Question

Meadow Brook Manor would like to buy some additional land and build a new assisted living center. The anticipated total cost is $29 million. The CEO of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire construction project. Management has decided to save $1.4 million a quarter for this purpose. The firm earns 7 percent compounded quarterly on the funds it saves. How long does the company have to wait before expanding its operations?

5.36 years

3.96 years

4.46 years

7.26 years

8.46 years

Answer 1

Answer is “4.46 years”

Desired sum = $29,000,000
Quarterly Saving = $1,400,000

Annual Interest Rate = 7.00%
Quarterly Interest Rate = 7.00% / 4
Quarterly Interest Rate = 1.75%

Let it will take n quarters to reach the desired goal

$1,400,000 * FVA of $1 (1.75%, n) = $29,000,000

Using financial calculator:
I = 1.75%
PV = 0
PMT = -1400000
FV = 29000000

N = 17.83

Number of Quarters = 17.83

Number of Years = 17.83 / 4
Number of Years = 4.46

Therefore, the company have to wait for 4.46 years before expanding its operations.