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E N G I N E E R I N G
E C O N O M Y
SOLUTIONS TO PROBLEM SET #6 – PROJECT EVALUATION CRITERIA
1.
The time distribution of cash flows associated with the project is as follows:
Time 0
:
50 000
Years 1 to 15
:
20 000  8000 = 12 000
To determine whether the project is worthwhile economically, the net present value may be
computed, i.e., the annual cash flows are first discounted at a rate of 20 percent, the minimum
acceptable return on investment, and then summed algebraically.
NPV = 50 000 + 12 000 (P/A,20%,15)
= 50 000 + 12 000 (4.6755) = $6106
The net present value is positive.
Therefore, the project is worthwhile
.
2.
The cash flow profiles of the proposals are:
PROPOSAL 1
Year
Time 0
1
2
3
4
5
Cash Flow
($)
1500
200
400
600
800
1000
PROPOSAL 2
Year
Time 0
1
2
3
4
5
Cash Flow
($)
1 500
?
200
200
200
200
i)
The rate of return (r) is the discount rate at which the net present value is zero.
For pro
posal 1, we have:
NPV = 1500 + [200 + 200 (A/G,r,5)] (P/A,r,5) = 0
Solving by trial and error (or with a financial calculator):
At r=21%, NPV=35.92
At r=22%, NPV=5.77
By linear interpolation, the rate of return is:
21 + [35.92 / (35.92 + 5.77)] 1% = 21.9%
ii)
Given that the proposals are equally acceptable at a discount rate of 14%, their net present
values must be equal at that rate.
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Proposal 1 – NPV @ 14%:
1500 + [200 + 200 (A/G,14%,5) [ (P/A,14%,5)
1500 + [200 + 200 (1.7399) ] 3.4331 = 381
Proposal 2 – NPV @ 14%:
1500 + CF
1
(P/F,14%,1) + 200 (P/A,14%,4) (P/F,14%,1)
1500 + CF
1
(0.8772) + 200 (2.9137) (0.8772) = 0.8772 CF
1
 989
Equating both net present values:
0.8772 CF
1
 989 = 381
Thus, the unspecified cash flow of proposal 2 in year 1 is $1562
.
3.
The time distribution of cash flows associated with the project is as follows:
Time 0
:
100 000
Years 1 to 7
:
70 000  30 000 = 40 000
Year 8
:
70 000  30 000 + 20 000 = 60 000
i)
Net present value:
NPV = 100 000 + 40 000 (P/A,15%,7) + 60 000 (P/F,15%,8)
= 100 000 + 40 000 (4.1604) + 60 000 (0.3269) =
$86 030
ii)
Future value equivalent:
FV = 100 000 (F/P,15%,8) + 40 000 (F/A,15%,7) (F/P,15%,1) + 60 000
= 100 000 (3.0590) + 40 000 (11.0668) (1.15) + 60 000 = $263 173
or,
FV = NPV (F/P,15%,8)
= 86 030 (3.0590) = $263 166
Note
:
Discrepancies are due to roundoff errors in the time value factors.
iii)
Equivalent annual value:
EAV = 100 000 (A/P,15%,8) + 40 000 + 20 000 (A/F,15%,8)
= 100 000 (0.2229) + 40 000 + 20 000 (0.0729) =
$19 168
or,
EAV = NPV (A/P,15%,8)
= 86 030 (0.2229) = $19 176
or,
EAV = FV (A/F,15%,8)
= 263 173 (0.0729) = $19 185
Note
: Discrepancies are due to roundoff errors in the time value factors.
3
iv)
Present value ratio:
PVR = NPV / 100 000
= 86 030 / 100 000 = 0.86
v)
Rate of return – Determine r such that:
100 000 + 40 000 (P/A,r,7) + 60 000 (P/F,r,8) = 0
Solving by trial and error (or with a financial calculator):
At r=37%, NPV=1008
At r=38%, NPV=1220.
By linear interpolation, the rate of return is:
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This note was uploaded on 10/06/2009 for the course MIME 310 taught by Professor Bilido during the Summer '08 term at McGill.
 Summer '08
 Bilido

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