Question

In: Finance

Consider the following two mutually exclusive projects:    Year Cash Flow (A) Cash Flow (B) 0...

Consider the following two mutually exclusive projects:

  

Year Cash Flow (A) Cash Flow (B)
0 –$344,278        –$14,518         
1 28,600        4,179         
2 50,000        8,052         
3 58,000        13,608         
4 408,000        8,500         

  

Whichever project you choose, if any, you require a 6 percent return on your investment.
a. What is the payback period for Project A?

   

b. What is the payback period for Project B?
c. What is the discounted payback period for Project A?
d. What is the discounted payback period for Project B?
e. What is the NPV for Project A?
f. What is the NPV for Project B ?

  

g. What is the IRR for Project A?
h. What is the IRR for Project B?
i. What is the profitability index for Project A?
j. What is the profitability index for Project B?

Solutions

Expert Solution

a. Payback Period for Project A= ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

= 3 + ( 207678 / 408000)

= 3.509014706

= 3.51 Years

Note:

Year Investment Cash Inflow Net Cash Flow
0 -3,44,278 -    -3,44,278 (Investment + Cash Inflow)
1 -    28,600 -3,15,678 (Net Cash Flow + Cash Inflow)
2 -    50,000 -2,65,678 (Net Cash Flow + Cash Inflow)
3 -    58,000 -2,07,678 (Net Cash Flow + Cash Inflow)
4 -    4,08,000 2,00,322 (Net Cash Flow + Cash Inflow)

b. Payback Period for Project B= ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

= 2 + ( 2287 / 13608)

= 2.17 years

Hence the correct answer is 2.17 years

Note:

Year Investment Cash Inflow Net Cash Flow
0 -14,518 -    -14,518 (Investment + Cash Inflow)
1 -    4,179 -10,339 (Net Cash Flow + Cash Inflow)
2 -    8,052 -2,287 (Net Cash Flow + Cash Inflow)
3 -    13,608 11,321 (Net Cash Flow + Cash Inflow)
4 -    8,500 19,821 (Net Cash Flow + Cash Inflow)

c.

Discounted Payback Period =

( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]

= 3 + ( 224,099.13/323,174.21)

= 3.69 years

Note:

Cash Flow Discounting Factor ( 6%) Present Value (Cash Flow * Discounting Factor) Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0 -3,44,278 1 -3,44,278.00 -3,44,278.00
1 28,600 0.9433962264150940 26,981.13 -3,17,296.87
2 50,000 0.8899964400142400 44,499.82 -2,72,797.05
3 58,000 0.8396192830323020 48,697.92 -2,24,099.13
4 4,08,000 0.7920936632380200 3,23,174.21 99,075.09

d.

Discounted Payback Period =

( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]

= 2 + ( 3409.30 / 11425.54)

= 2.298392899 years

= 2.30 Years

Note:

Cash Flow Discounting Factor ( 6%) Present Value (Cash Flow * Discounting Factor) Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0 -14,518 1 -14,518.00 -14,518.00
1 4,179 0.9433962264150940 3,942.45 -10,575.55
2 8,052 0.8899964400142400 7,166.25 -3,409.30
3 13,608 0.8396192830323020 11,425.54 8,016.24
4 8,500 0.7920936632380200 6,732.80 14,749.04

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