Most financial decisions, such as the purchase of assets or procurement of funds, affect the firm’s cash flows in different time periods. For example, if fixed asset are purchased it will require immediate cash outlays sand will generate cash flows during many future periods. Similarly, if firm borrows funds from the bank it receives cash now and commits an obligation to pay interest and repay principal in future periods. Cash flows become logically comparable when they are appropriately adjusted for their differences in time and risk. This is where Time Value of Money concept comes.

The recognition of the time value of money concept and risk is extremely vital in financial decision making. If the timing and risk of cash flows is not considered, the firm may make decision which do not maximize the owner’s welfare. The welfare of the owners would be maximized when net worth or net value is created from making a financial decision. What is Net Present Value? It’s a time value concept. Money has time value. A rupee today is more valuable then a rupee a year hence.

## Reasons for individual’s Time Preference for Money

### 1. Uncertainty

An individual is not certain about future cash receipts, he prefers receiving cash now.

### 2. Preference for Consumption

Most people have subjective preference for present consumption over future consumption of goods and services either because of the urgency of their present wants or because of the risk of not being in a position to enjoy future consumption that may be caused by illness or death. As money is the means by which individuals acquire most goods and services, they may prefer to money have now.

### 3. Investment Opportunities

Most individuals prefer present cash to future cash because of the available opportunities to which they can put present cash to earn additional cash. For e.g., an individual who is offered Rs. 100 now or Rs 100 one year from now would prefer Rs 100 now if he could earn interest of Rs 5 by putting in the saving account in the bank for one year. His total cash in one year from now will be Rs.105.

## Dimensions of Time Value of Money

### Future Value of a Single Amount:

Suppose you have Rs. 1000 today and you deposit it with a financial institution, which pays 10% interest compound annually, for a period of 2 years.

#### Formula of Future Value of Single Amount:

**FVn = PV (1+k) n**

Where,

FVn = future value n years hence

PV = present value

k = interest rate per year

n = number of year for which compounding is done.The factor (1+k) n is referred to as the compounding factor or the Future Value Interest Factor (FVIFk,n)

**Illustration 1:** If you deposit Rs. 1000 today in a bank which pays 10% interest compounded annually, how much will the deposit grow to after 8 years and 12 years?

**Answer: **

### Future Value of Annuity:

An annuity is a series of periodic cash flows (payments or receipt\pts) of equal amounts. The premium payment of a life insurance policy, for example, is an annuity.

**Illustration 2:** Suppose you deposit Rs 1000 annually in a bank for 5 year and your deposits earn a compound interest rate of 10%. What will be the value of series of deposits at the end of 5 years?

**Answer:** Rs 1000(1.10) 4 + Rs 1000(1.10) 3 + Rs 1000 (1.10) 2 + Rs 1000(1.10) 2 + 1000 (1.10)

=Rs 6105

### Present Value of a Single Amount:

The present value of a future cash inflows or outflow is the amount of current cash flow that is equivalent desirability, to the decision maker, to a specified amount of cash to be received or paid at the future date. The process of determining the present value of a future payment or a series of future payments is called discounting.

**Illustration 3**: Suppose someone gives you Rs 1000 six year hence. What is the present value of this amount if the interest rate is 10%?

**Answer:** The present value is

= Rs 1000 (PVIF10%, 6)

= Rs 1000 (0.5645)

= 564.5

**Illustration 4:** Find the present value of Rs 1000 receivable 20 years hence if the discount rate is 8%.

**Answer:**

**Illustration 5:** Present value of a 4 year annuity of Rs 10000 discounted at 10%?

**Answer: **

PVA4 = 10000(PVIFA10%,4)

= 10000(3.170)

= 31700