A semiconductor firm is considering opening a new plant. The plant will generate profits of $100 million at the end of each of three years after the first year of production and then no profits after that. If the interest rate is 10%, what is the maximum cost (to the nearest million) the firm is willing to pay now for the plant?
A)$300 million
B)$249 million
C)$273 million
D)$100 million

Question

Quizplus · Accepted Answer

To calculate the maximum cost the firm is willing to pay now, we need to find the present value of the future profits at a discount rate of 10%.

Using the formula for present value of an annuity, we get:

PV = (Profits / (1 + r)^n) x ((1 - (1/(1 + r)^n))/r)

where PV is the present value, Profits is the annual profit, r is the discount rate, and n is the number of years.

Plugging in the values, we get:

PV = (100 / (1 + 0.1)^1) x ((1 - (1/(1 + 0.1)^3))/0.1)
PV = 247.68 million(approximately)

Therefore, the maximum cost the firm is willing to pay now is $249 million (rounded to the nearest million) which is option B.

A Semiconductor Firm Is Considering Opening a New Plant