Question

  Vanderheiden Inc. is considering two average-risk alternative ways of producing its patented polo shirts. Process S has a cost of $9,000 and will produce net cash flows of $6,000 per year for 2 years. Process L will cost $12,000 and will produce cash flows of $5,000 per year for 4 years. Both projects can be repeated if needed. No inflation is expected over the next 4 years. If Vanderheiden’s WACC is 10%, what is the common life NPV of project S and L respectively? Which one is the most profitable project?

Answer 1

Step 1: Identification of Alternatives

Alternative 1 : Process S
Alternative 2 : Process L  

Step 2 : Calculation of Net present value in case of Process S
Net Present Value (NPV) = Present value of cash inflows - Present value of cash outflows

Particulars	Period	Amount	PVF @ 10%	Present Value
Cash Outflows:
Cost of Process	0	($9,000.00)	1	($9,000.00)
Cash Inflows:
Annual Cash Inflows	1-2	$6,000.00	1.73553719	$10,413.22
Net Present Value				$1,413.22

Step 2 : Calculation of Net present value in case of Process L
Net Present Value (NPV) = Present value of cash inflows - Present value of cash outflows

Particulars	Period	Amount	PVF @ 10%	Present Value
Cash Outflows:
Cost of Process	0	($12,000.00)	1	($12,000.00)
Cash Inflows:
Annual Cash Inflows	1-4	$5,000.00	3.169865446	$15,849.33
Net Present Value				$3,849.33

Step 3 : Calculation of Common life NPV of Project S and L

In order to calculate common life NPV of project S and L we would calculate the Equivalent Annual NPV which will show the NPV earned annually for both the projects.  

Equivalent Annual NPV = NPV / PVAF(r,t)
where r = required rate of return
t = life of project

	Process S	Process L
Life	2 years	4 years
NPV	$1,413.22	$3,849.33
PVAF (10%,n)	1.73553719	3.169865446
Equivalent Annual NPV	$814.29	$1,214.35

Decision: Since, the equivalent annual NPV of Process L is higher than that for Process S. It means Process L is more profitable.

Note :
PVF(r,t) = (1/(1+r))^n
PVAF = (1/(1+r))^1 + (1/(1+r))^2 +...+(1/(1+r))^n