Present value
Present value
The present value is the current value of a single or series of cash payments to be received/paid at future date, discounted at a specified interest rate.
Present value= Future Value/(1+rate of interest per period)^No. of periods
Example.
Mrs Sharon wishes to purchase a car in 3 years from now which will cost her $35,000 in 3 years. If the bank offers her an interest of 4% per annum, what amount he must deposit today so that she can buy car in 3 years time.
So amount that Mrs. Sharon must deposit today is the present value of the future sum ($35000)
Present value= Future Value/(1+rate of interest)^3
Present value= 35000/(1+0.04)^3
Present value = 35000/1.1249
Present Value = 31,114.87
Present value of annuity
The present value of annuity is a single equivalent value of series of equal cash payments to be received / paid at a regular interval on future dates, discounted at a specified interest rate.
PV of Ordinary annuity = Annuity * PV of Ordinary Annuity factor
Annuity is series of equal sum of money that is received / paid at constant intervals in the future.
The annuity factor is calculated as
PV of Ordinary Annuity factor = [1-(Discount factor of last year)/ Discount rate] = [1- 1/(1+r)^n]/r
(Note: Present value of annuity can be calculated by adding the sum of the present value of each cash flow to be received/paid.
PV of Annuity = PV of cash flow1 + PV of cash flow 2 …………………….+PV of cash flow n
The is the lengthy generally not followed for annuity)
Example
Mr. Bruce is planning to purchase a pension plan under which he would receive $5000 at the end of every year for next 15 years. What amount should Mr. Bruce pay today (fair value) if the he can earn a 5% per annum?
Now the Amount he should pay is the PV of annuity for amount of 5000 and discount rate of 5%
PV Annuity Factor= [1- 1/(1+.05)^15]/.05 = 10.3797
The present value of annuity is = 10.3797 * 5000=$51898.29
(Note:
When annuity is paid/received at the end of every year its called ordinary annuity. The above formula for PV annuity factor is for PV of ordinary annuity.
When annuity is paid/received at the beginning of every year it called annuity due. The formula is for
PV annuity due factor = PV of Ordinary Annuity Factor*(1+r) )
Future Value
Future value is given sum of money's "worth" at a specified time in the future assuming a certain interest rate.
Future value = Original Sum of Money * (1+ interest rate per period)^ No. of periods
Example
Suppose Mr. Bond have deposited $5,000 in bank account. If my bank offers 8% interest rate annually , how much would Mr. Bond receive after 5 years?
The amount Mr. bond would have after 5 years is the future value.
Future value = present value * (1+rate of interest)^5
Future value = 5000* (1+0.08)^5
Future value = $7346.64
Future value of annuity
Future value of annuity is the future value of a series of payments (annuity) to be received / paid at a regular interval on future dates, compounded at a specified interest rate.
FV of ordinary annuity = Annuity * FV Ordinary Annuity factor
Annuity is series of equal sum of money that is received / paid at constant intervals in the future.
The annuity factor is calculated as
FV ordinary Annuity factor = [(1+r)^n-1]/r
(Note: FV value of annuity can be calculated by adding the sum of the FV value of each cash flow to be received/paid.
FV of Annuity = FV of cash flow1 + FV of cash flow 2 …………………….+FV of cash flow n
The is the lengthy generally not followed for annuity)
Example
Mrs. Susan deposit $1000 every year in her bank deposit for next 5 years. What is the amount she will accumulate at the end of five year. Rate of interest is 7%.
The amount Mrs. Susan would have after 5 years is the future value of annuity
FV annuity factor = {(1+.07)^5-1}/.07 = 5.7507
FV = 1000*5.7507= $5750.70
(Note:
When annuity is paid/received at the end of every year it called ordinary annuity. The above formula for annuity factor is for ordinary annuity.
When annuity is paid/received at the beginning of every year it called annuity due. The formula is for annuity due factor = FV of Ordinary Annuity Factor*(1+r) )
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