The next effective tactics we are going to look at is their ability to shift you from purchasing assets out of retained earnings, thru savings or cash, whatever you want to call it, over into actually borrowing money in order to finance the purchase of assets. So what we are going to be doing is using the same $10,000 car that we used in the example before and using that $10,000 car, as the purchasing of the vehicle with cash, we are going to go ahead and create an analysis of the purchase of the vehicle with a loan. Essentially, what we are going to do is, evaluate this with PW criteria. We are going to pick the one with PW closest to positive infinite.

So in the example we are going to have this $10,000 car, the cost basis, which is exactly what we had before. The other thing I am doing is that I am giving you a loan rate. We are not going to create a very special kind of loans; we do not have to every single month. What we are going to do is make it so you only have to make one loan payment a year, and your payments are going to be in the year after you purchased the vehicle. So what I’ve done here to figure out what the payment is used a spreadsheet function, which is payment (pmt(B17,5,B10)) in order to find what the payment is supposed to be, but you guys know that what you’re supposed to is find “A” given you know “P” (A/P,i,N). So the “P” in this case is $10,000 and you are looking for “A” given you know “P,” the interest rate is just the interest rate per payment period, in this case that’s an annual rate, so it’s 7% and you’re going to be making just 5 payments on this particular car.

So were going to spread out the loan over which you depreciate the asset. So your annual payments are $2,438.91 and what I have created over here is an amortization table. So here are the years and notice that the first year you do not make any payments and here are those identical payments every single year after that you make. And what I have done is expanded it out so that you can actually see what is the interest expense, what is the principle payment, and what is the balance remaining. And we need to split these guys up, although this is the payment you make, this interest expense is the only part that shows up on your Income Statement. And so what I’ve done is said, well look, you have originally borrowed $10,000, there’s what the payment is and if you recall, how you calculate the interest expense is you multiply the balance remaining, which is $10,000 times that loan rate per payment period. That gets you to the interest expense that is contained within the full payment. In this case, out of the payment of $2,438.91, $700 of that is interest, which later on will be used to reduce your taxable income. The balance, and I mean that literally all I am doing is taking the payment less the interest expense, is going to give the principle payment. And that goes toward withering away how much you borrowed. So what you do then to find out the balance remaining after the first payment is, you just take you balance remaining and subtract off the principle payment. And that is how much you owe after you have made your first payment. And you do similar things with each payment thereafter. If you look at the interest expense here in your 2nd payment, all that you’re doing is taking the balance remaining from after you’ve made your 1st payment and multiplying it by the interest rate right here and that gives you the interest expense in that 2nd payment. So again, principle payment is just the difference between interest expense and payment. And then what you are doing is subtracting that principle payment from the previous years’ balance remaining to get the new balance remaining. And since this is a fully amortizing loan, the balance remaining goes to zero, as you make your last payment. So this right here is your full amortization table and we are only going to be using this interest expense, as well as this payment series.

So let us zoom on up really fast to go ahead and take a look at our analysis of what happens cause of taxes here. And I’ve laid out the years, just as we had in the previous example and instead of having a $10,000 purchase right here, what we’re going to see is negative cash flows for all these payments you’re making. So these are exactly these same payments down here. So if you were looking at this in a personal finance basis, you can see these negative cash flows and you can also calculate what the PW of that is at the MARR of 5%, something we have done before. So just remember that in a personal finance basis, if you paid cash for this, the PW would be $10,000 and if you go ahead and finance it with this kind of loan, it has a PW of negative $10,559.19. From a personal finance point of view, you would rather pay cash for this vehicle rather than take out a loan. You are going to see that is different in a business context.

Now, this stream of depreciation is exactly the same as in our example when we purchased with cash. Just because your financing the car does not mean that depreciation changes. It remains exactly the same. This is still going to be an additional expense, which is going to reduce your taxable income, which is going to reduce your taxes. There is, however, this additional interest expense because you took out a loan, and that is the interest expense. So what we have is just that interest expense off of the amortization table and so you know that the 1st time you make a payment, it will cost you $700 in interest and so on down the line. So, because we now have these two sources of expenses because you purchase this vehicle, the additional interest expense is there because you financed the asset, you’re going to have some larger tax savings than you did when it was just a cash purchase. So what I have here is, and I will just show you the formula (=(C3+D3)*$B$15), is that I am just adding in those two expenses and I am multiplying it by that combined tax rate that we calculated before. And this is going to be the reduction in taxes that are there because those expenses reduced your taxable income, therefore reduced your taxes. And you can check out the After-Tax Cash Flows because you have gone ahead and collected those tax savings. So all I am doing here in this case, is saying, “here’s what your pre-tax cash flow is” and adding to it the tax saving, that’s column E, producing your After-Tax Cash Flow when you purchased this vehicle. Now, know the 1st year, you have a positive After-Tax Cash Flow and after that negative increments.

You can contract with what you have on the asset cash purchase, right back over here. We had negative cash flows in the year purchased and then positive cash flows. But please note that the numbers here are smoothed out a bit. I have gone ahead and used that MARR to find the PW of these cash flows. And I find that the PW of these cash flows is -$6,102.44. Now, you can compare that with what we calculated for the PW of these cash flows when you purchased with cash, that -$6,316.21, I just transferred it over there. And what you see is that the PW of purchasing this asset with a loan, rather than cash, is closer to positive infinite. So from a business point of view, you would rather take out a loan in order to finance the purchase of this vehicle than to pay for it in cash. It simply makes better financial sense. Now, it seems contradictory, but it has to do with that interest expense reducing your taxable income. And it is something else that does not really happen in a personal finance context. Now if you want a rough guide on when that interest expense is going to, uhh, that interest rate is going to be beneficial to you, there is idea of a pre-tax and post-tax rate. Let me give you a quick example, cause you notice that the loan rate was only 7%, you still, which 7% is larger than the MARR of 5%, and you still kind of went for it. Well, you can alter this thing around to like 9% (the loan rate), and everything recalculates. And it is not quite right. You can alter this to 8%, there you go, and you still want to go ahead and take the loan.

But the idea is that these two interest rates, that 8% loan and that 5% MARR, are not exactly comparable. The 5% rate is an after-tax rate and the 8% rate is a pre-tax rate. And so you can kind of approximately take your loan rate, your pre-tax rate, and turn it into an after-tax rate by just going ahead and taking that loan rate and multiplying it by one less your combined tax rate (=B17*(1-B15)). And that roughly converts it into an after-tax rate, enough so you can make a comparison and say “well look, the after-tax rate on this loan”, this 8% loan is 4.79%, which is less that 5%. It is probably a good idea. This approximation is approximate and works when you are dealing with some longer payment series, otherwise it falls short. Anyway, the main point to get across that in a business context, it often makes sense in order to finance the purchase of a vehicle in situations where in personal finance context you would not think about doing.