Question

A company is trying to decide between TWO projects that would provide the same necessary service and each project can be repeated indefinitely at the same cost and same cash flows.

The first project costs $7,000 and is expected to generate cash flows of $4,250 for NINE years.

The second project cost $10,000 and is expected to generate cash flows of $4,400 for ELEVEN years

While the replacement chain approach is a valid option, you currently cannot use a spreadsheet for your analysis.

Given that both projects are expected to be repeated indefinitely WITHOUT a change in initial cost, use the Equivalent Annual Annuity (EAA) approach to determine the best project.

The company's cost of capital is 9%.

Use the Equivalent Annual Annuity (EAA) approach (NUS in the calculator) to analyze the two projects.

What is the Net Present Value (NPV) of the better choice?

Answer 1

Equivalent Annual Annuity =r*NPV/1-(1+r)^(-n) r is the cost of capital n is the number of periods r is given as 9%

NPV=Total PV of inflows -Initial outflow

For first project Initial outflow =$7,000 and Cash inflow =$4,250 for 9 years cost of capital is 9% PVAF =1-(1+r)^(-n)/r

PVAF for 9 years at 9% =5.9952 Total Pv of inflows =$4,250*5.9952=$25,479.6 NPV =$25,479.6-$7,000 =$18,479.6

EAA =.09*$18479.6/1-(1+.09)^(-9) =$1663.164/.53957 =$3,082.387

For Second project Initial outflow =$10,000 and cash inflow =$4400 for 11 years cost of capital =9% PVAF for 11 years at 9%=6.8052 Total PV of inflows =$4400*6.8052=$29,942.88 NPV =$29,942.88-$10,000 =$19,942.88

EAA =.09*$19942.88/1-(1+.09)^(-11) =$1794.859/.61246 =$2930.573

The first project is the better option due to higher Equivalent Annual Annuity

The NPV of the better choice (First Project)

For first project Initial outflow =$7,000 and Cash inflow =$4,250 for 9 years cost of capital is 9% PVAF =1-(1+r)^(-n)/r

PVAF for 9 years at 9% =5.9952 Total Pv of inflows =$4,250*5.9952=$25,479.6 NPV =$25,479.6-$7,000 =$18,479.6