Equal Annual Return Formula

Equal Annual Return Formula

Formula for Equal annual return has been given below. Equal annual return formula has been explained with an example.

Annual Return =         = Present Cash flow                                     Annuity Factor

Equal Annual Return Formula Calculation

Equal return cash flows can be calculated by dividing the present cash outflow with annuity factor. It is important to remember that equal annual return is calculated with the help of annuity factor due to time value of money concept.

Equal Annual Return Formula Example

NPV or Present Value = 120,000

Period required for project = 5 Years

Rate of Return = 14%

Calculate equal return from project at required rate of return?

Solution

In first place we would calculate the annuity factor, and then with the help of that annuity factor, the annual equal return would be calculated.

Annuity Factor

= 1-(1.14)^-3

     .14

=2.3216

Annual Return

Annual Return =         = Present Cash Flow

                                    Annuity Factor  

= 120,000/2.3216

=51,688

Objective of Equal Annual Return

Primary objective of calculating equal annual return is to compare mutually exclusive project with different project life. Equal annual return makes this comparison possible, and project with a high equal annual return is selected.

 Equal Annual Return Example

                                    Project A                     Project B

NPV                            160,000                      220,000

Period                            3                                      4

Discount                        6%                                   8%

Solution

                                  Project A                     Project B

NPV                            160,000                      220,000

Annuity Factor               2.678                          3.312

Equal Annual Return      59,746                       66,425        

Project B will be selected, because it is offering high amount of equal annual return.

Future Value Growing Annuity Formula

Future Value Growing Annuity Formula

Growing Annuity or future value of growing annuity can be calculated with following formula. It is important to note that for growing annuity future as well as present value may be calculated. In this article we have explained future value of Growing annuity.

Future Value Growing Annuity Concept 

Growing annuity concept is very similar to the regular annuity due concept, however in case of growing annuity the amount of payment (contribution) in an investment plan is increasing with a constant rate. Growing annuity concept has been explained with an example

i= interest Rate

g=Growth rate

n= period

C=Deposited amount

Future Value Growing Annuity Formula Example

Deposited Amount = 5,000

Annual Growth in Deposit   = 4%

Interest Rate = 10%

Period =5 Years

Solution

Annuity Factor =10,000x [(1+10%)⁵-(1+4%)⁵]

                                            10%-4%

=5000 x [1.610 – 1.2166]/.1-.05

=5000 x 7.868

=39340

 Growing Annuity

Future Value Annuity Due Formula

Future Value Annuity Due Formula

Future value of annuity due is calculated to determine the future value of the series of payment regularly made to a financial institution. This concept is widely used in insurance company.

Where;

C= Payment

i= Rate of interest

n= number of period (payment made)

 Future Value of Annuity Due

Future value of annuity due is basically calculating the Final or future value of series of payment made in an investment scheme on annual bases. Future value of annuity due concept has been explained with an example.

Annuity Due Formula Example

Amount Deposited= 4000

Period = 4 Years

Interest Rate =12%

Solution

Annuity Factor =C x [(1+i)ⁿ-1] x (1+r)

                                      i

= Cx [(1+12%)⁴-1] x (1+12%)

             12%

= 4000x (4.7793 x 1.12)

=4000 x 5.353

=21410

Future Value of annuity may also be calculated by following table, but this is method is a time consuming exercise.

	Series of Payment	Interest	Future Value
1	4000	(1.12)4	6294
2	4000	(1.12)3	5619
3	4000	(1.12)2	5017
4	4000	(1.12)1	4480
			21,410

Above example shows that person will receive an amount of 21,410 as result of series of payment he made in four years.