Question

2. (30 points) You invest $x today at 8% APR compounded annually for 5 years (you invest only once). Your friend also invests some amount at the same time at 8% APR compounded annually for 5 years. However, she invests an additional amount equal to the accumulated interest at the end of each year. You both end up having the same amount at the end of 5 years. In order to achieve this, your initial investment must have been t times as much as your friend's. What is t? 3(40 points) Assume your best investment opportunity gets you 10% per year but you would like to enter the electric scooter market. Cost Structure: If you enter the market today (year zero), you have $480,000 as fixed costs and 40 +100 as variable costs. All costs are due when the production starts. You will be in the short run for three years, that is, the production will end the capital will be exhausted at the end of three years. Sales: You will be able to sell 1/3 of the production at year 1(one year after the production starts), 1/3 of it at year 2, and the rest at year 3. Assume that price you can charge for your product stays at $8,000 throughout the production process You don't have any money now but assume that you can borrow and lend money at 10% APR anytime you want. If you start the production a year from today (year 1), the sales description stays the same, that is, you can sell your product in three years following the start of production beginning one year after the production. However, you will have enough time to make necessary adjustments to have your variable costs go down by 9% and fixed costs go down to $435,000. Should you enter this market? If so, should you start production today or in a year?

Answer 1

For 2nd: - Basically the friend is earning 4% APR Hence, we can say that X(1 + 8%)^5 = t times (1 + 4%)^5 t = (1.08/1.04)^5 t = 1.207680575.