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What is Equivalent Annual Annuity (EAA)?

 To evaluate the project performance capital budgeting tools are used like internal rate of return (IRR), Average rate of return (ARR), discounted payback period, Net Present Value (NPV) etc. these tools are also used to make a decision to invest in those big projects( which needs huge amount to invest) or not?

These tools are helpful to compare two or more than two projects whose time interval of cash flows are same to know which project is more beneficial for the company.

But these tools are not beneficial to use when the time period of the cash inflow are not same. In that case equivalent annual annuity is used.

Equivalent Annual annuity: It is used when projects are mutually exclusive. The time interval of cash inflows of projects is differ from one another. With the help of it we can find the measure each projects correctly according to their cash flows in given period.

Formula:

EAA = NPV*r / 1-(1+r) ^-n

Where as

EAA = Equivalent Annual Annuity

NPV = Net Present Value

R = rate of return

N = number of years

Example: Suppose Company XYZ wants to invest Rs. 50,000 for that Company have two projects A and B. Both the projects have given 8 % per annum rate of return. Find out which project is good for the company in compare to another. Other information is as follows:

Project A

Project B

15,000

8,000

18,000

12,000

7,000

10,000

 

4,500

 

Solution:

Years

Project A

Project B

Discount rate(0.08)

Present value  of project A

Present Value of project B

 

(50,000)

(50,000)

 

(50,000)

(50,000)

1

15,000

8,000

1.08

13,888.89

7,407.41

2

18,000

12,000

1.1664

15,432.10

10,288.07

3

7,000

10,000

1.259712

5,556.83

7,938.32

4

 

4,500

1.36048896

 

3,307.63

NPV

 

 

 

-15,122.19

-21,058.57

EAA = NPV*r / 1-(1+r) ^-n

Project A:

= -15,122.19*0.08 / 1-(1+0.08) ^-3

=   -1,209.7752 / 1-(1/1.259712)

=   -1,209.7752 / 1 – 0.793832241

= -1,209.7752/0.206167759

= Rs. -5867.92

Project B:

= -21,058.57*0.08 / 1-(1+0.08) ^-4

= -1, 684.6856/ 1-(1/1.36048896)

= -1,684.6856/ 1 – 0.735029853

= -1,684.6856/0.264970147

= Rs. -6358.02

Project A is better option in comparison to project B.

Example: Find out which project is more beneficial for the company and the rate of return is 10% and further information is given below:

Project P

Project Q

(1,00,000)

(1,00,000)

30,000

30,000

34,000

25,000

28,000

23,000

 

19,000

 

Solution:

Years

Project P

Project Q

Discount rate

Present value of project P

Present value of project Q

0

(1,00,000)

(1,00,000)

10%

(1,00,000)

(1,00,000)

1

30,000

30,000

1.1

27,272.73

27,272.73

2

34,000

25,000

1.21

28,099.17

20,661.16

3

28,000

23,000

1.331

21,036.81

17,280.24

4

20,000

19,000

1.4641

13,660.27

12,977.26

5

 

15,000

1.61051

 

9,313.82

Total

 

 

 

90,068.98

87,505.21

 

NPV of project P= Present Value of Cash inflows – Initial investment

= 90,068.98 – 1, 00,000

= Rs. -9,931.02

NPV of project Q = Present value of cash inflows – Initial investment

= 87,505.21 -1, 00,000

= Rs. – 12,494.79

EAA of project P = -9,931.02*0.10 / 1-(1+0.10) ^-4

= -993.102/1-(1/1.4641)

= -993.102 / 1- 0.683013455

= -993.102 / 0.316986545

= Rs.-3,132.95

EAA of project Q = -12,494.79*0.10 / 1-(1+0.10) ^-5

= -1,249.479/1-(1/1.61051)

= -1,249.479 / 1- 0.620921323

= -1,249.479 / 0.379078677

= Rs.-3,296.09

Project P is better than Project Q

 

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