(A) Discounting:
One important but difficult part in the process of transactions in the
capital market is about appropriate investment decisions. How does one
decide whether a certain type of investment will be profitable or not?
Let us continue with our earlier example:
A lender who gives a loan of $1000 receives $1100
after a year and $1210 after two years when the rate of interest is 10
percent. These future values of present lending are determined by the
compounding process.
Future Value V = K (1 + r)1 = 1000(1 + 0 .10) 1 = 1000(1 .1) = 1100
V = K (1 + r)2
= 1000(1 .10)2 = 1000 (1.21) = 1210
In this example, K is the
present lending value and V, the future value. Since we already know
the expected future income, to arrive at its equivalent present value,
we need to reverse the process or discount the future values at the rate
of the current interest rate.
(B) Investment Decisions:
There is a similar method employed for discounting future streams of
income which is applicable in making appropriate investment decisions.
Let us assume that a taxi driver wants to purchase his own car and to
use it as a taxi for earning regular income. Suppose the present market
price of the taxi cab is $1000. The present rate of interest
(discount) is 10 percent. The life of the taxi is likely to be four
years. During these years the taxi driver expects to earn an average
annual income of $3000. At the end of the fourth year the vehicle
cannot any more be used as a taxi but can be sold out as scrap at a
value of $1000. Keeping this in mind the driver has to decide if it
will be worth purchasing the car. At a glance it appears that the taxi
will bring a total income of $12000 (3000 ´
4) plus scrap value of $1000. The sum of $13000 as future income on
the present investment is attractive. However, other factors must also
be considered. The expected income streams in the future have to be
discounted at the rate of 10 percent because the market rate of interest
acts as an opportunity cost. The taxi owner could have earned this
much by depositing $10000 with the bank if he were to possess such
resources. Otherwise he could have borrowed $10000 from the bank and
promised to pay interest charges. The present discounted value of these
expected incomes would be as follows:
In the present case the discounted value of 10509.59
exceeds the investment value of $10,000 by $509.59. Therefore the
investment decision is profitable. If the present value were lower than
the total investment, and subsequently, if the difference were negative
then the investment decision would not have been profitable.
Let us assume that the market rate of interest is as
high as 15 percent but retain the initial investment amount of $10,000
and the final scrap value of $1000. The present discount value of the
capital asset will be negative and it will not be worth while to invest
in it. Discounted values of the expected incomes in this case are as
follows:
Since the net addition to the income is negative, an investment decision will not be profitable.
Let us briefly summarize the two cases.
Case 1: Profitable Case 2: Net Profitable
Initial Investment $10000 Initial Investment $10,000
Rate of Interest 10% ; Rate of Interest 15%
Scrap value $1000 Scrap value $1000
Sr. No. | Expected Annual Income | Discounted Present Value | Expected Annual Income | Discounted Present Value |
1 | 3000 | 2727.27 | 3000 | 2608.7 |
2 | 3000 | 2479.34 | 3000 | 2268.43 |
3 | 3000 | 2253.94 | 3000 | 1972.52 |
4 | 3000 | 2049.04 | 3000 | 1715.26 |
1000 | 2040.04 | 1000 | ||
10509.59 | 9564.91 | |||
-10000 | -10000 | |||
Net Value | +509.59 Net Value | -435.09 |
(C) Practical Difficulties: A decision
regarding investment is a complex and difficult activity. To compute
discounted values and to compare them with expected income is a
formidable task. The method explained above is quite similar to the
Keynesian concept of Marginal Efficiency of Capital (MEC). In
actual decision making there are further risks involved. We have
assumed fixed average future expected returns. We have also assumed
uniform constant rate of interest. Both these expectations are likely
to go wrong. Such conditions of uncertainty take away the possibility
of accurate investment decision making. The only conclusion we can draw
is that investment decisions are likely to be more profitable at a relatively lower rate of interest and less profitable at a relatively higher rate of interest. Therefore a lower rate of interest which simultaneously falls is more favorable to investment activity.
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