Question

In: Finance

Meadow Brook Manor would like to buy some additional land and build a new assisted living...

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 $1.4 million a quarter for this purpose. The firm earns 6 percent compounded quarterly on the funds it saves. How long does the company have to wait before expanding its operations?

a. 3.99 years b. 7.99 years c. 3.49 years d. 6.79 years e. 4.89 years

Can you show me how to do this in excel? Thank you

I would like to use a formula in excel to solve it.

Solutions

Expert Solution

Interest rate p.a. 6%
Year Quarter Quartlery Saving Principal for Interest calculation Interest for the quarter Accumulated Balance
Year 1 1 1,400,000             1,400,000       21,000       1,421,000
Year 1 2 1,400,000             2,821,000       42,315       2,863,315
Year 1 3 1,400,000             4,263,315       63,950       4,327,265
Year 1 4 1,400,000             5,727,265       85,909       5,813,174
Year 2 1 1,400,000             7,213,174     108,198       7,321,371
Year 2 2 1,400,000             8,721,371     130,821       8,852,192
Year 2 3 1,400,000           10,252,192     153,783     10,405,975
Year 2 4 1,400,000           11,805,975     177,090     11,983,064
Year 3 1 1,400,000           13,383,064     200,746     13,583,810
Year 3 2 1,400,000           14,983,810     224,757     15,208,567
Year 3 3 1,400,000           16,608,567     249,129     16,857,696
Year 3 4 1,400,000           18,257,696     273,865     18,531,561
Year 4 1 1,400,000           19,931,561     298,973     20,230,535
Year 4 2 1,400,000           21,630,535     324,458     21,954,993
Year 4 3 1,400,000           23,354,993     350,325     23,705,318
Year 4 4 1,400,000           25,105,318     376,580     25,481,898

Accumulated Balance = Principal for Interest Calculation + Interest for the quarter

Principal for Interest Calculation = Accumulated Balance of the previous quarter + Quarterly Savings

Quarter 3 accumulated balance of Year 4 is 23,705,318; Quarter 4 accumulated balance of Year 4 is 25,481,898. The earnings and investment in this quarter 4 is 25,481,898 - 23,705,318 = 1,776,580

The total cost of investment is 25,000,000. If the earning and investment for the entire quarter (i.e. for 0.25 years) is 1,776,580, to reach the 25,000,000, we have to find out at what time we will reach 1,294,682 (25,000,000 - 23,705,318), which is 0.25 / 1,776,580 * 1,294,682 = 0.18 years.

So in year 4, the required time is 3 quarters + 0.18 years, if converted into year = (0.25 x 3) + 0.18 = 0.93 years

Therefore the company has to wait for 3.93 years.


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