2. Time Value of money
Time Value of Money is an important concept in financial management. It can be used to
compare investment alternatives and to solve problems involving loans, mortgages, leases,
savings, and annuities. It is based on the concept that money that you have today is worth
more than the promise or expectation that you will receive money in the future. Money that
you hold today is worth more because you can invest it and earn interest
A key concept of Time Value of Money is that a single sum of money or a series of equal,
evenly-spaced payments or receipts promised in the future can be converted to an equivalent
value today. Conversely, you can determine the value to which a single sum or a series of
future payments will grow to at some future date.
The time value of money (TVM) refers to the fact that $1 today is worth more than $1 in the
future. This is because the $1 today can be invested to earn interest immediately. The TVM
reflects the relationship between present value, future value, time, and interest rate. The time
value of money underlies rates of return, interest rates, re quires rates of return, discount
rates, opportunity costs, inflation, and risk. It reflects the relationship between time, cash flow,
and an interest rate.
There are three ways to interpret interest rate:
1. Required rate of return is the return required by investors or lenders to postpone their
current consumption.
2. Discount rate is the rate used to discount the future cash flows to allow for the time value
of money (that is, to bring future value equivalent to present value).
3. Opportunity cost is the most valuable alternative investors give up by choosing what they
could do with the money.
In a certain world, the interest rate is called the risk-free rate. For investors preferring current
to future consumption, the risk-free interest rate is the rate of compensation they require to
postpone current consumption. For example, the interest rate paid by T-bills is a risk-free rate
of interest.
In an uncertain world, there are two factors that complicate interest rates:
1. Inflation: When prices are expected to increase, lenders charge not only an opportunity cost
of postponing consumption but also an inflation premium that takes into account the
expected increase in prices. The nominal cost of money consists of the real rate (a pure rate
of interest) and an inflation rate (a pure rate of interest) and an inflation premium.
2. Risk: Companies exhibit varying degrees of uncertainty concerning their ability to repay
lenders. Lenders therefore charge interest rate to incorporate default risk. The return that
borrowers pay thus comprises the nominal risk-free rate (real rate + an inflation premium)
and a default risk premium.
3. Compounding is the process of accumulating interest over some period of time. Compounding
period is the number of times per year in which interest is paid. Continuous compounding
occurs when the number of compounding periods becomes infinite, that is, interest is added
continuously.
Discounting is the calculation of the present value of some known future value. Discount rate is
the rate used to calculate the present value of some future cash flow. Discounted Cash Flow is
the present value today of some future cash flow.
When you make a single investment today, its future value that will be received an N year from
now is as follows:
FVN = PV X (1 + r)N
Where
• FV = future value at time n
• PV = present value
• r = interest rate per period
• N = number of years
.A key assumption of the future value formula is that interim interest earned is reinvested at
the given interest rate (r). This is known as compounding.
In order to receive a single future cash flow N years from now, you must make an investment
today in the following amount:
Notice that the future cash flow is discounted back to the present. Therefore the interest rate is
called the discount rate.
You should be able to calculate PVs and FVs using your calculator, where
• N = number of periods
• I/Year = yield in market place or the Required Rate of Return
• PV = present value
• PMT = payment amount per period
• FV = the future value of the investment
One can solve for any of the above variables. Just input the other variables and solve for the
unknown. Using the calculator on the test will prove to be a very time efficient manner of
calculating present values and future values.
4. We have, already seen that value or business is a function of expected profit and cost of capital,
for a given amount of expected profit, value of business is maximum when cost of capital is
minimum. The Capital Asset Pricing Model (CAPM) is a general relationship between risk and
desired return i.e. cost of capital. In other words, CAPM tells us the cost of capital for a given
level of risk.
Measuring Returns
Return from a security consists of dividend (in case of shares) or interest (in case of debt
interest) and price appreciation.
Example
Price per share of Mark Ltd. at the beginning and end of 2003-04 were Rs.125 and Rs.135
respectively.
The company declared Rs.15 as dividend for 2003-04
Compute rate of return earned by an investor who acquired one share at the beginning of
2003-04.
Solution
The investor earned Rs.15 as dividend.
In addition, he can sell the share to realize Rs. 10 (Rs.135 - Rs.120) as profit.
Total amount earned by the investor = Rs. + Rs.10 = Rs.25
The rate of earning = (Rs.25/Rs.125) x 100 = 20%
In all our future discussion the rate of return will always be computed as above and so it is
worth at this stage to write process in general form
Let Dividend/ Interest = D1
Opening and closing security prices = Po and P1 respectively, then:
D1 + (P1 - P0)
Rate of Return (R1) = ------------------------------------ x 100
P0
5. Expected Return
The return from a security depends on several uncertain factors. The past experiences and
other information however, make, it possible in most cases to assign probability estimates to
these factors. The expected return from a security can be determined using probability
estimates.
Example
The rate of return from a security depends on market conditions, which can be either good or
bad. The rate of return is expected to be 25% if market condition is good and 15% if market
condition is bad. The probability of good market condition is 60%.
Expected (Mean) return = 0.6 x 25% + 0.4 x 15% = 21%
