# Investment Function

__Meaning of Investment__

“By investment is meant an addition of capital such as occurs when a new house is built or a new factory is built. Investment means making an addition to the stock of goods in existence.”

__The Decision to Invest__

The decision to invest is different as compared to the decision to buy consumer goods. This is due to the following reasons:

- A firm must make a decision whether to go for capital expansion or buy an existing asset like equity in another company.

- Most of the Capital goods have a long life and one can only several years later as to whether the investment in these capital goods has been profitable or not.

- When a firm has decided to expand it will have to decide as to whether the cost of borrowing in greater than the return expected on the new investment undertaken by the firm.

A firm investment decision is based on the relationship between three elements:

- Expected income flow from capital good under consideration: As the future is uncertain a crucial decision of the firm in making its investment decision is regarding two aspects:

- An estimate of the future flow of income that the capital asset under consideration is expected to yield over its entire life.

- The expected life of the capital good which may last more than expected or may become obsolete before its lifetime due to technological advancements.

- The purchase price of the good in question: Often there exists an uncertainty regarding the price at which the good is to be purchased. This is more for projects where new machines and equipment are involved and where the cost may undergo change over time.

- The rate of interest prevailing in the market which again is subject to fluctuations. It is important to note that any calculations that relate to the future must take into consideration the fact that the returns over the future have a much lower worth as compared to the same returns today.

- While making an investment decision relating to future, a calculation may be made regarding the present value of the capital asset and the discounted rate of return on the asset.

Let us see few illustrations which explain various models of investment.

__Illustration 26__

Presume that $ 200 is to be received by an individual after a period of 1 year. The market rate of interest is 20 %. How much must he invest today?

__Solution__

The discounted present value of $ 200 is

Ro = __ 200 __

(1+0.20)

= 166.67

**This implies that to get a sum of $200 at the end of 1 year is $166.67 must
be invested today at an interest of 20% pa.**

Equation (2) can be written as

Ro = __ Rn __

(1+r)^n

Where (1+r) = discount rate

__ Rn __ = the
discounted present value of Rn

(1+r)^n

We consider the determination of the present value of a bond. Bonds yields a yearly
income, say R, until it reaches maturity at the end of n years when it returns the
principle amount, P the present value of the bond is

V = __ R __+ __ R __+ __ R __+….+ __ R __+ __ P __

(1+r) (1+r)^2 (1+r)^3 (1+r)^n (1+r)^n

Alternatively, a machine is expected to yield an income stream of R1, R2, R3 to Rn over a period of its entire life. At the end, it has a scrap value of J. The market rate of interest is r. the present value of the returns from the machine is

V = __ R____1 __+ __ R____2 __+ __ R____3 __+….+ __ Rn __+ __ J __

(1+r) (1+r)^2 (1+r)^3 (1+r)^n (1+r)^n

__Illustration 27__

Suppose the annual expected returns from a machine are $70 thousands over a period of years, which is the expected economic life of the machine. The scrap value of the machine is $ 40 thousands.

The market rate of interest is 20 %. The cost of the machine is $ 150,000. Find the present value of expected returns from the machine. Is it able to invest in the machine.

__Solution__

The present value of the expected returns from the machine is

V = __ R____1 __+ __ R____2 __+ __ R____3 __+….+ __ Rn __+ __ J __

(1+r) (1+r)^2 (1+r)^3 (1+r)^n (1+r)^n

V = __ 70,000 __+ __ 70,000 __+ __ 70,000 __+ __ 70,000 __+ __ 40,000 __

(1+0.20) (1+0.20)^2 (1+0.20)^3 (1+0.20)^4 (1+0.20)^5

V = __ 70,000 __+ __ 70,000 __+ __ 70,000 __+ __ 70,000 __ + __ 40,000 __

(1.20) (1.20)^2 (1.20)^3 (1.20)^4 (1.20)^5

V = __ 70,000 __+ __ 70,000 __+ __ 70,000 __+ __ 70,000 __ + __ 40,000 __

1.20 1.44 1.728 2.073 2.488

V = 58,333 + 48,611 + 40,509 + 33,767 + 16,077

**V = 197,297**

**As the discounted present value of the returns from the machine is $197,297,
which is greater than the cost of the machine, $ 150,000 the investment in the
machine is profitable.**

__Illustration 28__

In the event, if it costs $ 6,000 to invest in a certain machinery and the life of the machinery is two years that is after two years it becomes quite useless having no value.

Presume further that in the first year of machinery is expected to yield income of $ 2,200 and in the second year $ 4,840.

__Solution__

By substituting these values in the above formula, we can calculate the value of r, which is the marginal efficiency of capital.

C = __ R1 __ + __ R2 __

(1
+ r) (1
+ r)^2

6,000 = __2,200__ + __ 4,840 __

(1+r) (1+r)^2

On calculating the value of r in the above equation it is found to be equal to 10. In other words, marginal efficiency of capital is here equal to 10 %. If we put the value of r, that is 10 in the above equation, we obtain the following:

6,000 = __2,200__ + __ 4,840 __

1.10 (1.10)^2

6,000 = 2,000 + 4,000

** 6,000 = 6,000**

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**Other topics under Consumption, Investment and Saving functions:**

- Accelerator theory of Investment
- Average Propensities, Marginal Propensity to Save
- Camouflaged Redundancy
- Classical Vs. Keynesian Models of income and Employment
- Concept of multiplier
- Consumption Function
- Complex Multiplier
- Criticisms of Keynesian Thesis
- Drift Theory of Consumption
- Foreign Trade Multiplier
- Government Expenditure
- Jorgenson's Neoclassical Notion of Investment
- Keynesian Postulations and Underdeveloped Countries
- Keynesian Theory of Income, Output and Employment
- Model of National Income Determination
- Principle of Acceleration and the Super Multiplier
- Principle of Acceleration and the Super Multiplier - Part I
- Thrift, Marginal Competence of Capital
- Saving Function
- Saving and Investment Equality
- Saving - Investment Parity
- Some New Theories of Investment
- Theory of Consumption Function
- Unemployment and Full Employment