Value and Return in terms of future value

The most financial decision, such as the purchase of assets or procurement of funds .affect the firms’ cash flows in different periods. For example, if a fixed asset is purchased, it will require an immediate cash outlay and will generate cash inflows during many future periods. Similarly, if the firm borrows funds from a bank or from any other source, it receives cash now and commits an obligation to pay cash for interest and repay the principal in future periods. The firm may also raise funds by issuing equity shares. The firm’s cash balance will increase at the time shares are issued, but as the firm pays dividends in the future , the outflow of cash will occur. Sound decision -making requires that the cash flows, which a firm is expected to receive or give up over a period of time. should be logically comparable. In fact, the absolute cash flow which differs in timing and risk are not directly comparable.
The recognition of the time value of money and risk is extremely vital in financial decision-making. If the timing and risk of cash flows are not considered, the firm may make decisions that may allow it to miss its objective of maximizing the owners’welfare. The welfare of owners would be maximized when wealth or net present value is created from making a financial decision.

                   TIME PREFERENCE FOR MONEY

Time preference for money is an individual’s preference for possession of
a given amount of money now rather than the same amount at some future time.
Three reasons may be attributed to the individual’s time preference for money.
b)preference for consumption
c)investment opportunities

                         REQUIRED RATE OF RETURN

Time preference for money is generally expressed by an interest rate. This rate will be positive even in the absence of any risk. It may be therefore called the risk. It may be therefore called the risk-free rate. For instance, if the time preference rate is 5 percent.It implies that an investor can forego the opportunity of receiving rs.100 if he is offered rs.105 after one year (rs.100 which he would have received now plus the interest which he could earn in a year by investing rs.100 at 5 percent).In reality, an investor will be exposed to some degree of risk. Therefore, he would require a rate of return, called risk premium, from the investment which compensates him for both time and risk. Thus the required rate of return will be
The required rate of return=Risk-free rate+Risk premium
The risk-free rate compensates for a time while risk premium compensates for risk. The required rate of return may also be called the opportunity cost of capital comparable risk. The interest rate account for the time value of money irrespective of an individual ‘s preference and attitudes.
Future value
What is Future value in terms of value and return
We just developed the logic for deciding between cash flows that are separated by one period, such as one year. But money investment decision involved more than one period. To solve such a multi-period investment decision, we simply need to cash flows one year apart.

            Future value of single cash flow

Suppose you have rs.100. You deposited this amount in a bank at 10 percent rate of interest for one year. How much future sum would you receive after one year? You would receive rs.110.
Future sum=Principal +Interest
what would be the future sum if you deposited rs.100 for two years? You would now receive interest on interest earned after one year:
Future sum= 100+(0.10*100)+0.10(100+(0.10*100)
You could similarly calculate a future sum for any number of year. We can express this procedure of calculating compound or future,value in formal terms.
Formula of future sum
Future sum=Principal+Interest on principal
The outstanding amount at the beginning of second year is F_{1}=P(1+i). The compound sum at the end of second year is will be:
Similarly,F_{3}=F_{2}(1+i)=P(1+i)^{3}  and so on. The general form of equation for calculating or(the future value of a lump sum after n periods may,therefore,be written as follows.
The term (1+i)^{n} is the compound value fact Re 1,and it always has a value greater than 1 for positive i,indicating that CVF increases as i and n increase.




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