MC Qu. 6-A10 Winston Enterprises would like to buy some additional land... Winst

Question

MC Qu. 6-A10 Winston Enterprises would like to buy some additional land...

Winston Enterprises would like to buy some additional land and build a new factory. The anticipated total cost is $171.6 million. The owner of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire expansion project. Management has decided to save $650,000 a month for this purpose. The firm earns 6 percent compounded monthly on the funds it saves. How long does the company have to wait before expanding its operations? (Do not round intermediate calculations.)

Winston Enterprises would like to buy some additional land and build a new factory. The anticipated total cost is $171.6 million. The owner of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire expansion project. Management has decided to save $650,000 a month for this purpose. The firm earns 6 percent compounded monthly on the funds it saves. How long does the company have to wait before expanding its operations? (Do not round intermediate calculations.)

Explanation / Answer

Solution :

Answer = 168.73 months

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Calculation shown below:

The future value of the annuity is calculated using the formula:

FV = A [ ( 1+r)n -1] /r

$ 171,600,000 = $ 650,000 [ ( 1+(0.06/12))12n-1] / 0.06/12

$ 171,600,000 = $ 650,000 [( 1.005)12n -1] / 0.005

[( 1.005)12n -1] / 0.005 = 264

[( 1.005)12n -1] = 1.32

1.00512n = 2.32

12n log 1.005 = log 2.32

12n = 168.73

n = 14.06 years

n = 168.73 months

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