Question

What is the yearly cost savings that Widgets, Inc. obtains by gluing widgets compared to welding them?

4.) Consider the following alternatives in the table below. <25 pts>

Alternative	A	B
Initial Cost	$900	$2,500
Uniform Annual Benefit	$220	$800
Useful Life (years)	20	10

The analysis period is 20 years, but there will be no replacement for Alternative B after 10 years. Based on a 6% interest rate and an annual cash flow analysis, state the equivalent uniform annual worth of each alternative. Also state which alternative is best to be selected and why

Answer 1

Under Equivalent Annual Uniform Worth we calculate the NPV as usual and then we dive the NPV with the PV of annuity factors of the project life. This will give the project earning on per year basis.

PV of annuity factors can be caluted as sum of all the anuitty till life of project.

(1/1.06^1)+(1/1.06^2)...........+ (1/1.06^n)

Under Alternative A

PV of Uniform Annual Benefit = $220   PVaf(6%, 20 Years)

PV of Uniform Annual Benefit = $220 11.4699

PV of Uniform Annual Benefit = $2,523.38

NPV = (PV of inflow - Outflow)

NPV = $1,623.38 ($2,523.38 - $900)

Equivalent Uniform Annual worth = NPV / PVaf(%, Years)

Equivalent Uniform Annual worth =$141.53 ($1,623.38/11.4699)

Under Alternative B

PV of Uniform Annual Benefit = $800   PVaf(6%, 10 Years)

PV of Uniform Annual Benefit = $800 7.3601

PV of Uniform Annual Benefit = $5888.08

NPV = (PV of inflow - Outflow)

NPV = $3,388.08 ($5888.08 - $2500)

Equivalent Uniform Annual worth = NPV / PVaf(%, Years)

Equivalent Uniform Annual worth =$460.33 ($3388.08 / 7.3601)

DECISION - Since Equivalent annual worth means comparing the 2 different project having 2 different life cycle under a sinlge 1 year terms. So basically it represent the NPV earned per Year no matter what the life is of. So we see that alternative B has having higher alternative ($460.33) as compared to alternative A ($141.53). Hence Alternative B is best.