2. James Manufacturing is in the market to purchase a 5+ Axis CNC Lathe. They ha
ID: 2779966 • Letter: 2
Question
2. James Manufacturing is in the market to purchase a 5+ Axis CNC Lathe. They have narrowed their choices to the three manufacturers listed in the following table. Using an internal rate of return analysis, determine which alternative, if any, should they select if James Manufacturing uses a MARR of 6% per year before income taxes. Compute all relevant internal rate of return values to two decimal places. Show all of your work. Daewoo Miyano Hitachi Manufacturer Initial Cost Salvage Value Annual Income Annual Cost Life, years $225,000-$185,0001 $170,000 $16,000 $18,000 $17,000 $64,000 $56,000 $17,500 |319,0001 12 $63,500 518,000, 12Explanation / Answer
Let us use trial and error method to calculate IRR .
Cash in-flow for last year = Annual income – Annual cost + salvage value
Cash in-flow for remaining year = Annual income – Annual cost
IRR of Daewoo
NPV at 18 %:
Year
Cash Flow
PV Factor @18 %
PV
0
($225,000)
1
($225,000)
1
$ 46,500
0.847457627
$39,407
2
$ 46,500
0.71818443
$33,396
3
$ 46,500
0.608630873
$28,301
4
$ 46,500
0.515788875
$23,984
5
$ 46,500
0.437109216
$20,326
6
$ 46,500
0.370431539
$17,225
7
$ 46,500
0.313925033
$14,598
8
$ 46,500
0.266038164
$12,371
9
$ 46,500
0.225456071
$10,484
10
$ 46,500
0.191064467
$8,884
11
$ 46,500
0.16191904
$7,529
12
$ 64,500
0.137219525
$8,851
NPV
$355
As NPV is positive, let us calculate NPV at 19 %
Year
Cash Flow
PV Factor @19 %
PV
0
($225,000)
1
($225,000)
1
$ 46,500
0.840336134
$39,076
2
$ 46,500
0.706164819
$32,837
3
$ 46,500
0.593415814
$27,594
4
$ 46,500
0.498668751
$23,188
5
$ 46,500
0.419049371
$19,486
6
$ 46,500
0.352142329
$16,375
7
$ 46,500
0.295917923
$13,760
8
$ 46,500
0.248670524
$11,563
9
$ 46,500
0.208966827
$9,717
10
$ 46,500
0.175602375
$8,166
11
$ 46,500
0.147565021
$6,862
12
$ 64,500
0.12400422
$7,998
NPV
($8,379)
IRR = R1+[ NPV1 x (R2-R1)%/(NPV1-NPV2)]
=18% + $355 x (19-18%)/($ 355-(-$8,379)
=18 % +$ 355 x 1 % / $8,734
=18 % + $ 3.55/$8,734
=18 % + 0.000406333
= 18 % + 0.04 %
= 18.04 %
IRR of Miyano
NPV at 7 %:
NPV '@ 7 %
Year
Cash Flow
PV Factor @7 %
PV
0
$ (185,000)
1.00000
$ (185,000)
1
$ 37,000
0.93458
$ 34,579
2
$ 37,000
0.87344
$ 32,317
3
$ 37,000
0.81630
$ 30,203
4
$ 37,000
0.76290
$ 28,227
5
$ 37,000
0.71299
$ 26,380
6
$ 54,000
0.66634
$ 35,982
NPV
$ 2,689.79
As NPV is positive, let us calculate NPV at 8 %
Year
Cash Flow
PV Factor @8 %
PV
0
$ (185,000)
1.00000
$ (185,000)
1
$ 37,000
0.92593
$ 34,259
2
$ 37,000
0.85734
$ 31,722
3
$ 37,000
0.79383
$ 29,372
4
$ 37,000
0.73503
$ 27,196
5
$ 37,000
0.68058
$ 25,182
6
$ 54,000
0.63017
$ 34,029
NPV
$ (3,240.57)
IRR = R1+[ NPV1 x (R2-R1)%/(NPV1-NPV2)]
=7% + $ 2,689.79 x (8-7%)/ ($2,689.79 -(-$3,240.57)
=7 % +$ 2,689.79 x 1 % / $ 5,930.35
=7 % + $ 26.8979 /$ 5,930.35
=7 % + 0.004535623
= 7 % + 0.45 %
= 7.45 %
IRR of Hitachi
NPV at 25 %:
NPV '@25%
Year
Cash Flow
PV Factor @25%
PV
0
($170,000)
1
($170,000)
1
$ 45,500
0.800000
$36,400
2
$ 45,500
0.640000
$29,120
3
$ 45,500
0.512000
$23,296
4
$ 45,500
0.409600
$18,637
5
$ 45,500
0.327680
$14,909
6
$ 45,500
0.262144
$11,928
7
$ 45,500
0.209715
$9,542
8
$ 45,500
0.167772
$7,634
9
$ 45,500
0.134218
$6,107
10
$ 45,500
0.107374
$4,886
11
$ 45,500
0.085899
$3,908
12
$ 61,500
0.068719
$4,226
NPV
$593
As NPV is positive, let us calculate NPV at 26 %
NPV '@26%
Year
Cash Flow
PV Factor @26 %
PV
0
($170,000)
1
($170,000)
1
$ 45,500
0.793651
$36,111
2
$ 45,500
0.629882
$28,660
3
$ 45,500
0.499906
$22,746
4
$ 45,500
0.396751
$18,052
5
$ 45,500
0.314882
$14,327
6
$ 45,500
0.249906
$11,371
7
$ 45,500
0.198338
$9,024
8
$ 45,500
0.157411
$7,162
9
$ 45,500
0.124930
$5,684
10
$ 45,500
0.099150
$4,511
11
$ 45,500
0.078691
$3,580
12
$ 61,500
0.062453
$3,841
NPV
($4,930)
IRR = R1+[ NPV1 x (R2-R1)%/(NPV1-NPV2)]
=25% + $ 593 x (8-7%)/ ($2,689.79 -(-$4,930)
=25 % +$ 593 x 1 % / $5,523
=25 % + $ 5.93 /$ 5,523
=25 % + 0.001072986
= 25 % + 0.10 %
= 25.10 %
As IRR of Hitachi is more than that of another two, Hitachi should be selected.
Year
Cash Flow
PV Factor @18 %
PV
0
($225,000)
1
($225,000)
1
$ 46,500
0.847457627
$39,407
2
$ 46,500
0.71818443
$33,396
3
$ 46,500
0.608630873
$28,301
4
$ 46,500
0.515788875
$23,984
5
$ 46,500
0.437109216
$20,326
6
$ 46,500
0.370431539
$17,225
7
$ 46,500
0.313925033
$14,598
8
$ 46,500
0.266038164
$12,371
9
$ 46,500
0.225456071
$10,484
10
$ 46,500
0.191064467
$8,884
11
$ 46,500
0.16191904
$7,529
12
$ 64,500
0.137219525
$8,851
NPV
$355
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