Financing Cash Purchase versus 0% Financing

[smstonypoint]

This posting is motivated buy a recent thread in which the merits of a cash purchase versus 0% financing were discussed. That discussion revealed some confusion/misunderstanding about how the choice between a cash purchase and 0% financing can be evaluated from an economic perspective. Old habits die hard, so if you will indulge a retired professor, I have perceived a "teachable moment."

http://www.tractorbynet.com/forums/k...nt-done-5.html

I will work through an example to show how "time value of money" concepts can be used to address the issue. I realize that some (many?) members may not be able to make a cash purchase of a large ticket item. However, the concepts can be applied to other choices.

This is a hypothetical example. You need to evaluate the decision based on your individual circumstances.

I chose a base model L2800 HST-1R for my example. Using the "Build My Kubota" tab at Kubota Tractor Corporation - Tractors | L Series | L2800 L3400 L4400, the MSRP is $15,042.

This model is eligible for either 0% downpayment, 0% interest for 60 months (Finance Promotional Rates) or a $1000 rebate for a cash purchase (Finance Customer Rebates).

Assuming that you have to pay the MSRP to qualify for the special financing, you would have to pay $15,042/60 months = $250.70 a month for each of the next 60 months. Assuming that you can't negotiate a lower price, you would be out $14,042 if you pay cash and take the rebate. [To keep things simple, I'm going to assume that you would pay any sales tax upfront if you finance. Thus, the sales tax is equivalent between the alternatives and can be ignored. I don't know anything about Kubota's requirements regarding insurance if you finance, so I will ignore them. However, the analysis can be modified to accommodate these items.]

A $1 today is worth more today than a $1 in the future if you can invest/ save the $1 today and earn a return/interest. To compare apples and apples, we need to compare the present values of the after-tax cash flows of financing versus a cash purchase.

The present value of the cash purchase outflow is $14,042. So what's the present value of the financing alternative? That involves constant periodic payments beginning next period and so is an ordinary annuity. You can use published annuity tables, a financial calculator, on-line calculators, spreadsheet software, etc. to find the present value.

I will use Excel. The syntax is =pv(periodic interest (discount) rate, # of periods, constant payment amount). The # of periods =60 and the constant payment amount is 250.70. The rub comes in determining the periodic discount rate. This is going to be unique for each individual according to his/her investment alternatives, the "riskiness" of those alternatives, and his/her marginal federal and state income tax rates. Note that the investment/savings opportunity has to allow for monthly withdrawals. A 5-year CD won't hack it.



I will use two alternatives to illustrate, 1% and 10% after-tax annual rates.
The present values are =pv(.01/12,60,250.7) = $14,666.18 and =pv(.1/12,60,250.7) = $11,799.29. Under the first case, it makes sense to pay cash: in the second case, it makes sense to finance.

The present values of the two alternatives are equal at an annual after-tax discount rate of 2.74% (rounded). Supposing your marginal federal/state income rate is 20%, this would correspond to a before-tax rate of 2.74%/.8 = 3.425%. So for this example, if you can earn more than 3.425% on your money before taxes, it pays to take the financing. If you earn less, the cash purchase makes sense.

If there are no questions, class is dismissed.

Steve

PS -- I'm getting old and suffer from senior moments. Please advise me of errors on my part. I'm used to being corrected, having been married for 40+years.

[TripleR]

Very interesting, thanks for posting.

[smstonypoint]

Very interesting, thanks for posting.

Please post any questions that you may have. I know it's a sickness, but I enjoy discussing financial economics.

Steve

[bigbull338]

ok i got a q for you.i pay cash for everything i buy.so when i bought my new Kubota i thought ok ill finance through kubota.well they ran my credit an said i had no credit.so whats the deal with that.

[tcartwri]

ok i got a q for you.i pay cash for everything i buy.so when i bought my new Kubota i thought ok ill finance through kubota.well they ran my credit an said i had no credit.so whats the deal with that.

If you don't use credit, or don't have regular loans that you pay, you will not have a fico score. I just went through this and it was a pain in the ***.

[smstonypoint]

ok i got a q for you.i pay cash for everything i buy.so when i bought my new Kubota i thought ok ill finance through kubota.well they ran my credit an said i had no credit.so whats the deal with that.

Sorry, I don't have a clue as to what the Kubota finance folks use for judging credit-worthiness. The only thing I can suggest is that you check your free annual reports at https://www.annualcreditreport.com/cra/index.jsp for any mistakes in your credit reports. You should report any mistakes and have them cleared up.

If there are no mistakes, you might want to investigate the means by which you can improve your FICO score. There are Web sites that provide tips in this regard.

I'm sorry that I can't provide any better info.

Steve

[Agrantina]

And I thought this was just a how to use a tractor forum.. Good post.. Question...If I had 3k to put down on a tractor would it be better to keep the 3k and try and earn more than 3% on it or use the 3k as a down payment? I guess this would not change your example... ?

AndyG

[bigbull338]

well we had it out with Kubota over it.an the kicker is i had just paid off a bank note 6 months earlier.so i called my banker an told her the deal,an she said write the check.so i made kubota take off $2000 for the intrest.so my banker said dont worry you can get a loan when you need it.

[smstonypoint]

Question...If I had 3k to put down on a tractor would it be better to keep the 3k and try and earn more than 3% on it or use the 3k as a down payment? I guess this would not change your example... ?

AndyG

Andy,

It would change the results. I will use 1% again to illustrate the mechanics for my example. The present value of the financing outflows would be calculated in Excel as =-3000 + PV(.01/12, 60, (15042-3000)/60). The result is $14,741.14, compared to $14,666.18 with no down payment.


There are several ways to calculate the "break-even" after-tax discount rate, but the easiest to describe is to just use trial and error in adjusting the periodic discount rate until you obtain a value of $14,042.

I hope that this helps.

Steve

[TripleR]

Please post any questions that you may have. I know it's a sickness, but I enjoy discussing financial economics.

Steve

Uh, thanks, I think it I have learned my lesson on posting about financial issues.