Question

Two possible routes for a power line are under study. In both cases, the power line will last 15 years, have no salvage value, have annual property taxes of 2% of first cost, and have a yearly power loss of $500/km.

	Around the lake	Under the lake
Length	16 km	6 km
First cost	$8800/km	$24,000 /km
Maintenance	$175/km/yr	$325 /km/yr

If 9% interest is used, FIND

1. EUAC (Under) (round to nearest $100)

2.  EUAC (Around)  (round to nearest $100)

3. Which alternative do you recommend? (Under/Around)

PLEASE USE EXCEL TO SOLVE AND PLS SHOW EXCEL FORMULAS

Answer 1

Workings

Formula	Description	Around the lake	Under the lake
A	Length (in Km)	16	6
B	First cost ($ per Km)	8800	24000
C = A*B	Total First cost (in $)	140800	144000
D	Maintenance cost each year /Km	175	325
E = A*D	Total Maintenance cost each year	2800	1950
F = C*2%	Annual property Taxes	2816	2880
G = A*500	Annual Power Loss	8000	3000
H = E+F+G	Total Cost per annum	13616	7830
I	Life in years	15	15
J	Salvage Value in $	0	0
K	Interest Rate	9%	9%

Answer to Question 1

Year	Cost	DF@9%	PV
0	144000	1	144,000
1	7830	0.917431193	7,183
2	7830	0.841679993	6,590
3	7830	0.77218348	6,046
4	7830	0.708425211	5,547
5	7830	0.649931386	5,089
6	7830	0.596267327	4,669
7	7830	0.547034245	4,283
8	7830	0.50186628	3,930
9	7830	0.46042778	3,605
10	7830	0.422410807	3,307
11	7830	0.38753285	3,034
12	7830	0.355534725	2,784
13	7830	0.326178647	2,554
14	7830	0.299246465	2,343
15	7830	0.274538041	2,150
Total		9.06068843	207,115
Sum of DF yr 1 to 15		8.06068843
EUAC	=207115/8.0606		25,694
			25700

Answer to Question 2

Year	Cost	DF@9%	PV
0	140800	1	140,800
1	13616	0.917431193	12,492
2	13616	0.841679993	11,460
3	13616	0.77218348	10,514
4	13616	0.708425211	9,646
5	13616	0.649931386	8,849
6	13616	0.596267327	8,119
7	13616	0.547034245	7,448
8	13616	0.50186628	6,833
9	13616	0.46042778	6,269
10	13616	0.422410807	5,752
11	13616	0.38753285	5,277
12	13616	0.355534725	4,841
13	13616	0.326178647	4,441
14	13616	0.299246465	4,075
15	13616	0.274538041	3,738
Total		9.06068843	250,554
Sum of DF yr 1 to 15		8.06068843
EUAC	=250554/8.0606		31,083
			31100

Answer to Question 3

Power line under the lake is recommended because of lower EUAC. The EUAC for power line construction under the lake is 25700 and the EUAC for power line construction around the lake is 31100 and hence power line under the lake will have a saving of $5400 per annum.