Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
CE 3080: Econ Eval & Optimization Name
Spring, 2013, Exam #2, 40 Points (ﬁrst) (last)
(Closed Book, Closed Notes, Equations are on Final Page)
1. (20 points) A site on a major river is being evaluated for a new lock and dam for
navigation purposes. Two
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
CE 3080: Econ Eval & Optimization Name
Spring, 2013, Exam #2, 40 Points (ﬁrst) (last)
(Closed Book, Closed Notes, Equations are on Final Page)
1. (20 points) A private company is considering the generation of electricity. Two
alternatives are possible: a
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
144 Solution
Equivalence
Cash ﬂow diagram:
$10,000
200 200 200 200 200 200 200 200 200 200
$10,000
Simple annual interest at 5% would return $500 per year on a similar investment versus
only $400 for the corporate bond. The corporate bond is not equiva
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
145 Suiutiﬂn
Present Worth, Future Worth
{a} F
{b} P
P
['3] P
l .1101)
1.112
1434
U H)
i
{d} F
{e} F
F
(f) P
P
{E} F
T933
T333
log{ '1'" .9313}
r1
11
[h] IUJJW
Ii III II .
 I1 H II 1 II II
II 1! ll
H I]
ll
lIIIH
111111.31.”
1.111111111111314: 111111.4
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
153 Solution
Sunk Cost, Opportunity Cost, and Present Worth Analysis
Develop the cash ﬂow table for college, treating the lost job opportunity as an opportunity cost.
Of course, tuition and other costs are also opportunity costs.
End College
of Year
0 0
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
1421 Solution
Uniform Series: Continuous Compounding
A=$1250
n=7(12)=84
 last monthly deposit at
V n = 6(12) = 72
P72
Approach: Find P72 for future expenditures, then determine A necessary to product
F72 = P72 
e’“ —1 r = .05/12 = .004167
P72 = A 7
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
1418 Solution
Standard Cash Flow Series
(a) Use geometric series, where
A1 = .05(45,000) = $2250 = ﬁrst year savings
g = 3% annual compound rate
i = 5% annual compound rate
n = 30 years
P = 225o[1(1+.o3)3°(1+.05)'3°]
.05 — .03
$49,319
F = P(F/P,i,n) =
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
1419 Solution
Uniform Series: Continuous Compounding
Under monthly compounding, the midmonth deposit is not seen until the end of the month,
therefore, the threeyear return stays the same: $12,160.68.
Under continuouscompounding, the number of subperi
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
1422 Solution
Capitalized Cost
A Pi
($1,600)(0.08)
$128/yr in perpetuity for the right to 0.7 AF/yr.
This is equivalent to:
$128 per year
= $182.86 per AF
0.7AF per year
1423 Solution
Capitalized Cost
$20m 10 10
T plus $1.5 m/y T
5 5 5 5 5
M etc.
20 4o
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
152 Solution
Sunk Cost and Present Worth Analysis
Develop the cash ﬂow for each alternative. Note that the fact that the student has ﬁnished one
year of college and has spent money on tuition and other costs has no bearing on the present
decision. First
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
(d) Incremental beneﬁtcost ratio analysis:
From the cash ﬂow of the incremental investment as in part (a), treating changes in
salvage as an addition or substraction from cost:
APWC = 200+20(P/F,8%,5)40(P/F,8%,10)
= 200+20(O.680583)40(O.463193)
= $
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
Note: A more accurate estimate of i* (nominal) is 18.55%, producing an estimate of
i*(real) as:
i* = M = i*(real) = 11_84%
1 AA’.
which, in the present worth equation above, produces
$1,000 z $1,000.09
either is close enough!
1619 Solution \Oﬁ’é
Nomina
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
16—7 Solution
MACRS Depreciation of Real Property
The purchase occurs before May 13, 1993, so the ﬁgures for 31 .5year nonresidential real
property applies in Table 16.3. Purchase date is July 7, with mid—month convention. Read from
Table 16.3.
Recover
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
1614 Solution
Individual Income Tax
Gross Income:
AGI:
$40,000 business income
+600 interest $42,000
+300 dividends 4000 self employed retirement plan
+1000 short term capital gain 3 800 1/2 of Soc Sec tax (self employed)
+100 taxable refund of S&L t
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
16—16 Solution
Before and AfterTax Rate of Return
(3) Calculate beforetax rate of return. $20,000 = 3,000(P/A,i*,4) + 3,000(P/G,i*,4)
The two factors must sum to 6.666667. Interpolating from Tables, App. A;
i*(before) = 14.9%
(b) Form the after~tax cas
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
164 Solution 5 p15 am
DDB Depreciation with Switch to SL
(a) Salvage in high: S=$20,000
2 2 1
DDBDt = _I\T(BV‘) = 6(BV‘) = 3(BVt)
For SL depreciation, L varies.
DDB Alternative SL Depreciation
Depreciation at SLDt = g1/L2! EVtSQ
Book Value in
Year Y
Economic Evaluation and Optimization in Civil and Environmental Engineering
CIVILEN 3080

Spring 2013
1510 Solution [0’05
Payback Period
100
A: $900+$100 from year 3: 2 yrs + 366 = 2.33 yrs
300
B: $700+$300 from year 3: 2 yrs + E = 2.60 yrs
100
C: $1,400+$100 from year 4: 3 yrs+ % =3.14 yrs
The investments would be ranked A, B, C, and A would be chosen.