In this chapter, we look at the concept of
time value of money
. Time value of money refers to the fact that a
dollar in hand today is worth no less than (usually more than) a dollar promised at some time in the future.
Hence, to determine the value current value of cash flows expected in the future is one of the most
important issues faced by a financial manager.
As we saw in the earlier chapter, there exists an interest rate which was defined as the cost of money. The
reason there is a time value of money is due to an interest rate. From a view of borrower, it is the cost to
get the right to use the money for a given period. From lender’s perspective, it is the value that he/she can
get by giving up the right to use the money for a given period of time. Therefore, interest rate can be often
considered as the time value of money.
Cash flow time line
– a tool used in time value of money analysis. Although, it is very simple, this
technique will help you visualize when the cash flows associated with a particular situation occur.
highly recommended to use the time line when you try to solve time value of money questions.
An example of time line:
Time 0 5% 1 2 3 4
Cash flows 0 $20 -$20 0 0
Time 0 is today, and time increases by an increment (period). Usually, we put periodic interest rate
between periods. As shown in the example, the periodic interest rate between time 0 and time 1 is 5%.
The bottom half of the time line represents cash flows. For example, there is a cash
, a receipt of
cash, at time 1. We know this is cash inflow because the cash flow is positive. On the other hand, there is
, a payment of cash, at time 2. Why is this cash outflow?
– the amount an investment is worth after one or more period. Mathematically, the future
value can be expressed as:
= PV(1 + i)
Sometimes, (1 + i)
, (Future Value Interest Factor for i and n).
For example, suppose you deposit $100 in a savings account that pays 5% interest rate per year. At the end
of the first year, the investment will grow to $105. This is a very simple one period case. However, as the
time horizon increases, things will become a little bit complicated. For instance, after two periods, your
investment will grow to $110.25 (100(1.05)(1.05). Notice that the value of the investment is not $110.