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 machinery. 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 present value.

For example:

Future payment = $10,000 three years from now

Present value = $10,000 / (1.06 x 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 payment = purchase price x 80% x amortization factor = $_______________*

*Round values to the nearest whole dollar.

Alternative 3. Lease the tractor for 4 years, then purchase it for the buyout price (see Table 1). Lease payments are due at the beginning of each year.

Comparison

Under which plan do you pay the most total dollars, before discounting? _______________________

Which alternative plan has the lowest present value, after discounting? __________________________

Which has the lowest payment at the time of purchase? _______________________________________

Which financing alternative would you choose, and why? _________________________________________

________________________________________________________________________________________

________________________________________________________________________________________

Answer 1

Alternative 1		64500
Alternative 2		Annual payment		64500*80%*.29857			15406
Alternative 3		Annual payment		12250
Under which plan do you pay the most total dollars, before discounting?
Alternative 1		64500
Alternative 2		74525
Alternative 3		79000
Most dollars paid in leasing (Alternative 3)
Which alternative plan has the lowest present value, after discounting?
Alternative 1		64500
Alternative 2		66283		20%*64500-PV(6%,4,15406,,)
Alternative 3		68757		12250-PV(6%,3,12250,,)+30000/1.06^4
Alternative 1 has lowest PV
Which has the lowest payment at the time of purchase?
Alternative 1		64500
Alternative 2		12900
Alternative 3		30000
Lowest payment is of Alternative 2
I would chose alternative 1 as it has lowest cost based on PV terms