Homework Soursewo alternative investment proposals are under consideration
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?
Solution
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 |
