we already know that money today is more
valuable than money tomorrow we should bear this in mind when adding
sums of money that will be received at different points in time
imagine the following cash flows which one is preferable do we want to
receive 100 and year 2 and 110 in year 3 4
alternatively a hundred and year one and a hundred and year two if we simply do
the math 210 is better than 200 so we should pick the first option this isn’t
necessarily true after we consider the time value of
money in finance we should never add sums of money without considering the
timing when the cash flow occurs this is very very important if I were to deposit
$100 in a bank I would expect the bank to compensate me for the right to use my
money let’s say that the money will stay in
the bank for a year and after one year the bank will repay me the initial
amount plus an interest of three percent so we will have future value equals
present value multiplied by the sum of one plus I where the present value is
the amount we are depositing and I is the interest rate that the bank will pay
us for depositing our money we would have future value equals a hundred
multiplied by the sum of one plus three percent equals one hundred and three
after one year we will receive one hundred and three dollars what if we
wanted to find the present value of a future cash flow how do we find the
present value of a cash flow that we will receive in the future starting from
the equation future value equals present value times the sum of one plus I we can
simply divide by the sum of one plus I and will obtain the present value equals
future value divided by the sum of one plus I
when we account for the time value of money in this way going backwards we
talk about discounting what if we wanted to make another
deposit after year one ends we would have a hundred times the sum of one plus
three percent which is the value at the end of year one and it will be deposited
for another year so at the end of year two we would have the sum of one plus
three percent multiplied by a hundred multiplied by the sum of one plus three
percent equals future value at year two the present value 100 is equal to the
future value divided by 1 plus 3% elevated to the second degree
so in general when we need to discount a future cash flow that is 10 years from
now we need to divide it by 1 plus I elevated to the nth degree
now that we have learned this we can go to our first example and calculate which
one of the two cash flows has a higher present value
here are the two sets of cash flows the first one involves a payment in year
two that is equal to a hundred and the other payment in year three is equal to
one hundred and ten in order to calculate present value
assuming an interest rate of 10% we need to use the formula that we have
here we will have a hundred / the sum of 1 plus 10% to the second
degree we are elevating to the second degree
because the cash flow is in two years from now then we will have a hundred ten
divided by the sum of 1 plus I to the 3rd degree because this is a cash flow
in year three the present value that we will obtain
from this equation is 165 it’s much lower than the simple sum of a hundred
and 110 now let’s calculate the value of the
other set of cash flows we will have a hundred discounted by one
year plus a hundred discounted by two years we obtained that the present value of
the second set of cash flows is 174 as you can see by discounting two sets of
cash flows and obtaining their present value we are able to compare them and
decide which one is preferable the selection of the discount rate is
rather important in this calculation for most people it is their marginal
borrowing rate the interest rate which a bank would apply to them
if we are considering an investor his discount rate will be the rate of return
that he expects on his investments Oh