Stemway Company requires a new manufacturing facility. It found three locations; all of which would provide the needed capacity, the only difference is the price. Location A may be purchased for $500,000. Location B may be acquired with a down payment of $100,000 and annual payments at the end of each of the next twenty years of $50,000. Location C requires $40,000 payments at the beginning of each of the next twenty-five years. Assuming Stemway's borrowing costs are 8% per annum, which option is the least costly to the company?

Question

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To determine the least costly option, we need to calculate the present value (PV) of each option using the given borrowing cost of 8% per annum as the discount rate. - For Location A, the cost is straightforward: $500,000.- For Location B, we use the formula for the present value of an annuity because it involves equal payments at the end of each period. The PV formula for an annuity is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment, r is the interest rate per period, and n is the number of periods. The down payment is made today, so its present value is simply $100,000. The annuity's present value is the $50,000 annual payments for 20 years at 8%, which calculates to approximately $500,840. Adding the down payment, the total PV is about $600,840.- For Location C, since payments are made at the beginning of each period, it's considered an annuity due. The formula for the present value of an annuity due is PV = P * [(1 - (1 + r)^-n) / r] * (1 + r), where P, r, and n have the same meanings. The present value of $40,000 payments at the beginning of each of the next 25 years at 8% calculates to approximately $449,678.Comparing the present values, Location C is the least costly option for Stemway Company.

Stemway Company Requires a New Manufacturing Facility