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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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