Question

Can someone explain to me whether we can compare the NPVs of Projects with different life times and Investment amounts? I know it has to do with the reinvestment assumption of cash flows but don´t really understand the sense behind it. Can someone please make this clear to me (best by using NPV calculations and tables for 2 different Projects with different Investment amounts)

Thanks a lot

Answer 1

Incase of two mutually exclusive projects with different Investment amounts and unequal lives we use Equivalent Annual Annuity Approach to evaluate the proposal.
EAA approach calculates the constant annual cash flow generated by a project over its lifespan if it was an annuity. When used to compare projects with unequal lives, an investor should choose the one with the higher EAA.
The equivalent annual annuity formula provides a comparison relative to time which eliminates the need for considering reinvestment with the same earnings as the current investment.
NPV approach itself assumes that interim cash flows are reinvested at project weighted average cost of capital (discount rate) itself.
Lets understand with example:
Project A (life 5 year)	Year
	0	1	2	3	4	5
Initial Outlay	$      (500,000)
Cash inflow		$       300,000	$       315,000	$    330,750	$      347,288	$    364,652
Discount Rate of project 10%
Discount factor @10% 1/(1+r)^n)		0.909	0.826	0.751	0.683	0.621
PV of Cash Inflow		$       272,727	$       260,331	$    248,497	$      237,202	$    226,420
PV of Cash Outflow	$      (500,000)
PV of Cash Inflow	$    1,245,177
NPV	$       745,177
Formula for EAA =	(r x NPV)
	(1 - (1 + r)^-n )
EAA for Project A =	(10%*745177)	=	74518	=	$      196,576
	(1-(1+10%)^-5)		0.379
Project B (life 7 year)	Year
	0	1	2	3	4	5	6	7
Initial Outlay	$      (600,000)
Cash inflow		$       275,000	$       288,750	$    303,188	$      318,347	$    334,264	$   350,977	$ 368,526
Discount Rate of project 10%
Discount factor @11% 1/(1+r)^n)		0.901	0.812	0.731	0.659	0.593	0.535	0.482
PV of Cash Inflow		$       247,748	$       234,356	$    221,688	$      209,705	$    198,370	$   187,647	$ 177,504
PV of Cash Outflow	$      (600,000)
PV of Cash Inflow	$    1,477,017
NPV	$       877,017
Formula for EAA =	(r x NPV)
	(1 - (1 + r)^-n )
EAA for Project A =	(11%*877107)	=	96472	=	$      186,116
	(1-(1+11%)^-7)		0.5183
Decision
EAA of Project A	$        196,576
EAA of Project B	$        186,116
Comparing these two projects, the 5 year project will return a higher amount relative to the time of the investment. Although the 7 year project has a higher NPV, the 5 year project can be reinvested and have additional earnings for the 2 years that remain on the 7 year project.
The EAA tells us about the average cash flow from each project, given their NPVs and useful lives