Time is Money

Time is Money (Time Value of Money)

This week’s Skype session did not have any set agenda. “How are you doing in your studies, you must be enjoying your college life”, I asked Apurva. “Well college life has been exciting for last 2 months but I have my exams starting from next week and I have not started studying. Time is running out and as they say, Time is Money, and if that is true, I have already lost lots of it”, she laughed. “There is a reason behind why they say Time is Money let us discuss that today”, I said. It was time to refresh Corporate Finance lectures that I had taken during the MBA program.

“If I offer you ₹ 100 today and ₹ 105 after one year, which one will you accept?” I asked. “I will accept both”, said Apurva with a huge smile on her face. This answer of hers reminded me that I was dealing with a talented yet very notorious cousin of mine and I had to be very specific in my questions. “I wish I could offer you both but you have to select between either of the choices”, I told her. “If I accept ₹100 today I loose on ₹5 but one year time frame is too long, you might forget about our deal in 1 years’ time which is very risky. I am confused but I trust my brother who is doing his MBA from an IIM so will go for ₹ 105”, she said. “Well that is not how decisions are made in real life, since the cash you are being offered is during two different time periods, it cannot be compared directly as value of money changes with time”, I started explaining her.

Money today is not same as money tomorrow it is actually worth more than in the future. Between ₹100 today and ₹100 one year after, ₹ 100 today is more valuable. In the offer that I made to you, it becomes even more difficult to compare because you need to compare ₹100 with ₹ 105 after one year which is comparing Apple with Oranges. Hence in order to compare the same, we need to compare both of them on a single time period which can be either one year hence or today. Let us compare them one year hence. What will be the value of the ₹ 100 today after one year? It depends on the earning potential of ₹100. You can put ₹100 today in the bank account with 4% saving rate which will give you ₹ 104 after 1 year or you can put it in a Bank FD for 1 year with the bank rate of 9% and get ₹ 109. If you are like Warren Buffet, the ace investor, you can also invest the amount in the equity market and get possible 15% return i.e. ₹ 115 , but  if the market performed badly the way it did in 2008 due to crisis you might see negative 15% return which will end up ₹ 85 in your hand after one year. Now the important thing is which of these will you compare with ₹ 105 which is confirmed amount that I will pay you if you decide to go for that option? Will it be ₹ 104(Saving), ₹109 (Fix Deposit), ₹ 115 (Equity when Good), ₹85 (Equity when Bad). If you consider saving/Equity when performed badly then ₹ 100 today is not a good option as its value one year hence is less than ₹ 105 and if you consider Fix deposit or Equity performance during good times, ₹ 100 today is good option as its value after one year is more than ₹ 105.

“It is like a KBC question with four options, do I get any lifeline? I go with a “Skypofriend” and would want to get this answer from my MBA cousin brother”, Apurva with a smile on her face again, managed to have a go at me yet again. She was in tremendous form today I thought. “The correct answer will be ₹ 109, please lock it”, I continued with a smile. We need to see a risk free opportunity with a maximum earning potential. The equity option with 15% return is maximum earning opportunity but has tremendous risk involved in it while the 4% saving rate is risk free but not maximum. Hence given the options fixed deposit rate is the maximum earning risk free opportunity and should be considered and with 9% rate ₹100 today, due to compounding it would be ₹ 100*1.09 i.e. ₹ 109 which is greater than ₹ 105 and hence it is wiser to accept ₹ 100 today than accepting ₹ 105 after one year.  Instead of giving 105 after one year if I would have given you ₹ 50 in year 1 and ₹ 60 in year two it becomes slightly more complicated. Now you have to compare all the cash flow in year 2. So ₹ 100 two years from now would be ₹ 100*(1.09)² i.e. ₹118.8 due to compounding. ₹ 50 would be would ₹ 50*1.09 i.e.₹ 54.5, due to compounding of 1 year. So now you are comparing ₹ 118.8 with ₹ (54.5+60=114.5). Since ₹118.8 is greater than ₹ 114.5, you would go for ₹ 100 today.

Now instead of comparing both the options in future time period it is better to compare them as of today since you have to make the decision today. The final result would be same but it is more meaningful for decision making. It means to compare between ₹ 100 today and ₹ 105 one year hence, instead of finding out value of ₹ 100 one year hence and comparing it with ₹ 105, now you need to find present value of ₹105 which you will receive one year hence. The way we did compounding in earlier case now we need to discount the future payment to the present value and compare. With the same 9% rate we now need to discount ₹ 105 which would be received one year hence to today. Hence sometimes 9% is also called as discount rate. To discount 105 to present value we need to divide 105 by 1.09 which is ₹ 96.33. Now it is ₹ 100 today vs. ₹ 96.33 today and obvious choice is ₹ 100 today. In the second example we discussed we would have to discount (divide) ₹ 50 by factor of 1.09 (i.e. ₹ 45.87) and ₹ 60 by factor of (1.09)² (i.e. 50.5) total of which comes out to be ₹96.37 (50.5+45.87=96.37) and it is less that 100 hence you would select ₹ 100 today. The end result is same as we had got earlier.

Managers of the large corporations use this method to select the project. They compare the initial investment that they would make in the project against the cash flow that the project would generate in future. If the sum of the discounted future cash flow to present is greater than the initial investment then they would go for the project. The important thing here to note is the real world situation is slightly more complicated as the discount rate we discussed does not remain constant. Manager of corporations need to predict these future discount rates as per the macro economic conditions and continuously check the viability of the project.

“I now understand how to compare different cash flow occurring at different time intervals. It was interesting to know that money cannot be compared on absolute terms in isolation with time. Indeed “Time is Money”, said Apurva. I wished her all the luck for her upcoming exams and ended the call on that note.

Image Reference: http://www.aziende-news.com/valore-del-tempo/