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Question: Elon Musk's newest venture is the Hyperloop service between Washington DC and Baltimore. The Hyperloop trains will offer customers a choice between coach and first-class tickets.

For the venture to comply with federal regulations, it must sell a minimum of 10 first-class tickets and a minimum of 10 coach tickets per trip. Currently the profit margin is $5 for each coach ticket and $8 for each first-class ticket. Due to safety reasons, the train total capacity is 50 travelers (excluding the crew). While first-class tickets are more profitable, first class seats take up more space relative to coach seats. The overall length of the seating area of the train is 2400 inches. The seat pitch for 1st class is 60 inches. The federally mandated seat pitch for coach class is 30 inches.

Another consideration for deciding on the allocation of the seats is the weight capacity of the train. The allowed total passenger payload is 10000 lbs. It is also known that first class customers are, on average, heavier than coach customers. The typical weight of a first-class customer is 200lbs, while the typical weight of a coach customer is 150lbs.

1. How many of each ticket should be sold in order to maximize profits?

2. How much would Hyperloop earn over a 10-year horizon with 365-day service, and 100 trains per day, assuming full utilization and assuming that Elon Musk agrees to implement your solution in part a)?

3. Due to an unprecedented outbreak of a novel infectious disease, the Hyperloop must either redesign all train cars to follow the CDC guidelines for social distancing or shut down all operations. The full redesign would cost $50 Million and reduce the available seating area, and thus the maximum seating area of each train by 50% (The maximum number of passengers is not restricted). Given that Elon Musk is unwilling to increase prices, how many of each ticket should be sold in order to maximize profits? Under the assumptions in (b) is the venture still profitable?

PLEASE SHOW EXCEL FORMULAS (OR ATTACH FILE) AND STEPS TO GET ANSWERS. Will give thumbs up to correct solution!!

(a) In the above we presumably use us CPI rate to deflate the usd prices. But is this result generalizable to all countriesis this conclusion necessarily also valid for Japanese or German investors? Why (not)? (b) If you think the result does not necessarily hold true elsewhere, what would you bet w.r.t. a hyper-inflator like Zimbabwe?: if inflation is much higher, then the real price of gold must have fallen even more no? (c) What would guarantee identical real price paths in all countries: APPP, RPPP, or what?

2. You hold a set of forward contracts on eur, against usd (=hc). Below I show you the forward prices in the contract; the current forward prices (if available) or at least the current spot rate and interest rates (if no forward is available for this time to maturity). Compute the fair value of the contracts. (a) Purchased: eur 1m 60 days (remaining). Historic rate: 1.350; current rate for same date: 1.500; risk-free rates (simple per annum): 3% in usd, 4% in eur. (b) Purchased: eur 2.5m 75 days (remaining). Historic rate: 1.300; current spot rate: 1.5025; risk-free rates (simple per annum): 3% in usd, 4% in eur. (c) Sold: eur 0.75m 180 days (remaining). Historic rate: 1.400; current rate for same date: 1.495; risk-free rates (simple per annum): 3% in usd, 4% in eur.

3. 60-day interest rate (simple, p.a.) are 3% at home (usd) and 4% abroad (eur). The spot rate moves from 1.000 to 1.001. (a) What is the return differential, and what is the corresponding prediction of the change in the forward rate? (b) What is the actual change in the forward rate? (c) What is the predicted change in the swap rate computed from the return differential? (d) What is the actual change in the swap rate?

4. 60-day interest rate (simple, p.a.) are 3% at home (usd) and 4% abroad (eur). The spot rate is 1.250. There are no spreads, as you probably noticed. (a) Check that investing eur 1m, hedged, returns as much as usd 1.25m (b) Check that if taxes are neutral, and the tax rate is 30%, also the after-tax returns are equal. (Yes, this is trivial.) (c) How much of the income from swapped eur is legally interest income and how much is capital gain or loss? (d) If you do not have to pay taxes on capital gains and cannot deduct capital losses, would you still be indifferent between usd deposits and swapped eur? A. The 6-month forward rate is

5. 60-day interest rate (simple, p.a.) are 3% at home (usd) and 4% abroad (eur). The spot rate is 1.250. (a) Check that borrowing eur 1m (=current proceeds, not future debt), hedged, costs as much as borrowing usd 1.25m (b) Check that if taxes are neutral, and the tax rate is 30%, also the after-tax costs are equal. (Yes, this is trivial.) (c) How much of the costs of bowwowing swapped eur is legally interest paid and how much is capital gain or loss? (d) If you do not have to pay taxes on capital gains and cannot deduct capital losses, would you still be indifferent between usd loans and swapped eur?

6. Groucho Marx, as Governor of Freedonia's central bank, has problems. He sees the value of his currency, the fdk, under constant attack from Rosor, a wealthy mutual-fund manager. Apparently, Rosor believes that the fdk will soon devalue from gbp 1.000 to 0.950. (a) Currently, both gbp and fdk interest rates are 6% p.a. By how much should Groucho change the one-year interest rate so as to stabilize the spot rate even if Rosor expects a spot rate of 0.950 in one year? Ignore the risk premiumthat is, take 0.950 to be the certainty equivalent. (b) If the interest-rate hike also affects Rosor's expectations about the future spot rate, in which direction would this be? Taking into account also this second-round effect, would Groucho have to increase the rate by more than your first calculation, or by less?

Which of the following are risks that arise when you hedge by buying a forward contract in imperfect financial markets? (a) Credit risk: the risk that the counterpart to a forward contract defaults. (b) Hedging risk: the risk that you are not able to find a counterpart for your forward contract if you want to close out early. (c) Reverse risk: the risk that results from a sudden unhedged position because the counterpart to your forward contract defaults. So if you then close out (to reverse the position) you might already have lost money, i.e. reversing may mean you lock in a loss. (d) Spot rate risk: the risk that the spot rate has changed once you have signed a forward contract.