36. Chingos and Daughters Construction is considering three investment propos- a
ID: 2786584 • Letter: 3
Question
36. Chingos and Daughters Construction is considering three investment propos- als: A, B, and C. Proposals A and B are mutually exclusive, and Proposal Cis contingent on proposal B. The cash flow data for the investments over a 10-year planning horizon are given below. The company has a budget limit of $1 million for investments of the type being considered currently. MARR = 15%. NCF(B) $600,000 $800,000 $470,000 10 years $70,000 $130,000 $65,000 $400,000 $600,000 $260,000 $270,000 NCF(A) NCF(C) Initial investment Planning horizon Salvage values Annual receipts Annual disbursements 10 years 10 years $130,000 $70,000 Determine which alternative should be selected using the internal i return method. rate dfExplanation / Answer
NCF(A) :
Initial Investment=$600,000
Net Annual Cash Inflow =Annual Receipts – Annual Disbursement
=$400,000-$130,000
=$270,000
10th Year Net Annual Cash inflow =Net Annual Cash Inflow + Salvage Value
=$270,000+$70,000
=$340,000
NCF(B) :
Initial Investment=$800,000
Net Annual Cash Inflow =Annual Receipts – Annual Disbursement
=$600,000-$270,000
=$330,000
10th Year Net Annual Cash inflow =Net Annual Cash Inflow + Salvage Value
=$330,000+$130,000
=$460,000
NCF(c) :
Initial Investment=$470,000
Net Annual Cash Inflow =Annual Receipts – Annual Disbursement
=$260,000-$70,000
=$190,000
10th Year Net Annual Cash inflow =Net Annual Cash Inflow + Salvage Value
=$190,000+$65,000
=$255,000
Let us compute IRR using trial and error method
Let us try with 43%
NCF(A)
Year
Net Cash flow
PV Factor @ 43%
PV
0
$ (600,000)
1.0000
$ (600,000.00)
1
$ 270,000
0.6993
$ 188,811.19
2
$ 270,000
0.4890
$ 132,035.80
3
$ 270,000
0.3420
$ 92,332.72
4
$ 270,000
0.2391
$ 64,568.34
5
$ 270,000
0.1672
$ 45,152.68
6
$ 270,000
0.1169
$ 31,575.30
7
$ 270,000
0.0818
$ 22,080.63
8
$ 270,000
0.0572
$ 15,441.00
9
$ 270,000
0.0400
$ 10,797.90
10
$ 340,000
0.0280
$ 9,508.64
NPV1
$ 12,304.22
As NPV is positive let us try with 44%
NCF(A)
Year
Net Cash flow
PV Factor @ 44%
PV
0
$ (600,000)
1.0000
$ (600,000.00)
1
$ 270,000
0.6944
$ 187,500.00
2
$ 270,000
0.4823
$ 130,208.33
3
$ 270,000
0.3349
$ 90,422.45
4
$ 270,000
0.2326
$ 62,793.37
5
$ 270,000
0.1615
$ 43,606.51
6
$ 270,000
0.1122
$ 30,282.30
7
$ 270,000
0.0779
$ 21,029.37
8
$ 270,000
0.0541
$ 14,603.73
9
$ 270,000
0.0376
$ 10,141.48
10
$ 340,000
0.0261
$ 8,868.58
NPV2
$ (543.88)
IRR= R1+NPV1(R2-R1)%/NPV1-NPV2
= 43 % + $ 12,304.22 x (44 -43)%/ 12,304.22 –( –543.88)
= 43 % + $ 12,304.22 x 1%/ (12,304.22 + 543.88)
= 43 % + $ 123.0422 / (12,304.22 + 543.88)
=43% +$123.0422/ $ 12,848.09
=43% +0.96%
=43.96%
NCF B:
Let us try with 40%
NCF(B)
Year
Net Cashflow
PV Factor @ 40%
PV
0
$ (800,000)
1.0000
$ (800,000.00)
1
$ 330,000
0.7143
$ 235,714.29
2
$ 330,000
0.5102
$ 168,367.35
3
$ 330,000
0.3644
$ 120,262.39
4
$ 330,000
0.2603
$ 85,901.71
5
$ 330,000
0.1859
$ 61,358.36
6
$ 330,000
0.1328
$ 43,827.40
7
$ 330,000
0.0949
$ 31,305.29
8
$ 330,000
0.0678
$ 22,360.92
9
$ 330,000
0.0484
$ 15,972.09
10
$ 460,000
0.0346
$ 15,902.94
NPV1
$ 972.73
As NPV is positive let us try with 41%
NCF(B)
Year
Net Cashflow
PV Factor @ 41%
PV
0
$ (800,000)
1.0000
$ (800,000.00)
1
$ 330,000
0.7092
$ 234,042.55
2
$ 330,000
0.5030
$ 165,987.63
3
$ 330,000
0.3567
$ 117,721.72
4
$ 330,000
0.2530
$ 83,490.58
5
$ 330,000
0.1794
$ 59,213.18
6
$ 330,000
0.1273
$ 41,995.16
7
$ 330,000
0.0903
$ 29,783.80
8
$ 330,000
0.0640
$ 21,123.26
9
$ 330,000
0.0454
$ 14,981.04
10
$ 460,000
0.0322
$ 14,810.40
NPV2
$ (16,850.67)
IRR= R1+NPV1(R2-R1)%/NPV1-NPV2
=40% + $972.73(41-40)% /($972.73-(-$16,850.67)
=40% + $9.7273/ $ 17,823.40
=40% +0.05%
NCF(C)
Let us try with 39%
NCF(C)
Year
Net Cashflow
PV Factor @ 39%
PV
0
$ (470,000)
1.0000
$ (470,000.00)
1
$ 190,000
0.7194
$ 136,690.65
2
$ 190,000
0.5176
$ 98,338.60
3
$ 190,000
0.3724
$ 70,747.19
4
$ 190,000
0.2679
$ 50,897.26
5
$ 190,000
0.1927
$ 36,616.73
6
$ 190,000
0.1386
$ 26,342.97
7
$ 190,000
0.0997
$ 18,951.78
8
$ 190,000
0.0718
$ 13,634.37
9
$ 190,000
0.0516
$ 9,808.90
10
$ 255,000
0.0371
$ 9,470.92
NPV1
$ 1,499.38
As NPV is positive let us try with 40%
NCF(C)
Year
Net Cash flow
PV Factor @ 40%
PV
0
$ (470,000)
1.0000
$ (470,000.00)
1
$ 190,000
0.7143
$ 135,714.29
2
$ 190,000
0.5102
$ 96,938.78
3
$ 190,000
0.3644
$ 69,241.98
4
$ 190,000
0.2603
$ 49,458.56
5
$ 190,000
0.1859
$ 35,327.54
6
$ 190,000
0.1328
$ 25,233.96
7
$ 190,000
0.0949
$ 18,024.26
8
$ 190,000
0.0678
$ 12,874.47
9
$ 190,000
0.0484
$ 9,196.05
10
$ 255,000
0.0346
$ 8,815.76
NPV2
$ (9,174.36)
IRR= R1+NPV1(R2-R1)%/NPV1-NPV2
=39% +$1,499.38 (40-39)%/$1,499.38-(-$9,174.36)
=39% +$14.9938 / $ 10,673.74
=39%+0.14%
=39.14%
Proposal A to be as It has Higher IRR
NCF(A)
Year
Net Cash flow
PV Factor @ 43%
PV
0
$ (600,000)
1.0000
$ (600,000.00)
1
$ 270,000
0.6993
$ 188,811.19
2
$ 270,000
0.4890
$ 132,035.80
3
$ 270,000
0.3420
$ 92,332.72
4
$ 270,000
0.2391
$ 64,568.34
5
$ 270,000
0.1672
$ 45,152.68
6
$ 270,000
0.1169
$ 31,575.30
7
$ 270,000
0.0818
$ 22,080.63
8
$ 270,000
0.0572
$ 15,441.00
9
$ 270,000
0.0400
$ 10,797.90
10
$ 340,000
0.0280
$ 9,508.64
NPV1
$ 12,304.22
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