1. (60 points) Consider a project of manufacturing and selling high-end smartwatches to wealthy customers. The...

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1. (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 4000 4000 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. (I.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. 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. 1. (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 4000 4000 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. (I.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. 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.