Question

Unequal

liveslong dash

ANPV

approach   Evans Industries wishes to select the best of three possible​ machines, each of which is expected to satisfy the​ firm's ongoing need for additional​ aluminum-extrusion capacity. The threemachines - A, B, and C -are equally risky. The firm plans to use a cost of capital of 11.9 %to evaluate each of them. The initial investment and annual cash inflows over the life of each machine are shown in the following table.  ​

	Machine A	Machine B	Machine C
Initial investment	92700	65600	100000
Year		Cash inflows
1	11200	10100	29500
2	11200	20200	29500
3	11200	30000	29500
4	11200	39200	29500
5	11200	-	29500
6	11200	-	-

a. Calculate the NPV for each machine over its life. Rank the machines in descending order on the basis of NPV.

b. Use the annualized net present value​ (ANPV) approach to evaluate and rank the machines in descending order on the basis of ANPV.

c. Compare and contrast your findings in parts​ (a​)and ​(b​). Which machine would you recommend that the firm​ acquire?

Answer 1

a)NPV =Total Pv of inflow-initial outflow discount rate =11.9%

PVAF=1-(1+r)^(-n) r is the discount rate n is the number of years

Machine A Inflows =$11,200 for 6 years Initial Investment =$92,700 So Total PV =$11,200*PVAF of 11.9% for 6 years =$11,200*4.1226=$46173.12 NPV =$46173-$92,700=($46527)

Machine B Outflow =$65,600 Inflows=Year 1 =$10,100 Year 2 $20,200 Year 3 30,000 Year 4 $39,200 Total PV of inflows =$10,100*.8936=$9025.36 Year 2 $20,200*.7987=$16133.74 Year 3=$30,000*.7137=$21,411 Year 4 =$39,200*.6381=$25,013.52 Total =$71,583.62 NPV=$71,583.62-$65,600=$5983.62

Machine C Outflow = $100,000 Inflows =$29,500 for 5 years Total pv of inflows =$29,500*PVAF for 11.9% for 5 Years =$29,500*3.6134=$106,595.3 NPV =$106,595.3-$100,000=$6,595.3

In descending order of NPV Machine C{$6595} , Machine B{$5983.62} , Machine A {-46,527}

b)Annualized NPV=ANPV=NPV/PVAF

For Machine A NPV =($46,527) Annuity factor =4.1226 ANPV =(11285.839)

For Machine B NPV=$5983.62 Annuity factor =3.043 ANPV=$5983.62/3.043=$1966.355

For Machine C NPV =$6595 Annuity Factor =3.6134 ANPV=$6595/3.6134=$1825.15

In descending order of ANPV Machine B{1966.355},Machine C {$1825.15},Machine A {-$11285.839}

c)According to NPV method the most beneficial machine is Machine C{6595}and according to ANPV the most beneficial machine is Machine B{1966.355}.ANPV method is the most efficient method when it comes to comparing projects with unequal lives since it conerts NPV into an annual annuity value .So the firm should acquire Machine B since it has the highest ANPV

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