Question

Mary, the plant manager of Southern Oregon Injection Molding, Inc. (SOIM), is pondering an interesting offer made by the president and majority shareholder, Kenny. Kenny recently turned sixty and is planning a gradual retirement. None of his children are interested in taking over the business and are currently pursuing careers unrelated to the plastics industry, so Kenny has decided to offer his controlling share to Mary.

SOIM began by manufacturing plastic lawn ornaments, including a colorful tropical bird that became a major fad in the 1980s. Pleased and amused by the success of his fanciful product, Kenny added rabbits, skunks, trolls, angels, and garden fairies to the product line. Under Mary’s leadership, SOIM has also become an important secondary supplier of plastic housings for speakers, cell phones, calculators, and similar products.

Marry started working at SOIM as a color technician shortly after graduating from Southern Oregon University with a degree in chemical engineering. Within five years, she became the plant manager, a position she has held for the last eight years. Along the way, she has earned an MBA through the evening program at Southern Oregon University.

Because SOIM stock is publicly traded, we can confidently assign a value of $10,000,000 to Kenny’s shares. Kenny has stated that he is open to any reasonable plan to finance the purchase.

Questions

1. Mary could probably borrow the money to purchase the shares outright because the shares would serve as collateral and dividends would cover a good part of the loan payments. The interest rate is 7%, and the lender will amortize the loan with a series of equal payments. What are the annual payments if the bank amortizes the loan over five, ten, or twenty years?

2. Repeat Question 1, but assume that Mary makes payments at the beginning of each year.

Answer 1

1). Interest rate r = 7%; Principal P = 10,000,000; n = 5, 10 or 15 years; payments are made annually. Annual payments can be found using PMT function or using PV of annuity formula.

P = PMT*(1 -(1+r)^-n)/r

PMT = (P*r)/(1 -(1+r)^-n)

PMT (with n = 5) = (10,000,000*7%)/(1-(1+7%)^-5) = 70,000/0.2870 = 243,890.69

PMT (with n = 10) = (10,000,000*7%)/(1-(1+7%)^-10) = 70,000/0.4917 = 142,377.50

PMT (with n = 15) = (10,000,000*7%)/(1-(1+7%)^-15) = 70,000/0.6376 = 109,794.62

2). If annual payments are made at the beginning of the year, then PMT can be found using the annuity due formula:

P = PMT*[1 + (1 -(1+r)^-(n-1))/r]

PMT = P/[1 + (1 -(1+r)^-(n-1))/r]

PMT (with n = 5) = 10,000,000/[1 + ((1-(1+7%)^-(5-1))/7%] = 10,000,000/1.2371 = 808,338.96

PMT (with n = 10) = 10,000,000/[1 + ((1-(1+7%)^-(10-1))/7%] = 10,000,000/1.4561 = 686,781.93

PMT (with n = 15) = 10,000,000/[1 + ((1-(1+7%)^-(15-1))/7%] = 10,000,000/1.6122 = 620,277.07