of apple, orange, cherry, and raspberry juices, and it markets a whole range of orange cocktails. With its skilled marketing and strong emphasis on product quality, the company has prospered. Today its brands are sold throughout the United States, with “Jolt” being its most successful product.
Foster’s management is currently evaluating a lite version of “Jolt” cocktail. A test marketing program carried out in 1995 at a cost of $150,000 showed enthusiastic acceptance for the product, which would cost more than regular “Jolt” but offer 30 percent fewer calories. Michael Baker and Jennifer Lane, recent business school graduates now working at the firm as financial analysts, must analyze this project and then present their findings to the company’s executive committee. Assume that you work for a consulting company that Foster uses to help with decisions such as this, and you have been assigned to work with Jennifer and Michael on the analysis.
Production facilities for the lite orange product would be set up in an unused section of Foster’s main plant. Relatively inexpensive used machinery with an estimated cost of only $400,000 would be purchased, but shipping costs to move the machinery to Foster’s plant would add another $20,000, and installation charges would amount to another $40,000. Further, Foster’s inventories (raw materials, work-in-process, and finished goods) would have to be increased by
$15,000 at the time of the initial investment. If used machinery is purchased, it would have a remaining economic life of 4 years, and will be depreciated the under the MACRS 3-year class. The depreciation allowances will be 0.33, 0.45, 0.15, and 0.07 in Years 1 through 4, respectively. The machinery is expected to have a market value of $50,000 after 4 years of use.
Foster’s management expects to sell 400,000 16-ounce cartons of the new lite product in each of the next 4 years. The price is expected to be $2.00 per carton. Fixed costs are estimated to be $100,000, and variable cash operating costs are estimated at $1.25 per unit. Note that operating costs are a function of the number of units sold rather than unit price, so unit price changes have no direct effect on operating costs.
In examining the sales figures, Jennifer Lane noted a short memo from Foster’s sales manager which expressed concern that the lite cocktail project would cut into the firm’s sales of the regular cocktail- this type of effect is called cannibalization. Specifically, the sales manager estimated that regular Jolt sales would fall by 5 percent if lite cocktail were introduced. Jennifer pursued this further with both the sales and production managers, and they estimated that the new project would probably lower the firm’s regular Jolt sales by $40,000 per year. However, this volume reduction would also reduce regular Jolt production costs by $20,000 per year. Foster’s federal-plus-state tax rate is 40 percent, and its overall cost of capital is 10 percent, calculated as follows:
WACC = wd kd (1 – T) + wsks = 0.5(10%) (0.6) + 0.5(14%) = 10.0%.
As they began to look into the situation, Jennifer and Michael learned that the Dogville Orange Association has expressed an interest in leasing the space that would be used to produce lite Jolt juice. The terms of the lease, if it were made, would call for Foster to receive rental payments of $25,000 at the end of each year, and, at the association’s insistence, the lease would have to run for 20 years. However, it is not at all certain that the association will ultimately agree to rent the space. Yet another consideration is the possibility that Foster could itself rent space in a local bottling facilities during the off-season. In that event, almost no capital would have to be invested in the project, but rental payments would have to be made to the bottler. Finally, Jennifer and Michael are aware of a concern the production VP has raised, namely, that although the space is not being used now, it will be needed for other products within the next 2 or 3 years, assuming normal growth in sales of those products.
Your task is to work with Jennifer and Michael to analyze the situation. You must recommend acceptance or rejection, and evaluate the project’s acceptability using the NPV, IRR, modified IRR (MIRR), and payback criteria. For the analysis, assume that the lite cocktail project is of average risk, in other words, it is in line with the overall firm risk. Jennifer and Michael are concerned about the proper estimation of the relevant cash flows associated with the project. For example, should the test marketing costs be charged to the project? How should the cannibalization effect be handled? How about the Orange Association’s interest in leasing the space that would be used for lite cocktail production and the other divisions’ plant needs 2 or 3 years hence? Jennifer and Michael wondered whether they should assume a neutral 3 percent general rate of inflation in their revenue and cost projections. Also, if the bottling plant is really available, how should this factor be taken into account?
A. What is Foster’s Year 0 net investment outlay on this project?
B. Estimate the product’s operating cash flows inclusive of cannibalization effects1.
C. What are the terminal non-operating cash flows of the project when the project is terminated at Year 4?
D. What are the project’s NPV, IRR, modified IRR (MIRR), and payback? Should the project be undertaken? [Remember: The MIRR is found in three steps: (1) compound all cash inflows out to the terminal year at the cost of capital, (2) sum the compounded cash inflows to obtain the terminal value of the inflows, and (3) find the discount rate that forces the present value of the terminal value to equal the present value of the net investment outlays. This discount rate is defined as the MIRR.]
E. What recommendation should Jennifer and Michael make to the executive committee? Should they recommend that the project be accepted, rejected, or studied further? Justify your answer.
1 Please incorporate the possible income to be generated from the lease of the space that will be allocated to Foster. The after tax income associated with the lease should be 25,000 x (1-0.4)=15,000.
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