# A Simple Query on Personal Finance - Purchase on Cash or Loan

Hi ,

I have a simple query , would appreciate if you guys can answer. Moderators please delete this post if you dont find this relevant to the community.

Query : -

Suppose I have 1 Lakh rs of cash in hand which I can invest for 7% CAGR after tax for 5 years. So as per my calculation after 5 years I will have 100000(1.07)^5 = 140255Rs.

Now if suppose I want to purchase a car and takes a car loan of 1 lakh rs at 9.5% , so my EMI comes out to be 2101 Rs per month. So in total I will pay 60*2101=126060 Rs in 5 years.

So my query is isnt it good to opt for a loan rather than paying in cash and invest the cash. Because net increase in value which I can see is 140255 (Cash inflow from investing) - 126060 (total cash outflow in paying EMI) = 14195 Rs.
This difference may increase if I am able to invest it at higher rate.

So what is beneficial in this case , purchasing the car by paying full cash of 1 lakh or taking a amortized car loan at 9.5% in which I have to pay absolute 26% more than 1 Lakh . i.e. 26060 Rs interest and invest my cash at 7% CAGR. If I calculate the I/Y for loan taking FV=126060 , PV=100000 CAGR comes around approx 5%

Can any one please correct me If I am going wrong somewehere in my calculations or missing something in my calculations. What should be the ideal case here.

Buying the car on cash or take a loan and invest equal amout.

I believe there is a flaw in calculation. Please calculate the total interest paid at 9.5% without paying the EMI. Otherwise in simple way please deduct the EMI amount from your 7% CAGR investment and calculate difference. Hope you understand.

In other words take the 2nd calculation you are paying 2101 per month for 5 years. If you invest same 2101 at RD at your conservative 7% interest the amount will be Rs.151134 compounding quarterly. and Rs.153145 calculating at 7.5% interest compounding quarterly. So actually you are paying Rs. 153145 amount to bank at current available interest rate.

So in your word FV=153145 PV=100000 CAGR will 9%. So your yield should be more than 9% after tax in comparison to bank loan. Please correct me if I am wrong.

What you said makes sense. But if the person has just that 1 lakh as savings for a rainy day and no other savings, then i would recommend going the EMI way. You dont want to end up in a financially weaker position by spending that 1 lakh right away.

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The car loan interest rate of 9.5% p.a. on reducing balance basis, is equivalent to a flat annual interest rate of appx. 5.25% (I derived this rate by trial and error, as below). I am assuming the EMI figure of 2101 is correct.

To expound a little:
Monthly repayment of principal amount of Rs 1 lakh over 60 months = Rs 1667 per month
Monthly interest payable at rate of 5.25% flat over 60 months = 1,00,000 * 5.25% / 12 = Rs 438 per month
Add both the above, and the monthly outgo = Rs 2105 (close to the EMI figure that you would be paying when interest rate if 9.5% reducing).

Simple Conclusion:
If, at the end of 1 year, you are able to generate a return on investment of more than 5.25%, then it makes sense to take the loan.

Sudhakar has taken it to the next level and inverted it, which is a great way of thinking. If I dont take the loan, then how much return I have to generate from the cashflows that I would have left with me. In both cases, loan option works out to be bett

Seen with very simple terms, you have 1 lac. You can either invest 1 lac or spend it (on car, holiday etc.).

What is not prudent is taking 1 lac loan while your networth (in spendable cash-terms) is 1 lac. So, youâ€™re playing with 2 lacs (1 lac your own and 1 lac borrowed).
If you take an EMI on car and invest your cash, in essence what you are doing is, you are â€śborrowing to investâ€ť.
God forbid, the market crashes and youâ€™re stuck with an overly reduced portfolio while still having to pay the interest; followed by all types of scary outcomes (impounding of your new car by bank etc.)

I, personally always spend/invest in my limits. I donâ€™t borrow a single paisa !!

My crazy conservatism apart, I do believe if you can generate real returns of more than 9% (Sudahkarâ€™s calculations above) yearly without losing sleep, you shall be fine.

@sammy11 Thanks for the comment. The effective rate is 5.25% for 9.5% reducing balance is due to the monthly payment of the principal. When someone has only 1L in hand and he is invested then the EMI outgo should come from the invested amount. Let us take a example.

I have 1Lac now. I do want to invest this money and take loan from the bank at 9.5% interest rate. My EMI for 5 years is Rs. 2101. I have to pay this EMI from my invested 1L and calculate the profit after 5 years.

If I invest 1L at Annuity at 10% growth My monthly receivable will be Rs. 2108 same as EMI payment. So that I can pay off my EMI.

So 9.5% monthly reducing balance comes to close to 10% growth. So atleast 10% after tax growth is required to match the EMI.

So I do not prefer for loan if it is not a liquidity concern. Please let me know If I have missed anything.

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Personal Finance is more to do with whether, can you afford the car or not? General behavior finance rules would say if the value of your car is more than 6 months salary combined, then there is something wrong in the thought process. EMI vs SIP is a very important question asked so I would post one of my articles on it
http://fin-kraft.com/2016/05/jack-or-jill/.

Another important part to note is that investment will give you return based on your method of selection. If you can only afford a 7.5% investment, there is no point in taking a 9.5% loan!

How can you make money by earning at 7% and spending at 9.5%? This is ridiculous! With the numbers you have given you are always better off paying in cash and avoiding the loan.

@soodhakar has worked out the numbers, you need to earn more than 10% (annual compounding) on your deposit for it to make sense to take the loan - the gap between 9.5% and 10% is because of monthly compounding vs annual; if your deposit also compounds monthly then you need the same 9.5% to be neutral between the two choices, and more than that to make sense to take the loan.

Let me try to reframe so that it is clear : the problem with your math is that you are not making a like to like comparision. In the second option where you take the loan, where is the money for the EMI coming from? Either you have to take it from the 1 lakh deposit, in which case you will see the money runs out before you repay the loan in 5 years, or you have some other income. To make it simpler let us assume you have salary of 2101 per month with which you can pay the EMI. But then to make it like to like, you have to include this salary into the first option working too, where there is no EMI and hence you can invest this salary.

So in reality your two options are (A) dont take the loan, pay 1 lakh in cash for the car, and invest the monthly salary of 2101 at 7% annual rate, or (B) take the loan at 9.5%, invest 1 lakh cash at 7%, and use the salary of 2101 to pay off EMI.

At the end of 5 years, option A will give you 150485 and option B will give you 100000(1.07)^5 = 140255â€¦ obviously not taking the loan is always better. Hope this is clear!

Simply put, you cannot make money by earning at a lower rate than spending. The only way to become a millionaire by spending more than you earn is to be a billionaire in the first place

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Most people have already pointed out the issues in your original post.

As a theoretical exercise, if you are confident that you can generate more returns than cost of capital (I.e rate of interest applicable to you) then you should leverage (I.e take the loan). In a perfect world, cash and credit can both be utilized as forms of payment, you can choose either.

Practically a few issues crop up though:

1. Debt is risk. The more you have, the riskier it is.
2. Black swan events can severely impact your debt repayment capacity or earning capacity. There is no margin of safety against black swan events. The only option is to diversify and pray.
3. There will be down payment, insurance, processing cost in addition to interest on the debt.
4. Emotionally, excessive debt can cause you health effects. These can be irreparable and if so the cost is enormous. There can be relationship effects also.

Debt can add discipline but take away freedom, judicious use of debt increases returns but requires a lot of maturity.