Question

8-14 The following four mutually exclusive alternatives A have no salvage value after 10 years. A B C D First cost $7500 $5000 $5000 $8500 Uniform annual benefit 1600 1200 1000 1700 Computed rate of return 16.8% 20.2% 15.1% 15.1% (a) Construct a choice table for interest rates from 0% to 100% (b) Using 8% for the MARR, which alternative should be selected?

Please explain thoroughly!

Engineering Economy

Answer 1

Solution:

8-14:

Given

four mutually exclusive alternatives have no salvage value after 10 years.

(a) The choice table for interest rates from 0% to 100% is as below:

a) Choice table
	NPV
Interest rate	A	B	C	D	Choice
0%	8,500.00	7,000.00	5,000.00	8,500.00	A or B
5%	4,854.78	4,266.08	2,721.73	4,626.95	A
8%	3,236.13	3,052.10	1,710.08	2,907.14	A
10%	2,331.31	2,373.48	1,144.57	1,945.76	B
15%	530.03	1,022.52	18.77	31.91	B
20%	(792.04)	30.97	(807.53)	(1,372.80)	B
25%	(1,787.19)	(715.40)	(1,429.50)	(2,430.14)	B
30%	(2,553.54)	(1,290.15)	(1,908.46)	(3,244.38)	B
35%	(3,155.93)	(1,741.95)	(2,284.96)	(3,884.43)	B
40%	(3,638.29)	(2,103.71)	(2,586.43)	(4,396.93)	B
45%	(4,030.99)	(2,398.24)	(2,831.87)	(4,814.17)	B
50%	(4,355.49)	(2,641.62)	(3,034.68)	(5,158.96)	B
55%	(4,627.25)	(2,845.44)	(3,204.53)	(5,447.71)	B
60%	(4,857.59)	(3,018.19)	(3,348.49)	(5,692.44)	B
65%	(5,054.92)	(3,166.19)	(3,471.82)	(5,902.10)	B
70%	(5,225.62)	(3,294.22)	(3,578.51)	(6,083.48)	B
75%	(5,374.59)	(3,405.94)	(3,671.62)	(6,241.75)	B
80%	(5,505.60)	(3,504.20)	(3,753.50)	(6,380.95)	B
85%	(5,621.66)	(3,591.24)	(3,826.03)	(6,504.26)	B
90%	(5,725.12)	(3,668.84)	(3,890.70)	(6,614.19)	B
95%	(5,817.91)	(3,738.43)	(3,948.69)	(6,712.78)	B
100%	(5,901.56)	(3,801.17)	(4,000.98)	(6,801.66)	B

(b) using 8% for the MARR the alternative that should be selected is:

By comparing the initial cost of various projects it is apparent that project B dominates project C. Since, at the same first cost B generates higher annual benefit than C. Hence, C can be discarded.

	Cost	Annual Benefit	Change in Cost	Change in Annual Benefit	Change in RoR
B	$5000	$1200
A	$7500	$1600	$2500	$400	9.6%
D	$8500	$1700	$1000	$100	0%

RoRB-A, 25 = 4(P/A, i, 10)

The value of i can be determined using linear interpolation technique. First assume i= 10%

Thus, RHS = $4 ×(1-(1/(1.1))^10)/0.1 = $ 24.578

Now assuming i=9%, we get RHS equal to

$4 × (1 - (1/1.09)^10)/0.09 = $ 25.671

As we can see the RHS is not equal to $25 in either cases but it lies in between these two rates. Hence by applying linear interpolation we can calculate RoR

25.671 25 RoRB-A 9 (10 9) 25.671 24.578

RORBA=9+0.613

RORB-A = 9.6per cent( Approximately)

Solving for i = 9.6%

Similarly,

10 1P/A, i, 10) RORD-A

RORD-A= 0percent(Approximately)

MARR is 8%

Therefore, Project A  must be selected

since ( RoR_B-A > MARR).