2. 2
• The level of investment does fluctuate, and there
are many variables such as the interest rate, the
level of income or output, the wage rate, the level
of technology, and the corporate tax rate which
influence the size and frequency of fluctuation.
4.1 Investment and the Rate of Interest
• The decision to invest depends upon whether or
not the expected returns on investment is greater
than the cost of borrowing the necessary funds;
or if the funds are already available whether the
expected returns are higher than interest earned
by lending out the funds (that is, the opportunity
cost).
3. 3
• The decision to invest in a machine (or any
capital good or project) depends upon whether
or not the investment is expected to yield more
revenue over its lifetime than it costs to
purchase and operate, i.e., whether it is
expected to add to total profits.
• If the expected total revenue exceeds total cost,
the machine should be purchased.
• But, a machine or any capital good usually has a
lifetime which extends over a number of years.
• It is necessary to know the present value of all
the future returns of a machine.
4. 4
• The machine should be purchased if the present
value of the returns exceeds the cost.
• For example, suppose that we expect (through
market surveys and econometric forecasting) a
particular machine to yield a return of $ R (say, $
100) in each of the next n years. Therefore, we
expect the total net returns from the machine
over the next n years to be
R1 + R2 + R3 + … + Rn + J
where J represents the scrap or salvage value of
the machine after n years of use.
5. 5
• Using the above information, the present value of
the stream of returns is as follows:
V = R1/(1+i) + R2/(1+i)2 + R3/(1+i)3 +
…+Rn/(1+i)n + J/(1+i)n
Where, V = The present value of the stream of
returns
i = Some appropriate interest rate
• Suppose that the machine initially costs $ 1000; i
is 0.05 and J equals 0.
6. 6
V = 100/(1.05) + 100/(1.05)2 + … +
100/(1.05)n
Or V = 100/0.05 ≈ 2000 as n gets very large
• Since V approaches $2000 and C = $1000 (the
present value of the expected stream of
returns is greater than the cost of the
machine), the entrepreneur should invest.
• With known life of a machine and also the
returns, V can be calculated and compared to
C.
7. 7
4.2 Return on Investment: Marginal Efficiency
of Capital
• The rational entrepreneur will invest in a machine
whenever the present value of the returns exceeds
the cost of borrowing, or, in the absence of
borrowing the opportunity cost of the available
funds.
• If the rate of return is r and, r is greater than i,
then, the machine should be purchased even if it is
necessary to borrow the funds.
• The expected rate of return r on any investment is
simply the discount rate which exactly equates the
value of all expected future earning to the cost of
the machine.
8. 8
We say that
C = R1/(1+r) + R2/(1+r)2 + R3/(1+r)3 + … + Rn/(1+r)n + J/(1+r)n
where, r = expected rate of return on investment
• r is called the marginal efficiency of capital (MEC),
a concept, which was used by J.M. Keynes.
Example:
1. Suppose that on an investment, the return is $100
per year and the initial cost of the machine is
$1000.
2. Assuming that the machine has an infinite life,
there is no salvage value to consider.
9. 9
Thus,
1000 = 100/(1+r) + 100/(1+r)2 + … + 100/(1+r)n
Or, 1000 = 100/r
This implies that, r = 0.10
• If i = 0.05 so that lending $1000 yields $50 as return, it
is wise to invest in the machine.
• The return from the machine or the MEC is twice as
much as the interest payment, since r = 2i.
• Whenever r is greater than i, V will exceed C. And, as
long as the MEC (r) is greater than the rate of interest
(i), or, as long as the present value of the stream of
future returns (V) exceeds the cost (C), investment
should take place.
10. 10
• Table 1 given in the next slide shows that the
entrepreneur should invest in Project 1 because it
adds more to the firm’s revenue than it does to
costs, and, thereby, increases total profit of the
firm. He should also invest in Project 2 for the
same reasons.
• He should be indifferent about Project 3 because
it adds equally to revenue and cost, and, thereby
leaves the total profits of the firm unchanged.
• He should not invest in Projects 4 and 5 because
they add more to costs than to revenues, and,
thereby decrease total profits of the firm.
11. 11
Investment
Project
r i (r – i)
1 0.10 0.05 0.05
2 0.08 0.05 0.03
3 0.05 0.05 0
4 0.04 0.05 - 0.01
5 0.03 0.05 - 0.02
Table 1: Investment Criteria
Investment should take place to the point where the marginal
efficiency of capital (r) equals to the cost of borrowing.
12. 12
4.3 Changes in Interest Rate and Investment
• If the rate of interest falls from 5 to 3 percent,
investment opportunities with rates of return just
over 3 percent become profitable.
• Under these circumstances, the entrepreneur
should increase his level of investment up to, but
not beyond, Project 5 (see Table 1 in previous
slide).
• As the rate of interest falls, the level of investment
increases, assuming that the MEC remains
unchanged.
14. 14
• The equation of the investment function as
shown in Fig. 1 is linear (for simplicity), which
is mentioned below:
I = d + ei
Where d is positive and e is negative.
• As e is negative, it indicates that the level of
investment increases as the rate of interest
falls.
• Similarly, d is positive, it indicates that when
the rate of interest falls to zero, the level of
investment will reach some maximum level, d.
15. 15
• For a given level of interest i0, the level of
investment would be I0. If the rate of interest
increases i2, investment level will fall to I2. If the
interest rate falls to i1, investment will increase to
I1, and eventually increase to d when i = 0.
4.4 Investment and the Level of National
Income
• As the level of national income increases,
investment opportunities become more plentiful,
and, so the level of investment, for any given rate
of interest, will increase. There would be an
upward shift in the investment function shown in
Fig. 1.
16. 16
• If the level of national income falls, the
investment function would shift to the left
indicating that, at all levels of the interest rate,
the level of investment will go down. This implies
lack of investment opportunities.
• In Fig. 2, it may be seen that for a given level of
the rate of interest i0, the investment function
(relating investment to income, the two being
positively correlated) is
I0 = f(Y)i0
• If the interest rate increases to i1, the investment
function would shift downwards to I1; and if the
rate of interest decreases to i2, the investment
function would shift upwards to I2.
18. 18
4.5 Changes in the Level of Income and
Investment: The Acceleration Principle
• Changes in the level of income is a more direct
determinant of the level of investment, which is
stated by the Acceleration Principle. The principle
is explained below:
• A firm decides to make an investment when it
expects its sales to increase.
• Assuming the same inventory levels, sales can
increase only when output increases.
• Thus, investment in any period by a firm may be
taken as a function of the expected increase in
output.
19. 19
• If the expected increases in output can be treated
as similar to the past changes in output,
investment in any given period can be made a
function of past changes in output. This is stated
by the acceleration principle.
• According to the acceleration principle:
It = f(Ot – Ot – 1)
where I = investment and O = output. This is a
general functional form.
• A specific formulation of this functional form
would be
It = v(Ot – Ot – 1)
20. 20
• For a national economy, the principle would be
stated as
It = v(Yt – Yt – 1)
• This formulation implies that there is a rigid
proportionate relationship between changes in
output or income (Y) and investment.
• The proportionate relationship is established
through v which is referred to as the accelerator
or acceleration coefficient.
• The acceleration coefficient may be called the
incremental capital – output ratio [(Kt – Kt-1)/(Yt –
Yt-1)], which is quite similar to capital – output
ratio.
21. 21
• The acceleration principle implies that output or
income must keep growing if net investment is to
be positive.
• If output stabilizes even at high level, net
investment will become zero (Table 2).
• The example is worked out assuming the
acceleration coefficient to be 2.
• Table 2 shows that when income stabilizes at 95,
net investment drops to zero.
• When income falls, net investment becomes
negative although output itself is at a high level.
22. 22
Time Period Income Net Investment
t 30 -
t+1 40 20
t+2 60 40
t+3 70 20
t+4 80 20
t+5 95 30
t+6 95 0
t+7 90 -10
Table 2: Changes in Income and Investment:
The Acceleration Principle
23. 23
Limitations:
• The rigid proportional relationship between
investment and increase in income as stated by
acceleration principle may not always hold good.
• If there is excess capacity in an industry, investment
need not be made to keep pace with increase in
output.
• The accelerator operates with greater force when all
capacity has been used up, and, therefore, an
increase in output will compel entrepreneurs to
invest.
• The proportionate relationship between increase in
output and investment may not be maintained
because of the lumpiness of capital.
24. 24
• Because capital is not always divisible (plant and
machinery are made with certain minimum
capacity), not every increase in output can be
matched by an appropriate level of investment.
Sometimes, it pays to install a capacity larger than
that required by the change in output and to let the
increase in output catch up with capacity later.
• The acceleration principle applies only to net
investment. Replacement investment (that is,
investment for replacement of machines, which
have become worn out), is not influenced by
changes in income or output. Even if income
remains at the same level, it will be necessary to
replace worn out machines.
25. 25
4.6 Investment and The wage Rate
• Wage rate may not influence investment as
directly as the rate of interest or the level of
income, but, is likely to influence investment
decisions by affecting the profitability of a
particular investment project.
• If we assume that the wage rate increases and
the level of employment does not fall, then the
wage bill must increase. For any particular
producer, such a situation might make a particular
investment less profitable than if the wage rate
had not increased.
27. 27
• Under such situations, the inducement to invest at
a particular level of income will be less.
• If the wage rate increases (from say w1 to w2) this
would cause the investment function (relating
investment to income) to shift downwards, i.e., for
the same level of income, investment will be less,
because the increase in the wage rate has made
any investment now less profitable than before
(Fig. 3).
28. 28
4.7 Technology and the Level of Investment
• Technological changes generally influence
investment decisions by causing a shift in the
investment function.
• Inventions may make existing capital equipment
obsolete. This will create need for new capital
equipment which will generate demand for
additional investible funds.
• In such a case, there will be an upward shift in
the investment function but it will be less
pronounced.
29. 29
4.8 Empirical Investment Functions
• More recent studies have attempted, through
regression analysis, to correlate changes in
investment with changes in such variables as
output, the rates of interest paid on debt
(bonds) and equity (stocks), the corporate tax
rate and the rate of price inflation.
• The elasticity of investment measures the
percentage change in investment induced by a
given percentage change in one of the
independent variables.
30. 30
• For example, the elasticity of investment to
output measures the percentage change in
investment induced by every percentage
change in output – if this equals 4, every one
percentage point increase in output would
produce four percentage point increase in
investment.
• The elasticity coefficients derived from some
regression analysis based on data for the
period 1975 to 1996 for the US economy are
given in the table (see next slide).
32. 32
Over the period, 1975 to 1996, the coefficients
indicate that:
• Each 10 percent increase in output results in a 8.3
percent increase in investment.
• Each 10 percent increase in the interest rate paid to
debt and equity instruments results in a 3.5 percent
and a 1.5 percent decrease in investment
respectively.
• Every 10 percent increase in the corporate tax rate
results in a 4.0 percent decrease in investment.
• Every 10 percent increase in the rate of price
inflation results in a 1.6 percent increase in
investment.
33. 33
• Over the period 1953 to 1968, changes in the
level of output was the most significant factor
influencing investment decisions.
• The corporate tax rate was the second most
significant variable followed closely by the
interest rate paid on bonds.
• This was followed by the interest rate on
equities and the rate of price inflation (these
two factors being of equal significance).
