Applegate Industries is planning to expand its production facility in a few years. New plant construction costs are estimated to be $4.50 per square foot. The company invests $850,000 today at 8% interest compounded quarterly. How many square feet of new facility could be built after 3.5 years? If the company waits 5 years and construction costs increase to $5.25 per square foot, how many square feet could be built? What do you recommend?

Question

Applegate Industries is planning to expand its production facility in a few years. New plant construction costs are estimated to be $4.50 per square foot. The company invests $850,000 today at 8% interest compounded quarterly. How many square feet of new facility could be built after 3.5 years? If the company waits 5 years and construction costs increase to $5.25 per square foot, how many square feet could be built? What do you recommend?

Answer 1

To determine the number of square feet of new facility that could be built after 3.5 years, we need to calculate the future value of the investment at the end of the period.

First, let's calculate the future value of the investment after 3.5 years using the formula for compound interest:

Future Value = Present Value * (1 + interest rate / number of compounding periods)^(number of compounding periods * time)

Present Value = $850,000
Interest Rate = 8% or 0.08 (converted to decimal)
Number of compounding periods per year = 4 (quarterly compounding)
Time = 3.5 years

Future Value = 850,000 * (1 + 0.08 / 4)^(4 * 3.5)

Next, we can determine the total amount of money available for construction costs:

Total Funds = Future Value - Initial Investment

Now, let's calculate the number of square feet that could be built:

Square Feet = Total Funds / Construction Cost per Square Foot

With this information, we can calculate the number of square feet that could be built after 3.5 years.

To calculate the number of square feet that could be built after 5 years, we'll follow the same steps but using the new construction cost per square foot of $5.25.

Finally, we can compare the two scenarios and provide a recommendation.

Let's do the calculations one step at a time:

Step 1: Calculate the Future Value after 3.5 years
Future Value = $850,000 * (1 + 0.08 / 4)^(4 * 3.5)
Future Value ≈ $1,014,381.10

Step 2: Calculate the Total Funds available for construction costs after 3.5 years
Total Funds = Future Value - Initial Investment
Total Funds = $1,014,381.10 - $850,000
Total Funds ≈ $164,381.10

Step 3: Calculate the number of Square Feet that could be built after 3.5 years
Square Feet = Total Funds / Construction Cost per Square Foot
Square Feet = $164,381.10 / $4.50
Square Feet ≈ 36,529.13

Step 4: Calculate the Future Value after 5 years
Future Value = $850,000 * (1 + 0.08 / 4)^(4 * 5)
Future Value ≈ $1,139,386.30

Step 5: Calculate the Total Funds available for construction costs after 5 years
Total Funds = Future Value - Initial Investment
Total Funds = $1,139,386.30 - $850,000
Total Funds ≈ $289,386.30

Step 6: Calculate the number of Square Feet that could be built after 5 years
Square Feet = Total Funds / Construction Cost per Square Foot
Square Feet = $289,386.30 / $5.25
Square Feet ≈ 55,034.36

Based on the calculations, after 3.5 years, Applegate Industries could build approximately 36,529.13 square feet of new facility. However, if the company waits for 5 years, they would have enough funds to build approximately 55,034.36 square feet.

The recommendation would be to wait for 5 years to maximize the funds available for construction costs and build a larger facility. The longer waiting period would result in a larger future value of the investment, allowing for a larger construction project.