(60 points) Consider a project of manufacturing and selling high-end smartwatches to wealthy customers. The length of the project is 10 years. The industry demand for high-end smartwatches next year will be 1 million units, and every year it will either increase by 3% (with 50% probability) or decrease by 3% (with 50% probability). Your market share next year will be 5%, and every year it will either increase by 1%-point (with 50% probability) or decrease by 1%-point (with 50% probability), but your maximum capacity of annual production is 100,000 watches per year. (I.e., if your market share would grow to a level which would require producing more than 100,000 watches per year, it will be capped at the level corresponding to 100,000 watches per year. Then, next year, it will again either increase by 1%-point or decrease by 1%-point, with the same capacity constraint being in effect.) The initial cost of the project is $10 million, which is used to purchase the equipment necessary to manufacture smartwatches. This initial cost is amortized over a 5-year period using the straight-line method. Every year, the annual inflation will be either 1% (with 50% probability) or 2% (with 50% probability). In the first year, fixed costs will be $100,000, and every year they will increase by the inflation. In the first year, variable costs will be $200 per unit, and every year they will increase by the inflation. If your market share drops to 0%, you abandon the project and sell your equipment for its book value or 20% of its initial price (whichever is higher). At the end of the 10th year, you sell the equipment for 20% of its initial price (if you have not sold it earlier already). The price at which you can sell the watches depends on the industry-wide demand in that year (a higher demand leads to a higher price). Namely, the price per unit is equal to industry demand +x, where x is a random number taking a value in the interval [-50,50] and it follows a uniform distribution (i.e., it takes all value within the given interval with equal likelihood). In any case, the unit price never drops below the actual variable costs per unit. (l.e., if the unit price would be lower than the variable costs per unit based on the above formula, then the unit price will be equal to the variable costs per unit.) The corporate tax rate is 25%. Assume that every payment and cash flow happens at the end of the year. 4000 a (42 points) Assume that the project is financed by equity only. Simulate a random outcome where you calculate the total cash flow of the project for each year (from the 1st to the 10th year). Then, simulate altogether 30,000 such random outcomes. Then, calculate the expected cash flow for each year. Using these expected cash flows, calculate the internal rate of return (IRR) of the project. b (18 points) Assume that the IRR calculated in the previous question is the unlevered firm's expected return on the project. I.e., the project value (without considering the cost of the initial investment) for an unlevered company is exactly equal to $10 million. Now, assume that you can partially or fully finance the project by debt. Namely, you can take out a loan for a 10-year period at an interest rate of 10%. The principal must be paid back in one lump sum at the end of the 10th year. The flotation fee of the loan is equal to 5% of the total loan amount, and it must be paid up front. (E.g., if you borrow $100,000, then the $100,000 0.05 = $5,000 flotation fee is paid immediately to the bank, and you receive only $95,000. But you still owe the bank $100,000, you need to pay $100,000 0.1 = $10,000 interest every year, and you need to repay $100,000 at the end of the 10th year.) The flotation fee is amortized over a 10-year period using the straight-line method. You are also eligible to take out a government-subsidized loan with the same conditions, the only exception being that the interest rate on the subsidized loan is 7% instead of 10%. (Note: you still need to pay a 5% up- front flotation fee.) If you take out a loan, some of your customers will be worried that your firm might go bankrupt in the future (i.e., it will not be able to make the interest payment and the principal repayment) and it will not be able to fulfill its warranty obligations towards the customers. Hence, some of these potential customers eventually decide not to buy your firm's product. The more debt your firm takes out, the more customers become worried about your firm going bankrupt. As a result, in order to keep the market share each year as postulated previously, you will need to spend more money on marketing activities. Namely, if you take out not more than $2,000,000 in debt, you will have no extra marketing expenses; if you take out between $2,000,001 and $4,000,000 in debt, the net present value of your extra marketing expenses will be $200,000; if you take out between $4,000,001 and $6,000,000 in debt, the net present value of your extra marketing expenses will be $400,000; and if you take out more than $6,000,000 in debt, the net present value of your extra marketing expenses will be $900,000. (These net present values already take into account the tax saving effects arising due to the additional costs.) How much debt will your firm take out to finance the project, and how much of the $10,000,000 initial investment needs to be financed by your own equity? If you decide to take out some debt, will you take out a loan from a bank or will you take out the government-subsidized loan? What will be the value of your firm? What will be the value of the equity of your firm?