Section 4.4.1 Discounted Payback Period for a Single Alternative 47 Reconsider P
ID: 2511713 • Letter: S
Question
Section 4.4.1 Discounted Payback Period for a Single Alternative 47 Reconsider Problem 5 (repeated here). Bailey, Inc., is considering buying a new gang punch that would allow them to produce circuit boards more effi- ciently. The punch has a first cost of $100,000 and a useful life of 15 years. At the end of its useful life, the punch has no salvage value. Labor costs would increase $2,000 per year using the gang punch, but raw material costs would decrease $12,000 per year. MARR is 5 percent/year. a. What is the discounted payback period for this investment? b. If the maximum attractive DPBP is 3 years, what is the decision rule for judging the worth of this investment? c. Should Bailey buy the gang punch based on DPBP?Explanation / Answer
Solution:
Part 1 ---
Discounted Payback Period --- Payback period is the length of time within which initial investment of the company will be recovered and returned back to the company. Discounted Payback period considers time value of money.
So we need to first calculate the Present Value of Annual Saving..
Annual Saving = Saving in Raw materials cost $12,000 -Increase in labor cost 2,000 = $10,000
Present Value and Cumulative Present Value
Year
Annual Cash Inflows (A)
PV factor @ 5% (B)
Present Value of Cash Inflows (A*B)
Cumulative Present Value of Cash Inflows
1
$10,000
0.952
$9,524
$9,524
2
$10,000
0.907
$9,070
$18,594
3
$10,000
0.864
$8,638
$27,232
4
$10,000
0.823
$8,227
$35,460
5
$10,000
0.784
$7,835
$43,295
6
$10,000
0.746
$7,462
$50,757
7
$10,000
0.711
$7,107
$57,864
8
$10,000
0.677
$6,768
$64,632
9
$10,000
0.645
$6,446
$71,078
10
$10,000
0.614
$6,139
$77,217
11
$10,000
0.585
$5,847
$83,064
12
$10,000
0.557
$5,568
$88,633
13
$10,000
0.530
$5,303
$93,936
14
$10,000
0.505
$5,051
$98,986
15
$10,000
0.481
$4,810
$103,797
$103,797
Initial Investment = $100,000
As per definition, discounted payback period is the length of time within which initial investment is recovered back to the company.
From the cumulative table it is clear that the amount is recovered between the year 14 & 15.
Discount Payback Period = 14 Years + (Initial Investment – Cumulative PV at lower level) / Present Value of Cash Inflow at higher level
= 14 Years + (100,000 – 98,986) / 4,810
= 14 Years + 0.21 Years
= 14.21 Years
Part b --- If the maximum attractive DPBP is 3 years, the investment is not worthful.
Under discounted payback period, the project should be selected which has lower DPBP.
Part c -- No, Bailey should not buy the gang punch based on DPBP.
Hope the above calculations, working and explanations are clear to you and help you in understanding the concept of question.... please rate my answer...in case any doubt, post a comment and I will try to resolve the doubt ASAP…thank you
Year
Annual Cash Inflows (A)
PV factor @ 5% (B)
Present Value of Cash Inflows (A*B)
Cumulative Present Value of Cash Inflows
1
$10,000
0.952
$9,524
$9,524
2
$10,000
0.907
$9,070
$18,594
3
$10,000
0.864
$8,638
$27,232
4
$10,000
0.823
$8,227
$35,460
5
$10,000
0.784
$7,835
$43,295
6
$10,000
0.746
$7,462
$50,757
7
$10,000
0.711
$7,107
$57,864
8
$10,000
0.677
$6,768
$64,632
9
$10,000
0.645
$6,446
$71,078
10
$10,000
0.614
$6,139
$77,217
11
$10,000
0.585
$5,847
$83,064
12
$10,000
0.557
$5,568
$88,633
13
$10,000
0.530
$5,303
$93,936
14
$10,000
0.505
$5,051
$98,986
15
$10,000
0.481
$4,810
$103,797
$103,797
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