Question

Please explain a situation in reality where the analyst would need to adjust for unequal lives by using the equivalent annuity technique? Please do this by citing a real example that a manager would face.

Answer 1

When we have two or more mutually exclusive projects which have different timelines of operation i.e. their project life varies then the Equivalent Annuity Technique is used for the capital budgeting decision.

The Equivalent Annuity approach calculates a constant annual cash flow generated by the project over its lifespan if it was an annuity and hence a project with the highest Equivalent Annuity is selected among all.

The formula for calculating :

C = (r x NPV) / (1 - (1 + r)^(-n) )

where C = equivalent annuity cash flow

NPV = net present value

r = interest rate per period

n = number of periods

REAL-LIFE EXAMPLE

Suppose a Renewable energy farm has two projects and it has to make a capital budgeting decision. Solar Park costs $20 million and a wind park would cost $35 million. The solar park would generate $7.5 million per annum for 5 years whereas the wind park would generate $8 million for 10 years. The company's cost of capital is 10%.

NPV for solar park = -20 million + (7.5 million)/(1.1) + (7.5 million)/(1.1^2) + (7.5 million)/(1.1^3) + (7.5 million)/(1.1^4) + (7.5 million)/(1.1^5)

NPV for solar park = $8.43 million

NPV for wind park = -35million + (8million)/(1.1) + (8million)/(1.1^2) + (8million)/(1.1^3) + (8million)/(1.1^4) + (8million)/(1.1^5) + (8million)/(1.1^6) + (8million)/(1.1^7) + (8million)/(1.1^8) + (8million)/(1.1^9) + (8million)/(1.1^10)

NPV for wind park = $14.16 million

EAA for solar park = (0.10)*(8.43)/ (1 - 1.1^(-5)) = $2.223 million

EAA for wind park = (0.10)*(14.16)/ (1 - 1.1^(-10)) = $2.304 million

So among both the projects, EAA for wind park is better than solar park. So the manager should slect wind park project.