Can anyone help me the following problem without Leaving the answer in the table
ID: 1107112 • Letter: C
Question
Can anyone help me the following problem without Leaving the answer in the table?
A "power saving" air conditioning system is being considered. It is estimated to cost $5,000 more than the inefficient system and expected to save $1, 300 per year in power costs. If the firm has a target ROI value of 12%, determine the payback using the incorrect method that does not consider TVM. Next, calculate the correct payback period using TVM techniques. Is this a reasonable expectation? If, under actual use, the system only saves $300 per year in power costs, how long will it take for the system to pay for itself? Is this a reasonable time period?
Explanation / Answer
Answer:
(a) Incorrect method refers to simple Payback Period (PBP) which refers to the time by when cumulative cash flows become zero.
Year
Cash Flow ($)
Cumulative Cash Flow ($)
0
-5,000
-5,000
1
1,300
-3,700
2
1,300
-2,400
3
1,300
-1,100
4
1,300
200
PBP lies between years 3 & 4.
PBP = 3 + (Absolute value of cumulative cash flow, year 3 / Cash flow, year 4)
= 3 + (1,100 / 1,300) = 3 + 0.85
= 3.85 years
(b) TVM-adjusted payback is computed using Discounted Payback Period (DPBP) which is the time by when cumulative discounted cash flows are zero
Year
Cash Flow ($)
PV Factor at 12%
Discounted Cash Flow ($)
Cumulative Discounted Cash Flow ($)
(A)
(B)
(A) x (B)
0
-5,000
1.0000
-5,000
-5,000
1
1,300
0.8929
1,161
-3,839
2
1,300
0.7972
1,036
-2,803
3
1,300
0.7118
925
-1,878
4
1,300
0.6355
826
-1,051
5
1,300
0.5674
738
-314
6
1,300
0.5066
659
345
DPBP lies between years 5 & 6.
DPBP = 5 + (Absolute value of cumulative discounted cash flow, year 5 / Discounted Cash flow, year 6)
= 5 + (314 / 659) = 5 + 0.48
= 5.48 years
This is a reasonable expectation provided cut-off payback periods are not exceeded.
(c) When annual saving = $300, cumulative discounted cash flow is computed as follows.
Year
Cash Flow ($)
PV Factor at 12%
Discounted Cash Flow ($)
Cumulative Discounted Cash Flow ($)
(A)
(B)
(A) x (B)
0
-5,000
1.0000
-5,000
-5,000
1
300
0.8929
268
-4,732
2
300
0.7972
239
-4,493
3
300
0.7118
214
-4,279
4
300
0.6355
191
-4,089
5
300
0.5674
170
-3,919
6
300
0.5066
152
-3,767
7
300
0.4523
136
-3,631
8
300
0.4039
121
-3,510
9
300
0.3606
108
-3,402
10
300
0.3220
97
-3,305
11
300
0.2875
86
-3,219
12
300
0.2567
77
-3,142
13
300
0.2292
69
-3,073
14
300
0.2046
61
-3,012
15
300
0.1827
55
-2,957
16
300
0.1631
49
-2,908
17
300
0.1456
44
-2,864
18
300
0.1300
39
-2,825
19
300
0.1161
35
-2,790
20
300
0.1037
31
-2,759
21
300
0.0926
28
-2,731
22
300
0.0826
25
-2,707
23
300
0.0738
22
-2,684
24
300
0.0659
20
-2,665
25
300
0.0588
18
-2,647
DPBP is not achievable because the discount factor getting increasingly smaller, cumulative discounted cash flow is falling at such a slow rate that it will not assume a zero value. This is not reasonable.
Year
Cash Flow ($)
Cumulative Cash Flow ($)
0
-5,000
-5,000
1
1,300
-3,700
2
1,300
-2,400
3
1,300
-1,100
4
1,300
200
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