Question

Consider the following two mutually exclusive projects:

   

Year	Cash Flow (A)				Cash Flow (B)
0	–$	315,500			–	40,300
1		42,000				21,500
2		63,000				19,000
3		68,000				16,500
4		415,000				14,600

   

Whichever project you choose, if any, you require a 12 percent return on your investment. When evaluating projects solely on the basis of payback, the firm payback requirement for projects is 2.3 years. You do not need to show each calculator keystroke but you do need to describe how you calculated each answer. (Round your answers to 2 decimal places)

  

a)	What is the payback period for each project? Indicate the best project you would accept, if either, based on this criteria.

b)	What is the discounted payback period for each project? Indicate the best project you would accept, if either, based on this criteria.

c)	What is the NPV for each project? Indicate the best project you would accept, if either, based on this criteria.

d) What is the IRR for each project? Indicate the best project you would accept, if either, based on this criteria.                   

e)	What is the profitability index for each project? Indicate the best project you would accept, if either, based on this criteria.

f) Based on your analysis above, which project will you finally choose, and why?

Answer 1

A) Payback period

Project A

project A
year	cash flow	cumulative cashflow
1	42000	42000
2	63000	105000
3	48000	153000
4	415000	568000

Pay back period= 3 years +[ (315500-153000)/ (568000-153000) ] * 12

3 years + (162500/415000) * 12

3 years + 0.3916* 12

3 years and 4.7 months

Payback period = 3.47

Project B

project B
year	cash flow	cumulative cashflow
1	21500	21500
2	19000	40500
3	16500	57000
4	14600	71600

Pay back period= 1 year +[ (40300-21500)/ (40500-21500) ] * 12

1 year + (18800/19000) * 12

1 year + 0.9895* 12

1 year and 11.8 months

Payback period = 1.12

Project B have a less pay back period. It is better to select project B on the basis of payback period and also it is less than the firms payback requirements.

B) Discounted Payback period

Project A

project A
year	cash flow	pvf @ 12%	pv of cashflow	cumulative cashflow
1	42000	0.892857	37500	37500
2	63000	0.797194	50223.214	87723.214
3	48000	0.71178	34165.452	121888.67
4	415000	0.635518	263740	385628.67

Discounted Pay back period= 3 years +[ (315500-121888.67)/ (385628.67-121888.67) ] * 12

3 years + (193611.33/363740) * 12

3 years + 0.5323* 12

3 years and 6.38 months

Discounted Payback period = 3.64

Project B

project B
year	cash flow	pvf @ 12%	pv of cashflow	cumulative cashflow
1	21500	0.892857	19196.4286	19196.429
2	19000	0.797194	15146.6837	34343.112
3	16500	0.71178	11744.3741	46087.486
4	14600	0.635518	9278.56394	55366.05

Discounted Pay back period= 2 years +[ (40300-34343.112)/ (46087.486-34343.112) ] * 12

2 year + (5956.888/11744.374) * 12

2 years + 0.5072* 12

2 years and 6.09 months

Discounted Payback period = 2.61

Project B have a less discounted pay back period. It is better to select project B on the basis of discounted payback period

C) Net Present Value (NPV)

NPV = Present value of cash inflow – Initial investment

project A
year	cash flow	pvf @ 12%	pv of cashflow
1	42000	0.892857	37500
2	63000	0.797194	50223.214
3	48000	0.71178	34165.452
4	415000	0.635518	263740
Total present value	385628.67
(less) cash outflow	-315500.00
Net Present Value (NPV)	70128.67

project B
year	cash flow	pvf @ 12%	pv of cashflow
1	21500	0.892857	19196.4286
2	19000	0.797194	15146.6837
3	16500	0.71178	11744.3741
4	14600	0.635518	9278.56394
Total present value	55366.05
(less) cash outflow	-40300.00
Net Present Value (NPV)	15066.05

Considering NPV both projects showing a positive value, project A is more profitable. Firm can go with project A (Accept project A)

D) Internal Rate of Return (IRR)

IRR = Lowest rate + [(NPV at lowest rate)/(NPV at lowest rate –NPV at highest rate)] * difference in rate

Project A

project A
year	cash flow	pvf @ 12%	pv of cashflow
1	42000	0.892857	37500
2	63000	0.797194	50223.214
3	48000	0.71178	34165.452
4	415000	0.635518	263740
Total present value	385628.67
(less) cash outflow	-315500.00
Net Present Value (NPV)	70128.67
project A
year	cash flow	pvf @ 20%	pv of cashflow
1	42000	0.833333	35000
2	63000	0.694444	43750
3	48000	0.578704	27777.778
4	415000	0.482253	200135.03
Total present value	306662.81
(less) cash outflow	-315500.00
Net Present Value (NPV)	-8837.19

= 12+(70128.67)/( 70128.67-(-8837.19))]*20-12

= 12+[70128.67/78965.86]*8

= 12+ 7

IRR for the project A = 19%

Project B

project B		project B
year	cash flow	pvf @ 20%	pv of cashflow		year	cash flow	pvf @ 32%	pv of cashflow
1	21500	0.833333	17916.6667		1	21500	0.757576	16287.879
2	19000	0.694444	13194.4444		2	19000	0.573921	10904.5
3	16500	0.578704	9548.61111		3	16500	0.434789	7174.0129
4	14600	0.482253	7040.89506		4	14600	0.329385	4809.0261
Total present value	47700.62		Total present value	39175.42
(less) cash outflow	-40300.00		(less) cash outflow	-40300.00
Net Present Value (NPV)	7400.62		Net Present Value (NPV)	-1124.58

= 20+(7400.62)/( 7400.62-(-1124.58))]*32-20

= 20+[7400.62/8525.2]*12

= 20+ 10.4

IRR for the project B = 30.4%

IRR in case of project B is higher than Project A, Hence project B is preferable.

E) Profitability index

Profitability index = Total present value of inflow/ Total present value of outflow

Project A

Profitability index = 385628.67/315500

Profitability index = 1.22       

Project B

Profitability index = 55366.05/40300

Profitability index = 1.37

Project B is acceptable, it showing a higher PI

F)

Project B is preferable, all the evaluation technique except NPV suggest project B. when we look in to the NPV value Project A showing high but when we deeply examine the NPV percent is less when compared to its cash inflow. So, it’s better to select Project B.