Time, Value & Money (TVM) - Definitions, RRR, FV, PV, Annuity, Formulas with Examples

Time,Value & Money (TVM)

Money is an object or token which is used to fulfill your desire. The value of money is constantly decreasing with respect to time. Investing with an interest are the key elements which boost the value of your money. For eg. If you have $1000 in a bank account with an interest of 6% for 2 years. Then it will grow up to $1123.60. This is called Compounding. While putting your money in bank is also like an investment for you. Maturity of money is very important during the selected period. If you are willing to withdraw money before the maturity period then the value of money will decreases and you will receive a less amount. This is called Discounting.

Required Rate of Return (RRR)

If an investor has an offer of receiving $100 now or $105 after one year at 5 per cent. He will forego the opportunity of receiving $100 now because this rate will be positive even in the absence of any risk. This is called risk-free rate. 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 compensate him both time and risk.

Thus the required rate of return (RRR) will ba calculated as :

RRR = Risk-free rate + Risk Premium

RRR is also called "opportunity cost of capital''.

Future Value (Compounding Value)

If an investor desire to know the future value of money from now after maturity period then the compounding measurement has been used for calculation.

Formula : FV = P x [1+(i*n)]

Compound Interest : P(1+i)^n = P(CVFn,i)

FV = future value

P = principal amount

PV = Present Value

i = interest rate

n = period

CVF = compound value factor

Example:

Suppose that $1000 are invested for 5 years with an interest rate at 10 per cent. What is the future value of it ? Calculate compoundingly also.

FV = $1,000*[1+(0.1*5)]=$1,500

FV = $1,000*[(1+0.10)^5] = $1,000(CVF_n,i) = $1,000*1.6105=$1,610.51

Present Value (Discounting Value)

If the investor desire to know the current value of future lump sum money in which he has to pay or lend someone then the measurement has been taken for calculation. In other words, money received in the future is not worth as much as an equal amount received today.

Formula: PV = FV/(1+r)^n

Discounting : PV = FV(PVFn,i)

PVF = present value factor

Example:

If an investor desire to get $10,000 in 10 years. He know that he can get 5 percent interest per year from a saving account during the time. How much should he put in the account now?

PV = $1,000/[(1+0.5)^10] = $1,000(PVF_n,i) = $6,139.13

Annuity (A)

Annuity is a fixed amount (payment or receipt) each year for a specified number of years. It is an contract aimed at generating steady income during retirement, where a lump sum payment is made by an individual to obtain certain amount immediately or at some point of future.

Formulas:

Future value of an annuity, FV = A[(1+i)ⁿ-1)/i]

FV = A(CVFA_n,i)

Present value of an annuity, PV = A*[1/i-1/(i(1+i)ⁿ)]

PV = A*PVFA_n,i

Example(a):

A person received an annuity of $5,000 for four years. If the rate of interest is 10 per cent, the present value of $5,000 annuity is:

PV = A*[1/i-1/(i(1+i)ⁿ)] = 5,000*[(1/0.10)-1/(0.10(1.10)^4)] = $15,850

PV =A(PVFA_{n,i) =} 5,000*3.1699 = $15,850

Example(b):

Suppose $100 are deposited at the end of each of the next 3 years at 10 per cent interest rate.

FV = A[(1+i)ⁿ-1)/i] = 100[(1+ 0.10)^3-1)/0.10] = $331