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## Lesson 25. METHODS OF CAPITAL BUDGETING, NPV METHOD, TIME VALUE OF MONEY

Module 5. Investment decision

METHOD OF CAPITAL BUDGETING, NPV METHOD, TIME VALUE OF MONEY

25.1 Time Value of Money

**25.1.1 Future value of present money**

* *A rupee today is worth more than a rupee in future. This is primarily due to its opportunity cost, i.e., interest. Interest will be added to the principle over time and hence its value increases. Future value of present sum is an important concept in financial analysis and this is called compounding. In the compounding process, the interest is added to the principal at the end of each time period which, in turn, earns interest. The future value of present investment in the project is calculated by using the well-known formula of compound interest

A = P (1+i)^{t}

.........(Eq. 25.1)

Where,

A = Future value of the present sum invested in the project,

P = Principal amount invested in the project,

i = Interest rate in per cent, and

t = Number of years.

Let us assume that investment made in an agricultural project is Rs. 10 crore and that the expected rate of return from the project is 80 per cent. We are interested to know what would be the value of investment made after 40 years. This could be readily found using the equation.

*Annuity*

By definition annuity means a stream of payments or returns over time. The future value of annuity can be estimated using the following equation.

A = P * (1+i)^{t} -1 / i

.........(Eq. 25.2)

Where,

A = Future value,

P = Annual investment,

t = Time period, and

i = Rate of interest.

**25.1.2 Present value of future money**

The present value of future sum is the current value of investment to be received in the future. This present value is worked out through discounting process in which the future sum is discounted back to the present time to find out its current or present value. The rationale behind this process is that a sum to be received in future is somewhat less now, because of time difference assuming a positive interest rate. Discounting is the inverse procedure of compounding. A present sum is compounded to know the future value and future sum is discounted to know the present value of future amount.

PW = P/ (1+i)^{t} Or P* 1 / (1+i)^{t}

^{ } ......... (Eq. 25.3)

Where,

PW = Present worth of future money,

P = Money value in future,

i = Rate of interest,

t = Project life period in years.

The present value of annuity or stream of constant annual payment is found out using the following formula

^{-t}/ i

Where,

PW = Present worth of future money,

P = Money value in future,

i = Rate of interest, and

t = Project life period in years.

Investment analysis is also called capital budgeting. The profitability of two or more alternative investment projects are determined through capital-budgeting technique. Four components are required for the analysis of investment. They are: (1) net cash revenues from different projects, (2) their costs, (3) terminal or salvage value of investment, and (4) interest or discount rate to be used.

Cash receipts less cash expenses give net cash revenue resulting from the alternative proposed projects.

The cost of investment is the actual total expenditure for its implementation. The terminal value of the project will also be estimated and it is set equal to the junk value for depreciable assets of the project. For simplicity junk value is assumed to be zero. The land values of the projects should be estimated at the market rate, at the time at which the project is terminated.

Another problem in economic analysis is with the estimation of discount rate. This discount rate is the opportunity cost of capital, which represents the minimum rate of return for justifying the investment. If the proposed investment in the project fails to earn this minimum rate of interest, then the capital should not be invested in the said project and alternative projects must be chosen as worthy of investment.

If capital is to be borrowed for investment on the project, then the discount rate chosen for the economic analysis should be higher than the cost of borrowed capital. Under risk situations, the discount rate is to be equaled to the expected rate of return from alternative projects of equal risk. Many problems are involved in deciding upon the actual rate of discount in project evaluation particularly, when the discount rate is to be adjusted to the risk. The methodology on the exact rate of discount to be used in the economic analysis is already discussed.

Broadly there are two methods of project appraisal, viz., undiscounted measures and discounted measures. In the undiscounted measures, payback period, ranking by inspection, proceeds per rupee of outlay, average annual proceeds of rupee outlay, etc., are important. Under discounted measures Net Present Worth (NPW), Benefit-Cost Ratio (B-C ratio), Internal Rate of Return (IRR), and Profitability Index are prominent.

25.2 Undiscounted Measures

The undiscounted measures are the naïve methods of choosing among the alternative projects. The methods listed under these measures often mislead in ranking of the projects and hence, choices go wrong.

**25.2.1 Ranking by inspection**

It is based on the size of costs and length of cash-flow stream. Suppose if the two projects are with the same investment and the same net value of production, but with difference in the length of the period, then the project with longer duration is preferred to the one with shorter time period. This leads to bias in the choice obviously due to the absence of more elaborate and appropriate analysis.