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# Equivalent annual annuity

### Equivalent Annual Annuity (EAA)

This approach used for projects which does not have equal lives. Another name of Equivalent Annual Annuity (EAA) is annualized NPV. In the question there are two machines with two different lives and their different NPV rates. Question asking to calculate Equivalent Annual Annuities of those machines and compare them which one is more useful for the firm. One of machine has 3 year lives and £32,066 NPV and other machine has 6 year lives and £40,658. With calculating Equivalent Annual Annuity we will find which investment will provide more return to the firm annuity

FORMULA

EAA = NPV/ PVIFAn,k

PVIFAn,k is Present Value Investment Factor of an annuity at n and k periods of interest rate factor instead of PVIFAn,k we can use another formula as below

PVIFAn,k = [1-1/(1+k)n]/k

and so,

EAA= NPV/ [1-1/ (1+k) n]/k

### 2-CACULATION AND COMPAIRING THE INVESTMENTS

Project A

NPV= £ 32,066

k= %10

n= 3 years

EAA = 32,066/[1-1/(1+0,10)^3]/0,10

EAA= £ 12,894

Project A will provide £12,894 per annual to the firm

Project B

NPV= £ 40,658

k= %10

n= 6 years

EAA = 40,658/[1-1/(1+0,10)^6]/0,10

EAA= £ 9,335

Project B will provide £ 9,335 per annual to the firm

Machine A more advantageous for the firm than Machine B according to Equivalent Annual Annuity calculation. But I am interested in their first set up cost if project A has price advantages as well I will be able to recommend for invest on Machine A

NPV= CF0+ PV n *1 / (1+k) n

Project A

32,066 = CF A + PV 1 * 1/ (1+ 0, 10) ^ 1 + ... + PV 3*1/ (1+ 0, 10) ^ 3

If we accept that every year this machine will supply the same amount of PV so PV will be equal to each other during the 3 years

PV will be £ 33,000 and CFA will be calculated £ 50,000 (initial cost of investment)

Project B

40,658 = CF B + PV 1 * 1/ (1+ 0, 10) ^ 1 + ... + PV 6*1/ (1+ 0, 10) ^ 6

If we accept that every year this machine will supply the same amount of PV so PV will be equal to each other during the 6 years

### 3- CONCLUSION

EAA and Initial Cost Calculations are showing that investing on Project A (it mean investing on Machine A) will bring more profits than investing on Project B (investing on Machine B) Machine B has more useful lives than Machine A but Machine B is much more expensive than Machine B. Because of initial cost and annual return advantages Firm should choose Machine A as their Project.

### 4- REFERENCES

• Baker, H.K. Powel, G.E (2005) Understanding Financial Management Blackwell Publishing Ltd, UK

### 5- BIBLIOGRAPHIES

• http://www.fao.org/docrep/w4343e/w4343e07.htm
• http://www.finance-lib.com/financial-term-equivalent-annual-annuity.html
• http://www.swlearning.com/finance/brigham/ffm10e/web_cd_appendixes/11D.pdf
• http://www.washburn.edu/sobu/rhull/cf12.html

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