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 4000 + 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.
1.
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.
