Mutual funds can effectively charge sales fees in one of three ways: front-end load fees, 12b-1 (i. e., annual) fees, or deferred (i. e., back-end) load fees. Assume that the SAS Fund offers its investors the choice of the following sales fee arrangements: (1) a 3% front-end load, (2) a 0.55% annual deduction, or (3) a 1% back-end load, paid at the liquidation of the investor's position. Also, assume that SAS Fund averages NAV growth of 12% per year. Required:
a. If you start with $100,000 in investment capital, calculate what an investment in SAS would be worth in three years under each of the proposed sales fee schemes. Which scheme would you choose?
b. If your investment horizon were 10 years, would your answer in Part a change? Demonstrate.
c. Explain the relationship between the timing of the sales charge and your investment horizon. In general, if you intend to hold your position for a long time, which fee arrangement would you prefer?

Suppose that two firms produce differentiated products and compete in prices. as in class, the two firms are located at two ends of a line one mile apart. consumers are evenly distributed along the line. the firms have identical marginal cost, $60. firm b produces a product with value $110 to consumers.firm a (located at 0 on the unit line) produces a higher quality product with value $120 to consumers. the cost of travel are directly related to the distance a consumer travels to purchase a good. if a consumerhas to travel a mile to purchase a good, the incur a cost of $20. if they have to travel x fraction of a mile, they incur a cost of $20x. (a) write down the expressions for how much a consumer at location d would value the products sold by firms a and b, if they set prices p_{a} and p_{b} ? (b) based on your expressions in (a), how much will be demanded from each firm if prices p_{a} and p_{b} are set? (c) what are the nash equilibrium prices?