Question

COMPARING TRACTOR FINANCING OPTIONS After land, machinery is often the largest single investment on a farm. Many dollars can be saved by carefully exploring all options for acquiring its use. The objective of this exercise is to compare three different plans for financing the purchase of a new tractor Financing Options A new tractor can be acquired by: 1. Outright purchase for cash, at a cost of $64,500. 2. Purchase by an installment contract with a down payment of 20 % of the purchase price and four equal annual payments, with a 7.5 % annual interest rate 3. A four-year lease plan with annual payments of $12,250 followed by a purchase at a buyout price of $30,000. Discounting future payments to their present value allows you to directly compare the financing plans. Each future payment is converted to a present value by dividing it by (1 +the discount rate) for each year into the future that it occurs. Assume your average cost of capital, minus inflation, is 6%, so you would use a factor of 1.06 per year to discount future payments to their I present value For example: Future payment $10,000 three years from now Present value $10.000(1.06x 1.06 x 1.06) $10,000/(1.06)3 $8,396 Alternative 1. Purchase tractor outright. There is no need to discount the payment, since it is made at the time of purchase. Purchase price $ Alternative 2. Pay 20 percent of the purchase price down and finance the remainder with 4 annual payments, beginning in one year. The amortization factor for a 4-year, 7.5 % interest loan is 29857 Annual paymcnt purchase price x 80% x amortization factor Present value Discount factor S before discounting 1.00 $ Down payment 1.06 $ 1st payment (in 1 year) (1.06)2 2nd payment (in 2 yxs) / (1.06)3 3rd payment (in 3 yrs)

Answer 1

Solution Alternative 1: Purchase Tractor outright Purchase Price $ 64500 Alternative 2 : Borrowing Down Payment Purchase Price X 20% 64500 X 20% 12900 $ Annual Payment Purchase Price X 80% X amortization factor 64500 X 80% X 0.29857 15406.21 before Discount Present Particulars depreciation factor value Down payment 12900 12900 $ 1st payment 15406.21 1.06 14534 2nd payment $ 15406.21 1.124 13711 3rd payment $ $ 12935 15406.21 1.191 4th payment 15406.21 1.262 12203 $ $ Total 74524.85 66283 Alternative 3 : Lease before Discount Present Particulars depreciation factor value 1st payment (now) 12250 12250 2nd payment (year 1) 12250 1.06 11557 $ 3rd payment (year 2) 10902 12250 1.124 $ 4th payment (year 3) 1.191 12250 10285 $ Buyout (year 4) 30000 1.262 23763 $ 79000 Total 68757 Comparision 1. Under Leasing most total dollars at $79000 is paid before Discounting. 2. Under Purchasing there is lowest present value at $64500 before Discounting. 3. Leasing has the lowest payment at 12500 at the time of purchase (meaning put to use) 4. We would chosse to purchase tractor outright as it has lowest present value at $64500