Time_Value_of_Money

Time Value of Money Which would you prefer – Rs 10,000 today or Rs 10,000 in 5 years? Obviously, Rs 10,000 today Money received sooner rather than later allows one to use the funds for investment or consumption purposes. This concept is referred to as the TIME VALUE OF MONEY!!

Reasons for Time Value of Money  Individuals prefer current consumption to future consumption.  Capital can be employed productively to generate positive returns.  In an inflationary period a rupee today represents a greater deal of purchasing power than a rupee a year hence.

Time Preference Rate & Required Rate  The time value of money is generally expressed by an interest rate. It is normally risk free rate.  If risk is involved, risk premium is added to the interest rate.  Required Rate = Risk Free rate + Risk Premium  The required rate of return may also be comparable with the opportunity cost of capital.

Compound Value The ability of an asset to generate earnings, which are then reinvested in order to generate their own earnings. In other words, compounding refers to generating earnings from previous earnings. Also known as \"compound interest\". Interest that accrues on the initial principal and the accumulated interest of a principal deposit, loan or debt. Compounding of interest allows a principal amount to grow at a faster rate than simple interest, which is calculated as a percentage of only the principal amount.

FVn = PV(1+ r)n FV = Future or Compound Value PV = Present Value r = rate of interest n = number of years (1+ r)n = the future value interest factor Simple Interest FV = PV(1+n*r)

Compounding Graphically

Semi Annual & Other Compounding Periods In case of semi-annual compounding there would be two compounding periods within the year. Interest is actually paid after every six months at a rate of one half of the annual (stated) rate of interest. Quarterly compounding means that there are four compounding periods within the year. Instead of paying the interest once a year, it is paid in four equal installments after every three months. A = P(1 + r/m)mn where m is the no. of times per year compounding is made.

Future Value at the Beginning of the Year 5% Compound Beginning Amount No. of years Interest of Year Deposited compounded Factor Future Value 1 1000 5 1.28 1276.28 2431.01 2 2000 4 1.22 3472.88 4410.00 3 3000 3 1.16 5250.00 16840.17 4 4000 2 1.10 5 5000 1 1.05

Future Value at the End of the Year 5% End of Amount Deposited No. of years Compound Future Value Year compounded Interest Factor 1 1000 4 1.22 1215.51 2 2000 3 1.16 2315.25 3 3000 2 1.10 3307.50 4 4000 1 1.05 4200.00 5 5000 0 1.00 5000.00 16038.26

Compound Value of an Annuity An annuity is an investment that you make, either in a single lump sum or through installments paid over a certain number of years, in return for which you receive back a specific sum every year, every half-year or every month, either for life or for a fixed number of years. Ordinary Annuity : A series of fixed payments made at the end of each period over a fixed amount of time. FVn = A (1+r)n - 1) ------------------- r Annuity Due : An annuity due requires payments to be made at the beginning of the period. FVn = A (1+r)n - 1) ------------------* (1 + r) r

Present Value Present Value of a future cash flow (inflow or outflow) is the amount of current cash that is of equivalent value to the decision maker. Discounting is the process of determining present values of a series of future cash flows. The compound interest rate used for discounting cash flows is also called the discount rate. FVn = PV(1+ r)n PV = FVn ------------- (1+ r)n

Present Value of an Uneven Series End of the Present Value Present Factor Value Year Cash Flows 1 500 0.909 454.5 2 1000 0.826 826 3 1500 0.751 1126.5 4 2000 0.683 1366 5 2500 0.621 1552.5 5325.5

Net Present Value The difference between present value of cash inflows and the present value of cash outflows. NPV is used in capital budgeting to analyze the profitability of an investment or project.