Calculate the IRR, NPV, and PI for projects with the following cash flows. Do ea
ID: 2764114 • Letter: C
Question
Calculate the IRR, NPV, and PI for projects with the following cash flows. Do each NPV and PI calculation at costs of capital of 9% and 13%. Round PI to two decimal places. Round IRR to the nearest whole percentage. Round NPV to the nearest dollar. Use a minus sign to indicate a negative NPV. An initial outlay of $4,500 and inflows of $1,000 for seven years. An initial outlay of $37,000 and inflows of $12,300 for four years. An investment of $66,000 followed by 12 years of income of $10,300. An outlay of $31,024 followed by receipts of $7,600 for six years.Explanation / Answer
(a) An Initial Outlay of $ 4,500 and Inflows of $ 1,000 for seven years
IRR
NPV = 0
0 = (1,000 (Present Value Annuity Factor ( i%, for 7 Years))) - 4,500
Let i = 10%
Then NPV = 1,000 (4.8684) - 4,500 = 368.40
Let i = 15%
Then NPV = 1,000 (4.1604) - 4,500 = (-)339.60
IRR = 10% + (339.60 / 708) x 5% = 12.39% or 12%
NPV (9%)
NPV = 1,000 (Present Value Annuity Factor (9%, 7 Years) - 4,500
= 1,000 (5.0330) - 4,500
= $ 533
NPV (13%)
NPV = 1,000 (Present Value Annuity Factor (13%, 7 Years) - 4,500
= 1,000 (4.4226) - 4,500
= (-)$ 77.40 or (-)$ 77
PI (9%)
PI = Present Value of Cash Inflows / Initial Investment
= 1,000 (5.0330) / 4,500
= 1.118 or 1.12
PI (13%)
PI = Present Value of Cash Inflows / Initial Investment
= 1,000 (4.4226) / 4,500
= 0.9828 or 0.98
(b) An Initial Outlay of $ 37,000 and Inflows of $ 12,300 for four years
IRR
NPV = 0
0 = (12,300 (Present Value Annuity Factor ( i%, for 4 Years))) - 37,000
Let i = 10%
Then NPV = 12,300 (3.1699) - 37,000 = (-)1883.50
Let i = 9%
Then NPV = 12,300 (3.2397) - 37,000 = 2,848.31
IRR = 9% + (2,848.31 / 4,731.81) x 1% = 9.60 % or 10%
NPV (9%)
NPV = 12,300 (Present Value Annuity Factor (9%, 4 Years) - 37,000
= 12,300 (3.2397) - 37,000
= $ 2,848.31 or $ 2,848
NPV (13%)
NPV = 12,300 (Present Value Annuity Factor (13%, 4 Years) - 37,000
= 12,300 (2.9745) - 37,000
= (-) $ 413.65 or (-) $ 414
PI (9%)
PI = Present Value of Cash Inflows / Initial Investment
= 12,300 (3.2397) / 37,000
= 1.076 or 1.08
PI (13%)
PI = Present Value of Cash Inflows / Initial Investment
= 12,300 (2.9745) / 37,000
= 0.988 or 0.99
(c) An Initial Outlay of $ 66,000 and Inflows of $ 10,300 for Twelve years
IRR
NPV = 0
0 = (10,300 (Present Value Annuity Factor ( i%, for 12 Years))) - 66,000
Let i = 10%
Then NPV = 10,300 (6.8137) - 66,000 = $ 4,181.11 or $ 4,181
Let i = 15%
Then NPV = 10,300 (5.4206) - 66,000 = (-) $ 10,167.82 or (-) $ 10,168
IRR = 10% + (4,181.11 / 14,348.93) x 5% = 11.46 % or 11%
NPV (9%)
NPV = 10,300 (Present Value Annuity Factor (9%, 12 Years) - 66,000
= 10,300 (7.1607) - 66,000
= $ 7,755.21 or $ 7,755
NPV (13%)
NPV = 10,300 (Present Value Annuity Factor (13%,12 Years) - 66,000
= 10,300 (5.9176) - 66,000
= (-) $ 5,048.72 or (-) $ 5,049
PI (9%)
PI = Present Value of Cash Inflows / Initial Investment
= 10,300 (7.1607) / 66,000
= 1.1175 or 1.12
PI (13%)
PI = Present Value of Cash Inflows / Initial Investment
= 10,300 (5.9176) / 66,000
= 0.924 or 0.92
(d) An Initial Outlay of $ 31,024 and Inflows of $ 7,600 for six years
IRR
NPV = 0
0 = (7,600 (Present Value Annuity Factor ( i%, for 6 Years))) - 31,024
Let i = 12%
Then NPV = 7,600 (4.1114) - 31,024 = 222.64
Let i = 15%
Then NPV = 7,600 (3.7845) - 31,024 = (-) 2,261.80
IRR = 12% + (222.64 / 2,484.44) x 3% = 12.27% or 12%
NPV (9%)
NPV = 7,600 (Present Value Annuity Factor (9%, 6 Years) - 31,024
= 7,600 (4.4859) - 31,024
= $ 3,068.84 or $ 3,069
NPV (13%)
NPV = 7,600 (Present Value Annuity Factor (13%, 6 Years) - 31,024
= 7,600 (3.9975) - 31,024
= (-)$ 643
PI (9%)
PI = Present Value of Cash Inflows / Initial Investment
= 7,600 (4.4859) / 31,024
= 1.099 or 1.10
PI (13%)
PI = Present Value of Cash Inflows / Initial Investment
= 7,600 (3.9975) / 31,024
= 0.9793 or 0.98
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