A company is planning to expand its business in a few years. New plant construction costs are estimated to be $4.75 per square foot. The company invests $850,000 today at 6% compounded quarterly/
a) How many square feet could be built in 3 1/2 years?
b) If the company waits for a total of five years, the construction costs increase to $5.10 per square foot. How many square feet could they build if they waited a total of five years?
c) What would you recommend that the company do and why?
How about giving this one a try ?
To solve these questions, we need to use the future value formula for compound interest.
The future value formula is:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value
PV = Present Value
r = Interest Rate
n = Number of times interest is compounded per year
t = Number of years
a) To find how many square feet could be built in 3 1/2 years, we need to calculate the future value of the $850,000 investment after 3 1/2 years.
Using the formula:
PV = $850,000
r = 6% = 0.06
n = 4 (compounded quarterly)
t = 3.5
FV = $850,000 * (1 + 0.06/4)^(4*3.5)
Calculating this will give us the Future Value (FV). Dividing the FV by the construction cost per square foot will give us the number of square feet that can be built.
b) Similarly, if the company waits for a total of five years, we need to calculate the future value at the increased construction cost.
PV = $850,000
r = 6% = 0.06
n = 4 (compounded quarterly)
t = 5
FV = $850,000 * (1 + 0.06/4)^(4*5)
Calculating this will give us the Future Value (FV). Again, dividing the FV by the construction cost per square foot will give us the number of square feet that can be built.
c) To recommend what the company should do, compare the number of square feet they can build in 3 1/2 years to the number of square feet they can build in 5 years. The option that allows them to build more square feet will be more favorable.
If the company can build more square feet by waiting for 5 years, it would be recommended to wait. However, if the difference is not substantial, the company could consider other factors such as demand, market conditions, and potential revenue, before making a decision.