A manufacturing company is thinking about building a new factory.The factory,if built,will yield the company $300 million in 7 years,and it would cost $220 million today to build.The company will decide to build the factory if the interest rate is
A)no less than 4.53 percent.
B)no greater than 4.53 percent.
C)no less than 5.81 percent.
D)no greater than 5.81 percent.

Question

Quizplus · Accepted Answer

To decide whether it is profitable to build the factory, the company needs to calculate the present value of the future revenue minus the cost of building the factory. The calculation is as follows:

PV = (300 million / (1 + r)^7) - 220 million

where r is the interest rate.

To determine the interest rate that makes the PV equal to zero (i.e., the break-even point), we can solve for r:

0 = (300 million / (1 + r)^7) - 220 million

(1 + r)^7 = 300/220

1 + r = (300/220)^(1/7)

1 + r = 1.0453

r = 0.0453 or 4.53%

Therefore, the company will decide to build the factory if the interest rate is no greater than 4.53%. Any interest rate lower than 4.53% will make the project even more profitable.

The answer is therefore B: no greater than 4.53 percent.

A Manufacturing Company Is Thinking About Building a New Factory