Background: The tables below are summaries of three projects (A, B, and C). Thes
ID: 2786632 • Letter: B
Question
Background: The tables below are summaries of three projects (A, B, and C). These are investments into capital assets, more specifically, commercial real estate. These types of investments will yield the investor a cash flow, and when the investor so chooses, a face value at maturity. Maturity can be forced only at the end of a year (i.e. the sale, and hence, forced maturity of this investment can be done at the end of year 1, OR the end of year 2, QR the end of year 3, etc.) Project A Cash Flow Face Value Initial Investment is $500,000 Year 1 Year 4 Year 5 Year 2 S 95,000 S 175,000 1,600,000 2,900,000 Year 3 S 220,000 S 3,600,000 $225,000 $3,660,000 S 215,000 3,500,000 Required Rate of Return is 15% Year 5 Project B Cash Flow Face Value Initial Investment is $700,000 Year 3 Year 4 S 440,000 S 7,300,000 Year 1 Year 2 S 310,000 380,000 $ 415,000 s 5200,000 6,400,000 6,900.000 7.300,000$7.800,000 $ 6,900,000 $7,800,000 Required Rate of Return is 15% Project C Cash Flow Face Value Initial Investment is $2,080,000 Year 1 Year 2 S 380,000 401,000 S 8,300,000 S 8,500,000 Year 3 Year 4 Year 5 425,000 S 430,000 $445,000 $8,700,000 S 8,900,000 Required Rate of Return is 15% Use the above tables to calculate the payback periods of each project. Rank these projects from quickest payback period to the longest payback period. (Round to the nearest month, for example if the answer is 3 years 2 months and 1 week, then an answer of 3 years and 2 months will suffice) 1.Explanation / Answer
Calculation of Pay Back Period
Project A
Year
Cash Flows
$
Cumulative Cash Flows $
0
-500000
1
95000
95000
2
175000
270000
3
215000
485000
4
220000
705000
5
225000
930000
Pay Back falls in year 3 and year 4
Therefore, Initial Investment – Cumulative Cash Flow of year 3 / Cash Flow of Year 4
= $(500000-485000)/220000=0.068 +YEAR 3=3.068 years or 3 years
Discounted Pay Back Period Rate of Return is 15%
Year
Cash Flows
$
Present Value Factor @ 15%
Discounted Cash Flows
Cumulative Cash Flows $
0
-500000
1
-500000
-500000
1
95000
0.8696
82612
82612
2
175000
0.7561
132317.50
214929.50
3
215000
0.6575
141362.50
356292.00
4
220000
0.5718
125796.00
482088.00
5
225000
0.4972
111870.00
593958.00
Pay Back falls in year 4 and year 5
Therefore, Initial Investment – Discounted Cumulative Cash Flow of year 4 / Discounted Cash Flow of Year 5
= $(500000-482088)/111870=4.160 years or 4 years 2 months
Project B
Year
Cash Flows
$
Cumulative Cash Flows $
0
-700000
-700000
1
310000
310000
2
380000
690000
3
415000
1105000
4
440000
1545000
5
470000
2015000
Pay Back falls in year 2 and year 3
Therefore, Initial Investment – Cumulative Cash Flow of year 3 / Cash Flow of Year 4
= $(700000-690000)/415000=0.024 + YEAR 2=2.024 years or 2 years
Discounted Pay Back Period Rate of Return is 15%
Year
Cash Flows
$
Present Value Factor @ 15%
Discounted Cash Flows
Cumulative Cash Flows $
0
-700000
1
-700000
-700000
1
310000
0.8696
269576
269576
2
380000
0.7561
287318
556894
3
415000
0.6575
272862.50
829756.50
4
440000
0.5718
251592.00
1081348.50
5
470000
0.4972
233684.00
1315032.50
Pay Back falls in year 2 and year 3
Therefore, Initial Investment – Discounted Cumulative Cash Flow of year 2 / Discounted Cash Flow of Year 3
= $(700000-556894)/272862.50=0.524 + year 2=2.524 years or 2 years 6 months
Project C
Year
Cash Flows
$
Cumulative Cash Flows $
0
-2080000
-2080000
1
380000
380000
2
401000
781000
3
425000
1206000
4
430000
1636000
5
445000
2081000
Pay Back Period = year 5
Discounted Pay Back Period Rate of Return is 15%
Year
Cash Flows
$
Present Value Factor @ 15%
Discounted Cash Flows
Cumulative Cash Flows $
0
-2080000
1
-2080000
-2080000
1
380000
0.8696
330448
330448
2
401000
0.7561
303196.10
633644.10
3
425000
0.6575
279437.50
913081.60
4
430000
0.5718
245874.00
1158955.60
5
445000
0.4972
221254.00
1380209.60
With the discount rate of 15%, the Investment won't pay back in 5 years.
Conclusion:-
As per Pay Back Period with simple Cash Flows:-
Project A 3 years
Project B 2 Years
Project C 5 years
Ranking:-
Project B , Project A ,Project C
Accept the project only if its payback period is LESS than the target payback period.
As per Pay Back Period with Discounted Cash Flows:-
Project A 4 Years 2 months
Project B 2 years 6 months
Project C No Pay Back Period
Ranking:-
Project B, Project A
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