Question

Winston Enterprises would like to buy some additional land and build a new factory. The anticipated total cost is $158.82 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 $590,000 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.)

Answer 1

Winston Enterprises needs to calculate the time needed to save $158.82 million at a 6 percent annual interest rate compounded monthly, saving $590,000 each month. We use the future value of an annuity formula for this purpose. The time frame can be calculated by solving for the number of monthly payments in the compound interest formula.

Step-by-step explanation:

The question concerns the length of time it will take for Winston Enterprises to save enough money to pay cash for a new factory expansion, given their monthly savings and an interest rate of 6 percent compounded monthly. To solve this problem, we apply the future value formula for compound interest. This is a typical business scenario where a firm is planning for expansion by investing in new equipment or facilities and making financial decisions based on its ability to fund such investments without seeking external financing.

To calculate the time frame for the savings to reach $158.82 million, we would use the formula for the future value of an annuity with monthly compounding interest: FV = P * [((1 + r)^n - 1) / r], where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of payments. The solution would require finding the number of months (n) that satisfies the equation, given that P = $590,000, r = 0.06/12 per month, and FV = $158.82 million.

Answer 2

Answer: 170.69

Step-by-step explanation:

Given that,

Anticipated total cost (Future value) = $158.82 million

= $158,820,000

Saving per month = $590,000

Interest received on savings = 6 percent (compounded monthly)

Future value = $158,820,000

`saving\ amount*((1+(r)/(12) )^(n-1) )/((r)/(12))`

`590,000*((1+(0.06)/(12) )^(n-1) )/((0.06)/(12))`

`((1.005)^(n-1))/(0.005)=269.1864`

Therefore,

n = 170.69 months

Company have to wait before expanding its operations for 170.69 months.