Question

Meadow Brook Manor would like to buy some additional land and build a new assisted living center. The anticipated total cost is $25 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 $1.5 million a quarter for this purpose. The firm earns 5 percent compounded quarterly on the funds it saves. How long does the company have to wait before expanding its operations?

a. 3.31 years

b. 4.71 years

c 6.61 years

d. 7.81 years

e. 3.81 years

Answer 1

this is calculated using NPER function in Excel with these inputs :

rate = 5%/4 - the annual rate of 5% is converted into a quarterly rate by dividing by 4 as there are 4 quarters in a year

pmt = -1,500,000 - this is the quarterly savings amount

pv = zero - the starting cash balance is not given and is therefore assumed to be zero

fv = 2,500,000 - this is the target savings at the end of the period

NPER is calculated as 15.2338. This is the number of quarters required to save $25 million. To find the number of years, we divide this by 4

number of years taken = 3.81 years