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# How do I convert a FMV Lease Rate Factor into an Interest Rate Percentage?

Launcher Kiffer3
Status Closed Mediated Closed 1 year, 4 months ago
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Financial Calculations Maths

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Hello & thank you for you interest & participation in this post.

I am interested in finding out the Interest Rate on a 60 month Fair Market Value Lease. The total cost of equipment is $35,000 with a Lease Rate Factor of .02120. It is for 4 black & white copiers brand new. I do not know the buyout of the previous leased equipment. My question is, what is the Formula to convert the Lease Rate Factor into an Interest Rate Percentage & what is the actual Interest Rate Percentage? ### Answers (1) • Sep 05, 2013 Hello, I have done a very basic job of it assuming that the fair market value at the end of the 5 year term will be zero (FMV = 0). I have calculated the annual lease rate which can be made equivalent to the annual interest rate. If you require more complex work, please send more details of what you require. Total amount to be paid over the lease period (TA) = Monthly lease payment x number of months; TA = (35,000 x 0.0212) x 60 = 742 x 60 = 44,520……………..(i) Total financial charge (TFC) = TA – Financed amount (FA) = 44,520 – 35,000 = 9,520……………………(ii) Financial charge per year (FCA) = TFC/(Number of years) = 9,520/5 = 1,904……(iii) Annual lease rate (ALR) = FCA/FA x 100 = 1,904/35,000 x 100 = 5.44%................(iv) Sumanta. Comments for results No comments yet. ### Clarifications Q: Hello again, I have another scenario for the residual case. In the previous instances, I have not considered the lesser taking back the copiers after the lease term is over. Since they will remain with you, the residual value will be made beneficial to you. In case the copier lesser agrees to take back the copiers at an accepted value of$2,275 at the end of the 60 month lease term, the following calculations become applicable.

FMC = (35,000 – 2,275) x 0.02128 = $696.40 In this case, the value the lesser is allowing you to use is the copier cost less the residual value as the copiers will be taken back after the term period. Total financial outgo = 696.4 x 60 = 41,783.28 The financial charge = 41,783.28 – 32,725 = 9,058.28 Financial charge (annualized) = (9,058.28)/5 = 1,811.66 Annual lease interest rate = 1811.66/32725 x 100 = 5.536% In this case again, the money factor will be – 5.536/2400 = 0.0023067 Please note that, in all cases, as there is no special provision for the money factor as per the lesser’s terms in your particular case, the money factor should not be made applicable. Thus, while I have academically illustrated your case with the money factor calculations, in real life you should seek advise of the equipment or automobile lesser before going for money factor calculations. Only if it is made applicable to a particular case should it be calculated on the basis of what I have shown you here and what you may have learnt elsewhere. Thanks, It’s been a pleasure working for you, Sumanta/ Asked by Sumanta Sanyal on Oct 10, 2013 A: No answer yet. Q: Hello, I have answered your questions. they are as below. I hope you will make a fast decision on my reward as we have festivities ahead this week in India and some money will help immensely. I am taking your questions one at a time. Firstly, as I have answered before, 1. Residual Value: On a simple basis, The net capital cost + residual value = 35,000 + 2,275 = 37,275 From my previous answer, all terms and conditions remaining constant, Financial charge per annum = 1,904. Therefore, interest rate on an annual basis = 1904/37275 x 100 = 5.108% In effect, this is slightly less than the rate found earlier at 5.44%. So. You benefit if some residual value remains and terms and conditions remain the same. You should also know the following. If you want to calculate the net financial charge on a monthly basis (FCM), the following has to be done – FCM = (Net capital cost + residual) x lease rate factor; It may be noted here that the residual is being added to the net capital costs, here$35,000. This is because, actually, you are being financed not only with the net capital cost but also the residual value which will be all yours after the lease payments are over. The US tax laws have quite complicated instructions for these and you should consult a tax lawyer for that. Anyway, leasing companies take everything into consideration when they make out the deeds.

The lease rate factor as in my previous work gives, FMC = (35,000 + 2,275) x 0.02128 = $793.212; From my previous answer, the net monthly lease payments may remain at$742, if you have negotiated with the dealer, but you can charge your account with the larger financial outgo as you are entitled to the benefit from charging the excess amount to your expenses but please consult a lawyer before doing so.

The excess monthly charge will be – 793.212 – 742 = $51.21. This additional benefit will accrue to you monthly if you can get the dealer to stick to the old rates when there was no residual left. For the entire 60 month period, the total additional benefit = 51.21 x 60 = 3,072.60 Of this,$2,275 will be credited to the copier assets account as the residual value amount at the end of the lease period. The remaining 3,072.6 – 2,275 = $797.6 will be the financial interest benefit accrued to the asset account. The total asset value at the end of the lease period can be$3,072.6 but you need to consult before you take steps.

Your net interest rate will apparently change as follows –

Total financial outgo – 793.21 x 60 = 46,320

Net capital cost depreciated during the period – 35,000 + 2,275 = 37,275

Financial charge = 46,320 – 37,275 = 9045

Annualized financial charge = 9045/5 = 1,809

Annual lease interest rate = 1809/37275 x 100 = 4.85%

II. Money Factor:

I am dealing with this in a simplistic manner. If you have the annual financial charge (FCA, see my previous answer though no residual value is taken previously) at simple interest without any other hidden financial costs as –

FCA = (C+F)r/2; where C is the initial capital cost (in the case of the copiers - $35,000) and F is the residual value ($2,275), and r/2 is the money factor (or lease factor) on an annualized basis.
Taking the money factor as m = r/2, it is noted that it is on an annualized basis and in decimals. To get the money factor on a monthly basis in percentage points, the following has to be done –

m = r/(2 ×12 ×100) = r/2400;

Since r is the annualized percentage rate, from the above equation,

r (the APR) = m x 2400.

III. The lease rate factor:

Previously, in the equipment leasing situation, even without considering the residual value, the lease rate factor at 0.02128 is actually the monthly interest charged together with the monthly asset value installments. In actuality, the annual lease rate interest (5.44%) from my previous work, which is a pure interest charge without any asset value installment in it, should be used to get the money factor for the lease in the old terms,

Money factor for the old terms as in my previous work = 5.44/2,400 = .002267

Since the money factor has to be multiplied with 2400, the interest rate has to be divided, as already explained in (II) above.

Similarly, the money factor for the new terms as in (I) above for the new lease rate interest is as follows – Money factor for the new terms = 4.85/2400 = 0.002021

Please note that the money factor decreases with the interest rates and vice versa.

I hope that suffices. I again request you to please make a fast decision on my reward.

Thanks,

Sumanta.

Asked by Sumanta Sanyal on Oct 09, 2013

A:
No answer yet.
Q:

Hello,

This is Sumanta. I would like to ask if my answer has satisfied you. If so, can the reward be allotted to me?

Sumanta.

Asked by Sumanta Sanyal on Sep 14, 2013

A:

Hello Sumanta,

Sorry for the delayed response.

I was able to find the interest rate, but I still want to reward you for your efforts. 1st a couple of questions.

1.) Lets assume the residual value is \$2,275. What is the new APR?

2.) is the money factor the same product for a car lease as the money factor for an equipment lease? Supposedly, you can take the money factor for a car lease (.003) & multiply it by 2400 & that will give you an APR of 7.2%. What makes 2400 the magic number?

When you do the same for an equipment lease, it comes out to 51.072 .02128 x 2400= 51.072

Am I missing something?

Thank you very much for your time!

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