After having gone through the process of determining the FV (future value) of a present money, now time to learn the process of finding out the PV (present value) of a future sum. This process is the reverse of compounding technique and is known as DISCOUNTING technique. We use this to know the amount to be invested today for achieving a target set for future. this can be divided into various heads:
A)PRESENT VALUE OF A LUMPSUM AND SERIES OF CASH FLOWS:The present value of a future sum will be worth less than the future sum because one forgoes the opportunity to invest and thus forgoes the opportunity to earn interest during that period. Say Rs.2200 is receivable at the end of the year and the expected rate of interest which a person can earn on his investments is 10% p.a. then the present value will be Rs.2000 you can calculate it using the formula below
→Where FV=future value=2200
→N=number of years =1
→R=rate of interest =10%
→PV=Rs. 2200*1/ (1+10)1
If you are availed with PV table then the formula will be
The returns on investment are generally spread over a number of years. The investments made now may yield returns for a period after sometime to determine the present value of future series of cash flows, the PV of different cash flows accruing at different times are to be calculated and then added. The PV of different cash flows can be ascertained by using the following formula:
Instead of above formula, the PV of different cash flows can be also be found out by using PV table.
B)Present Value of An Annuity:In the above case, the cash flows may be different amount .but in certain cases, the investor may receive may receive only constant returns over a number of years
For example interest on debentures/fixed deposits etc. is fixed in its nature. Such fixed return is termed as the annuity to ascertain the PV of annuity, the formula given below may be used:
→PV if annuity=Annuity amount *1/(1+r)n
→Where r= rate of interest
→n=number of years
C)Present Value of Annuity Due:The PV of annuity discussed above is based on the presumption that the cash flows occur at the end of each of the periods starting from now. However, in practice, the cash flow may also occur in the beginning of each period that situation is called annuity due. This can be done using the formula below
→PV of annuity due = (annuity amount*PVAF)*(1+R)
For example: If Rs.2000 is receivable at the beginning of next 5years starting from now and the rate of interest is 8%. Then the PV of annuity due may be calculated as follows:
Annuity amount = Rs.2000
Rate of interest =8%
Present value of annuity for rs.1 for 5 years at 8%= 3.933
PV of annuity due = (2000*3.933)(1+0.08)
D) Present Value of Perpetuity:Perpetuity is a stream of payments or a type of annuity that starts payments on a fixed date and such payments continue forever i.e. perpetually.
EXAMPLE: I) dividend on irredeemable preference share capital
II)scholarships paid perpetually from an endowment fund
The present value of perpetuity can be ascertained by using the following formula:
→PV of a constant perpetuity = C/R
→Whew c= cash flow i.e. interest, dividend, etc,
→R = interest rate per payment period
E) PR Value of Growing Perpetuity:
A growing perpetuity is an infinite series of periodic cash flows which grow at a constant rate per period. The PV of growing perpetuity can be determined by applying the formula below
→PV of a growing perpetuity= C/R-G
→Where C = cash flow
→R = rate per payment period
→G = rate of growth in cash flows
However, it may be noted that the above formula can be used only if the rate of interest is more than the rate of growth (R>G)
For example, a company is expected to declare a dividend of Rs.4 at the end of the first year from now and this dividend is expected to grow 5% every year. what is the PV of this stream of dividend if the rate of interest is 10%
So going with the formula
→PV = C/R-G
→C = cash flows i.e. dividend
→R = rate of interest =10%
→G = rate of growth in cash flows
→PV = 4 / (10%-5%)
→PV = 4 / 5%
→PV = Rs. 80
F) Present Value of A Growing Annuity:A growing annuity is a finite series of equal and periodic cash flows growing at a constant rate every period.
→PV of growing annuity = C/R-G(1-(1+G/1+R)n)
→Where C = cash flow
→R=rate of interest
→G=growth rate and n= life of annuity
G) Sinking Fund:It is a fund created by investing a certain amount annually at compound interest for a certain period, at the end of which such accumulated funds are used to discharge a known liability the annuity for a given period or to replace a working asset. In this case, the annual accumulation becomes the annuity for a given period where each of the annual accumulations will be invested for the remaining period so that the total accumulation at the end of the given period is equal to the target amount.
Example: What amount should be accumulated every year at 12% rate of interest so that it ultimately becomes 200000 after 5 years?
FV = S F instalment * ((1+R)n-1)/R
200000 = S F instalment * (1+0.12)5)-1)/0.12
200000 = S F instalment * (7.623416)
S F instalment = 200000/7.626416 = Rs.26235.
Therefore this amount should be accumulated and invested to accumulate a total of Rs.200000 by end of 5 years.
Here we assume that annual SF instalment payment was made at the end of each of the period.
That’s all pals under the topic time value of money, hope everything is included in it. For practising more follow the upcoming quiz on time value of money for JAIIB.
JAIIB Classes by Ramandeep Singh - Get details here