Question

Imagine that someone offers you $X today or $1,500 in 5 years. If the interest rate is 4 percent, then you would prefer to take the $X today if and only is ?

the answer is: X > 1,232.89

(please show your work)

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

the answer is: no greater than 4.53 percent (please show your work)

Answer 1

Answer 1:

Amount today = X

Amount after 5 years = 1500

Interest rate = 4%

An individual would prefer X today only of the value of 1500 after 5 years is less than X. It means

X > 1500/(1+0.04)^5

X > 1232.89

Answer 2:

Cost today = 220 million

Yield after 7 years = 300 million

The company will decide to build the factory if the value of the cost incurred after 7 years is less than 300.

Value of 220 after 7 years < 300

220*(1+i)^7 < 300

(1+i)^7 < 1.363636364

1+i < 1.0453

i < 0.453

i < 4.53%