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/