wo alternative investment proposals are under consideration for a vacant owner b
ID: 1255803 • Letter: W
Question
wo alternative investment proposals are under consideration for a vacant owner by Urban Development Corporation. Plan A would require an immediate investment of $120,000 and first-year expenditure for property taxes, maintenance, and insurance of $4,000, with this amount expected to increase at a rate of $1,000 per year. Plan B would have a first cost of $170,000 and total first-year expenses of $9,000, with an increase of $1,000 per year. The economic life of each project is forecast to be 10 years; and at the end of this time, only the facilities from Plan B with a value of $50,000 are expected to salvage. During the life of the project, the facility in plan A is expected to produce $34,000 annually, whereas Plan B is expected to produce $42,000 . a) Determine the rate of return of each plan. b) Determine the rate of return of the Additional investment required in Plan B compared with Plan A. c) Which plan should Urban Development select if the company uses a MARR of 12 percent?
Explanation / Answer
Working notes:
(1) For each plan,
Net Annual Benefit = Annual Benefit - Annual Expense
(2) For plan B, Net Annual Benefit in terminal year (year 10) is higher by $50,000 (Salvage Value).
(3) Rate of Return is the Internal Rate of Return (IRR) computed using Excel function =IRR(Value 1, Value 2,.....Value n) where "Value" is the Net Annual Benefit, undiscounted.
(4) Based on MARR of 12%, the plan choice will be made based on NPV of the plans. NPV is the sum of all cash outflows and inflows discounted at 12%. The plan with higher positive NPV should be chosen.
Calculations as follow:
Plan A
Year
Initial Cost ($)
Annual Benefit ($)
Annual Cost ($)
Net Annual Benefit ($)
Net Cash Flow ($)
Discount Factor @12%
Discounted Net Annual Benefit ($)
(A)
(B)
(C)
(D) = (B) - (C)
(E) = (D) + (A)
(F)
(G) = (E) x (F)
0
-1,20,000
-1,20,000
1.0000
-1,20,000
1
34,000
4,000
30,000
30,000
0.8929
26,786
2
34,000
5,000
29,000
29,000
0.7972
23,119
3
34,000
6,000
28,000
28,000
0.7118
19,930
4
34,000
7,000
27,000
27,000
0.6355
17,159
5
34,000
8,000
26,000
26,000
0.5674
14,753
6
34,000
9,000
25,000
25,000
0.5066
12,666
7
34,000
10,000
24,000
24,000
0.4523
10,856
8
34,000
11,000
23,000
23,000
0.4039
9,289
9
34,000
12,000
22,000
22,000
0.3606
7,933
10
34,000
13,000
21,000
21,000
0.3220
6,761
IRR (%) =
18.12%
NPV ($) =
29,253
Plan B
Year
Initial Cost ($)
Annual Benefit ($)
Annual Cost ($)
Net Annual Benefit ($)
Net Cash Flow ($)
Discount Factor @12%
Discounted Net Annual Benefit ($)
(A)
(B)
(C)
(D) = (B) - (C)
(E) = (D) + (A)
(F)
(G) = (E) x (F)
0
-1,70,000
-1,70,000
1.0000
-1,70,000
1
42,000
9,000
33,000
33,000
0.8929
29,464
2
42,000
10,000
32,000
32,000
0.7972
25,510
3
42,000
11,000
31,000
31,000
0.7118
22,065
4
42,000
12,000
30,000
30,000
0.6355
19,066
5
42,000
13,000
29,000
29,000
0.5674
16,455
6
42,000
14,000
28,000
28,000
0.5066
14,186
7
42,000
15,000
27,000
27,000
0.4523
12,213
8
42,000
16,000
26,000
26,000
0.4039
10,501
9
42,000
17,000
25,000
25,000
0.3606
9,015
10
92,000
18,000
74,000
74,000
0.3220
23,826
IRR (%) =
13.66%
NPV ($) =
12,302
(a) Rate of return are:
Plan A: 18.12%
Plan B: 13.66%
(b) Question not clear. There is no mention of any additional investment for plan B anywhere in the question.
(c) Since NPV of of plan A is higher than plan B, plan A should be chosen.
Plan A
Year
Initial Cost ($)
Annual Benefit ($)
Annual Cost ($)
Net Annual Benefit ($)
Net Cash Flow ($)
Discount Factor @12%
Discounted Net Annual Benefit ($)
(A)
(B)
(C)
(D) = (B) - (C)
(E) = (D) + (A)
(F)
(G) = (E) x (F)
0
-1,20,000
-1,20,000
1.0000
-1,20,000
1
34,000
4,000
30,000
30,000
0.8929
26,786
2
34,000
5,000
29,000
29,000
0.7972
23,119
3
34,000
6,000
28,000
28,000
0.7118
19,930
4
34,000
7,000
27,000
27,000
0.6355
17,159
5
34,000
8,000
26,000
26,000
0.5674
14,753
6
34,000
9,000
25,000
25,000
0.5066
12,666
7
34,000
10,000
24,000
24,000
0.4523
10,856
8
34,000
11,000
23,000
23,000
0.4039
9,289
9
34,000
12,000
22,000
22,000
0.3606
7,933
10
34,000
13,000
21,000
21,000
0.3220
6,761
IRR (%) =
18.12%
NPV ($) =
29,253
Plan B
Year
Initial Cost ($)
Annual Benefit ($)
Annual Cost ($)
Net Annual Benefit ($)
Net Cash Flow ($)
Discount Factor @12%
Discounted Net Annual Benefit ($)
(A)
(B)
(C)
(D) = (B) - (C)
(E) = (D) + (A)
(F)
(G) = (E) x (F)
0
-1,70,000
-1,70,000
1.0000
-1,70,000
1
42,000
9,000
33,000
33,000
0.8929
29,464
2
42,000
10,000
32,000
32,000
0.7972
25,510
3
42,000
11,000
31,000
31,000
0.7118
22,065
4
42,000
12,000
30,000
30,000
0.6355
19,066
5
42,000
13,000
29,000
29,000
0.5674
16,455
6
42,000
14,000
28,000
28,000
0.5066
14,186
7
42,000
15,000
27,000
27,000
0.4523
12,213
8
42,000
16,000
26,000
26,000
0.4039
10,501
9
42,000
17,000
25,000
25,000
0.3606
9,015
10
92,000
18,000
74,000
74,000
0.3220
23,826
IRR (%) =
13.66%
NPV ($) =
12,302
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