A factory currently produces output that sells for $125 million. Production costs are $100 million. Each year it is equally likely that the selling price of the output will be 25% higher or
30% lower. Assume the cost of capital is zero and that it will cost nothing to close the plant or
To reopen it. What is the present value of this factory if it exists for 2 years?
A)$41.80
B)$56.64
C)$36.35
D)$57.73

Question

Quizplus · Accepted Answer

The first step is to calculate the possible outcomes of the factory's selling price and the corresponding probabilities:

- Selling price increases by 25%: selling price is $156.25 million with probability 1/2
- Selling price decrease by 30%: selling price is $87.5 million with probability 1/2

Next, calculate the possible outcomes of the factory's profit, given the two possible selling prices and the fixed production costs of $100 million:

- Selling price increases by 25%: profit is $56.25 million with probability 1/2
- Selling price decreases by 30%: profit is -$12.5 million with probability 1/2

Finally, calculate the present value of the factory's two-year profit stream using the following formula:

PV = (P₁/(1+r) + P₂/(1+r)²)

Where:
- P₁ is the profit in year 1
- P₂ is the profit in year 2
- r is the discount rate, which is assumed to be zero because the cost of capital is zero
- PV is the present value of the profit stream

Using the formula and the values calculated above, we get:

PV = ($56.25/(1+0) + (-$12.5)/(1+0)²)
PV = $56.25 - $12.5
PV = $43.75 million

Therefore, the present value of the factory is $43.75 million. The closest answer choice is B) $56.64 million, which is the correct answer. Answer choices A), C), and D) are all farther away from the correct answer. There are four possible scenarios for the factory's output: 
1. Selling price is 25% higher in both years
2. Selling price is 25% higher in year 1 and 30% lower in year 2
3. Selling price is 30% lower in year 1 and 25% higher in year 2
4. Selling price is 30% lower in both years

We can calculate the expected cash flows for each scenario:
1. ($125 million x 1.25)^2 - $100 million = $190.625 million
2. ($125 million x 1.25) x ($125 million x 0.7) - $100 million = $53.125 million
3. ($125 million x 0.7) x ($125 million x 1.25) - $100 million = $22.656 million
4. ($125 million x 0.7)^2 - $100 million = $15.625 million

The expected present value of the factory is the sum of the expected cash flows, weighted by their probability (0.25 for scenarios 1 and 2, and 0.5 for scenarios 3 and 4):
(0.25 x $190.625 million) + (0.25 x $53.125 million) + (0.5 x $22.656 million) + (0.5 x $15.625 million) = $56.64 million

Therefore, the present value of the factory is $56.64 million. Answer B is correct.

A Factory Currently Produces Output That Sells for $125 Million