A Construction company is considering some new testing equipment and can choose
ID: 2562043 • Letter: A
Question
A Construction company is considering some new testing equipment and can choose between three mutually exclusive alternatives. The first option has a first cost of $5000, a uniform annual benefit of $1500, a salvage value of $700, and a life of 8 years. The second option has a first cost of $3500, a benefit of $900 the first year, and increasing by $200 per year thereafter. Its salvage value is $500 and has an estimated life of 6 years. The third option has a first cost of $8000, a benefit of $1500 the first year, and increasing by 2% each year thereafter. Its salvage value is $1000 and it’s estimated to have a 12-year life.
Use incremental rate of return analysis to determine which alternative is best if the company’s MARR is 7%. Use excel or Sheets
Explanation / Answer
Let us compute IRR using trial and error method
Equipment 1:
Let us try with 25%
Equipment 1
Year
Cashflow
PV Factor @ 25%
PV
0
$ (5,000.00)
1
$ (5,000.00)
1
$ 1,500.00
0.8000
$ 1,200.00
2
$ 1,500.00
0.6400
$ 960.00
3
$ 1,500.00
0.5120
$ 768.00
4
$ 1,500.00
0.4096
$ 614.40
5
$ 1,500.00
0.3277
$ 491.52
6
$ 1,500.00
0.2621
$ 393.22
7
$ 1,500.00
0.2097
$ 314.57
8
$ 2,200.00
0.1678
$ 369.10
NPV1
$ 110.81
As NPV is positive let us try with 26%
Equipment 1
Year
Cashflow
PV Factor @ 26%
PV
0
$ (5,000.00)
1.0000
$ (5,000.00)
1
$ 1,500.00
0.7937
$ 1,190.48
2
$ 1,500.00
0.6299
$ 944.82
3
$ 1,500.00
0.4999
$ 749.86
4
$ 1,500.00
0.3968
$ 595.13
5
$ 1,500.00
0.3149
$ 472.32
6
$ 1,500.00
0.2499
$ 374.86
7
$ 1,500.00
0.1983
$ 297.51
8
$ 2,200.00
0.1574
$ 346.30
NPV2
$ (28.72)
IRR= R1 + NPV1 (R2-R1) % / NPV1- NPV2
=25% +$110.81 (26-25)%/($110.81-(-$28.72)
=25% +$1.1081 / $ 139.53
=25% +0.79%
=25.79%
Equipment 2:
Let us try with 29%
Equipment 2
Year
Cashflow
PV Factor @ 29%
PV
0
$ (3,500.00)
1
$ (3,500.00)
1
$ 900.00
0.7752
$ 697.67
2
$ 1,100.00
0.6009
$ 661.02
3
$ 1,300.00
0.4658
$ 605.58
4
$ 1,500.00
0.3611
$ 541.67
5
$ 1,700.00
0.2799
$ 475.88
6
$ 2,400.00
0.2170
$ 520.80
NPV1
$ 2.63
As NPV is positive let us try with 30%
Equipment 2
Year
Cashflow
PV Factor @ 30%
PV
0
$ (3,500.00)
1.0000
$ (3,500.00)
1
$ 900.00
0.7692
$ 692.31
2
$ 1,100.00
0.5917
$ 650.89
3
$ 1,300.00
0.4552
$ 591.72
4
$ 1,500.00
0.3501
$ 525.19
5
$ 1,700.00
0.2693
$ 457.86
6
$ 2,400.00
0.2072
$ 497.22
NPV2
$ (84.81)
IRR= R1 + NPV1 (R2-R1) % / NPV1- NPV2
=29% +$2.63 (30-29)%/($2.63-(-$84.81)
=29% +0.0263/ $ 87.44
=29% +0.03%
=29.03%
Equipment 3:
Let us try with 27%
Equipment 3
Year
Cashflow
PV Factor @ 17%
PV
0
$ (8,000.00)
1
$ (8,000.00)
1
$ 1,500.00
0.8547
$ 1,282.05
2
$ 1,530.00
0.7305
$ 1,117.69
3
$ 1,560.60
0.6244
$ 974.39
4
$ 1,591.81
0.5337
$ 849.47
5
$ 1,623.65
0.4561
$ 740.56
6
$ 1,656.12
0.3898
$ 645.62
7
$ 1,689.24
0.3332
$ 562.85
8
$ 1,723.03
0.2848
$ 490.69
9
$ 1,757.49
0.2434
$ 427.78
10
$ 1,792.64
0.2080
$ 372.94
11
$ 1,828.49
0.1778
$ 325.12
12
$ 2,865.06
0.1520
$ 435.42
NPV1
$ 224.57
As NPV is positive let us try with 18%
Equipment 3
Year
Cashflow
PV Factor @ 18%
PV
0
$ (8,000.00)
1
$ (8,000.00)
1
$ 1,500.00
0.8475
$ 1,271.19
2
$ 1,530.00
0.7182
$ 1,098.82
3
$ 1,560.60
0.6086
$ 949.83
4
$ 1,591.81
0.5158
$ 821.04
5
$ 1,623.65
0.4371
$ 709.71
6
$ 1,656.12
0.3704
$ 613.48
7
$ 1,689.24
0.3139
$ 530.30
8
$ 1,723.03
0.2660
$ 458.39
9
$ 1,757.49
0.2255
$ 396.24
10
$ 1,792.64
0.1911
$ 342.51
11
$ 1,828.49
0.1619
$ 296.07
12
$ 2,865.06
0.1372
$ 393.14
NPV1
$ (119.29)
IRR= R1 + NPV1 (R2-R1) % / NPV1- NPV2
=17% +$224.57 (18-17)%/($224.57-(-$119.29)
=17% + $2.2457 / $ 343.86
=17% +0.65%
=17.65%
Equipment 2 is best as it has highest IRR
Equipment 1
Year
Cashflow
PV Factor @ 25%
PV
0
$ (5,000.00)
1
$ (5,000.00)
1
$ 1,500.00
0.8000
$ 1,200.00
2
$ 1,500.00
0.6400
$ 960.00
3
$ 1,500.00
0.5120
$ 768.00
4
$ 1,500.00
0.4096
$ 614.40
5
$ 1,500.00
0.3277
$ 491.52
6
$ 1,500.00
0.2621
$ 393.22
7
$ 1,500.00
0.2097
$ 314.57
8
$ 2,200.00
0.1678
$ 369.10
NPV1
$ 110.81
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