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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