Question 1:
A plant engineer is considering two types of solar water heating systems:
Initial Cost
Annual Savings
Annual Maintenance
Expected Life
Salvage Value
Model (A)
$7,000
$700
$100
20 years
$400
Model (B)
$10,000
$1,000
$50
20 years
$500
The firm’s MARR is 6%. Based on the IRR criterion, which system is a better choice?
Solution:
Calculating the IRR for both alternatives
PW (A) = -$7,000 + $600 (P/A, i, 20) + $400 (P/F, i, 20) = 0
By trial and error, IRR (A) = 6.01 %
PW (B) = -$10,000 + $950 (P/A, i, 20) + $500 (P/F, i, 20) = 0
By trial and error, IRR (B) = 7.25 %
As both alternatives have an IRR higher than the MARR, check the incremental IRR from A to B:
PW (B - A) = -$3,000 + $350 (P/A, i, 20) + $100 (P/F, i, 20) = 0
By trial and error, IRR (B – A) = 9.97 %
As IRR (B – A) > MARR, then choose alternative B
Question 2:
A half dozen cost-reduction proposals have been forwarded by the industrial engineering department. A
20% rate of return is expected, and all equipment investments are to be written off in 5 years with no
salvage value. Use the IRR method to answer the following:
Proposal
Combine
Rearrange
Modify
Eliminate
Up Quality
Make Safer
Equipment Cost
25,000
60,000
20,000
20,000
40,000
30,000
Net Annual Savings
9,500
21,500
7,000
9,000
17,000
10,000
(a) Which proposal should be selected if only one can be accepted?
(b) Which proposal(s) should be selected if all proposals are independent and there is effectively
unlimited capital available for cost-reduction projects?
(c) Which combination of alternatives should be chosen for a total investment cost of at least $50,000,
but not less than $100,000 (proposals are independent)?
Solution:
MARR = 20%
N=5
Sorting the proposals by their benefits in an ascending order:
Proposal
Annual
Savings
7,000
(P/A, i,
5)
2.8571
IRR
A: Modify
Annual
Cost
20,000
B: Eliminate
20,000
9,000
2.2222
34.9
C: Combine
D: Make Safer
E: Up Quality
F: Rearrange
25,000
30,000
40,000
60,000
9,500
10,000
17,000
21,500
2.6315
3.0000
2.3529
2.7906
22.1
AB

BC
-ve
BD
-ve
BE
28.65%
EF
4.06%
26.1
19.9
31.8
23.2
a) If only one solution would be accepted (Mutually exclusive):
Choose Alternative E. (Up Quality)
b) In case of independent alternatives with unlimited funds
Choose All alternatives (IRR >20%), that is all alternatives except alternative D (make safer)
c) Which Combination of Projects with limited resources?
Proposal
1: A + E
2: B + E
3: A + B + C
4: C + E
5: A + F
6: A + B + E
7: B + F
8: A + C + E
9: B + C + E
10: C + F
Cost
Annual
Savings
IRR
60
60
65
65
80
80
80
85
85
85
24
26
25.5
26.5
28.5
33
30.5
33.5
35.5
31
28.6
32.9
27.7
29.6
22.9
30.2
26.2
27.9
30.9
24.1
Choose proposal # 9 (Eliminate + Combine + Up quality)
Accept
Accept
24
-ve
Accept
26
22.11
Accept
69
41.04
Question 3:
The capital budget for a company included $50,000 for the purchase of new machine. The MARR is
10% after taxes. Its useful life is four years and expected salvage after 4 years is $5,000. During the four
years, it is estimated to save $20,000 per year in maintenance costs while its annual operating costs are
$5,000. The machine is in class 29 (CCA rate of 50% straight-line class -- half year rule is applicable).
The firm has an effective income tax rate of 42%. Should the machine be bought?
i=10%, t=42%
(1)
Year
0
1
2
3
4
(2)
BTCF
-50000
15000
15000
15000
15000
(3)
CCA rate
25%
50%
25%
-
(4)
CCA
12500
25000
12500
-
(5)=(2)-(4)
Taxable Income
(6)
Tax @42%
2500
-10000
2500
15000
1050
-4200
1050
6300
(7)
ATCF
-50000
13950
19200
13950
8700
Salvage
5000
Disposal tax effect
-2100
End of year 4: UCC=0. Since Salvage > UCC, CCA Recapture applies.
Disposal tax effect =(S-UCC)t= (5000 - 0)0.42 = $2,100.00
PW = -50,000+13,950(P/F,i,1)+19,200(P/F,i,2)+13,950(P/F,i,3)+(8700+5000-2100)(P/F,i,4)
= $-3,046.70 <0 Therefore, do not buy.
Question 4:
For the investment problem described in question 3, assume that a loan of $30,000 is obtained at 9%, to
be repaid over a 4 year period in equal annual amounts covering repayment of principle and interest. All
other aspects of this problem are the same as described in question 3. Should the machine be bought?
Loan = 30,000 @ 9%.
A=30,000(A/P,9%,4)=$9260
(1)
(2)
(3)
(4)
(5)
Year BTCF
CCA
Loan
Interest
Repayment on loan
0
1
2
3
4
-50000
+30000
=20000
15000
15000
15000
15000
(6)=(2)-(3)-(5)
Taxable income
(7)
Tax @ 42%
(8)=(2)-(4)-(7)
ATCF
-20000
12500
25000
12500
0
9260
9260
9260
9260
2700
2109.60
1466
764.5
-200
-12109.60
1034
14235.5
-84
-5086
434
5979
5824
10826
5306
-239
5000
salvage
-2100
Disposal tax
effect
Interest calculation:
Yr.1: 30000x0.09 = 2700
Yr.2: [30000-(9260-2700)](0.09)= 23440x0.09=2109.60
Yr.3: [23440-(9260-2109.6)](0.09) = 16289x0.09=1466
Yr.4: [16289-(9260-1466)](0.09)= 8495x0.09 = 764.50
PW=-20000+5824(P/F,i,1)+ ….+(5000-2100-239)(P/F,i,4) = +$45.60 (Buy the machine)