ENG 106
Homework #5 Solutions
Winter 2012
Note:
Unless otherwise stated, cash flows are in actual dollars and i and
MARR are market rates.
5.28a&c: A newly constructed bridge costs $10,000,000. The same bridge is estimated to need renovation every 10
years at a cost of $1,000,000. Annual repairs and maintenance are estimated to be $100,000 per year.
a) If the interest rate is 5%, determine the capitalized equivalent cost of the bridge.
c) Repeat the analysis with an interest rate of 10%.
Interest rate is 5%.
Construction = Pc = 10,000,000
Renovation = Pr = A/
ι
= 1,000,000 *(A/F, 5%, 10)/
ι
= 1,000,000 *()/.05 = 1,590,000
(alternatively, could calculate effective interest rate for 10 yrs :
ι
e = (1.05)10 – 1 = 63%
and then calculate Pr = A/
ι
e =
1,590,000, as above)
Maintenance = PM = A/
ι
= 100,000/
ι
= 100,000/.05 = 2,000,000
CE(5%) = Pc+Pr +PM = $13,590,000
Repeat the analysis with an interest rate of 10%.
Pc = 10,000,000
Pr = A/
ι
= 1,000,000 *(A/F, 10%, 10)/
ι
= 1,000,000 *()/.1 = 627,000
PM = A/
ι
= 100,000/
ι
= 100,000/.1 = 1,000,000
CE(10%) = Pc+Pr +PM = $11,627,000
(As interest rate increases, CE decreases. But note that market
ι
and inflation rate are coupled, so the actual-dollar
amounts on the time line would also probably be larger if the market rate was higher due only to inflation.)
5.39 Consider the following two mutually exclusive investment projects:
A
B
n
Cash Flow
Salvage Value
Cash Flow
Salvage Value
0 -$12,000
-$10,000
1 -$2,000
$6,000
-$2,100
$6000
2 -$2,000
$4,000
-$2,100
$3,000
3 -$2,000
$3,000
-$2,100
$1,000
4 -$2,000
$2,000
5 -$2,000
$2,000
Salvage values represent the net proceeds (after tax) from disposal of the assets if they are sold at the end of year
listed. Both projects will be available (and can be repeated) with the same costs and salvage values for an indefinite