Question

Consider the following two mutually exclusive projects:

Year	Cash Flow (A)				Cash Flow (B)
0	–$	364,000			–$	52,000
1		46,000				25,000
2		68,000				22,000
3		68,000				21,500
4		458,000				17,500

Whichever project you choose, if any, you require a return of 11 percent on your investment.

a-1. What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
  

a-2. If you apply the payback criterion, which investment will you choose?
  

Project A

Project B

b-1. What is the discounted payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
  


b-2. If you apply the discounted payback criterion, which investment will you choose?
  

Project A

Project B

c-1. What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
  


c-2. If you apply the NPV criterion, which investment will you choose?
  

Project A

Project B

d-1. What is the IRR for each project? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
  


d-2. If you apply the IRR criterion, which investment will you choose?
  

Project A

Project B

e-1. What is the profitability index for each project? (Do not round intermediate calculations and round your answers to 3 decimal places, e.g., 32.161.)
  


e-2. If you apply the profitability index criterion, which investment will you choose?
  

Project A

Project B

f. Based on your answers in (a) through (e), which project will you finally choose?
  

Project A

Project B

Answer 1

a-1. What is the payback period for each project?

Project A

Year	0	1	2	3	4
Cashflow(in $)	(364,000)	46,000	68,000	68,000	458,000
Cumulative Cashflow(in $)	(364,000)	(318,000)	(250,000)	(182,000)	276,000

Payback Period = A+(B/C)

where

A - last period containing negative cumulative cash flow

B - absolute value of cumulative cash flow in A

C - cash flow during the period after A

Payback Period = 3 + (182000/458000)

= 3 + 0.39737991266

= 3.40 Years

Project B

Year	0	1	2	3	4
Cashflow(in $)	(52,000)	25,000	22,000	21,500	17,500
Cumulative Cashflow(in $)	(52,000)	(27,000)	(5,000)	16,500	34,000

Payback period = 2 + (5000/21500)

= 2 + 0.23255813953

= 2.23 years

a-2. If you apply the payback criterion, which investment will you choose?

Project B as it has lower Payback period.

b-1. What is the discounted payback period for each project?

Project A

Year	0	1	2	3	4
Cashflow(in $)	(364,000)	46,000	68,000	68,000	458,000
PVF @11%	1	0.901	0.812	0.731	0.659
Discounted Cashflow (Cash flow * PVF)	(364,000)	41,441	55,190	49,721	301,699
Cumulative Cashflow(in $)	(364,000)	(322,559)	(267,368)	(217,647)	84,052

Discounted Payback Period = 3 + (217647/301699)

= 3 + 0.72140444615

= 3.72 Years

Project B

Year	0	1	2	3	4
Cashflow(in $)	(52,000)	25,000	22,000	21,500	17,500
PVF @11%	1	0.901	0.812	0.731	0.659
Discounted Cashflow (Cash flow * PVF)	(52,000)	22,523	17,856	15,721	11,528
Cumulative Cashflow(in $)	(52,000)	(29,477)	(11,622)	4,099	15,627

Discounted payback period = 2+(11622/15721)

= 2 + 0.73926595

= 2.74 years

b-2. If you apply the discounted payback criterion, which investment will you choose?

Project B as it has lower  Lower Discounted Payback period.

c-1. What is the NPV for each project?

Project A

ear	0	1	2	3	4
Cashflow(in $)	(364,000)	46,000	68,000	68,000	458,000
PVF @11%	1	0.901	0.812	0.731	0.659
Discounted Cashflow (Cash flow * PVF)	(364,000.00)	41,441.44	55,190.33	49,721.01	301,698.79

NPV = PV of Inflows - PV of Outflows

= (41441.44+55190.33+49721.01+301698.79) - 364000

= 448051.57-364000

= 84051.57

Project B

Year	0	1	2	3	4
Cashflow(in $)	(52,000)	25,000	22,000	21,500	17,500
PVF @11%	1	0.901	0.812	0.731	0.659
Discounted Cashflow (Cash flow * PVF)	(52,000)	22,522.52	17,855.69	15,720.61	11,527.79

NPV = (22522.52+17855.69+15720.61+11527.79)-52000

= 67626.62-52000

= 15626.62

c-2. If you apply the NPV criterion, which investment will you choose?

Project A as it has Higher NPV

d-1. What is the IRR for each project?

Project A

IRR is the rate at which NPV=0. ie: PV of inflows = PV of outflows. It is calculated by trial and error method.

Lets find NPV at say 18%.

Year	0	1	2	3	4
Cashflow(in $)	(364,000)	46,000	68,000	68,000	458,000
PVF @18%	1	0.847	0.718	0.609	0.516
Discounted Cashflow (Cash flow * PVF)	(364,000.00)	38,983.05	48,836.54	41,386.90	236,231.30

NPV1 = (38983.05+48836.54+41386.90+236231.30) - 364000

= 365437.80-364000

= 1437.80

Since NPV is positive, Take a higher rate say 19%

Year	0	1	2	3	4
Cashflow(in $)	(364,000)	46,000	68,000	68,000	458,000
PVF @19%	1	0.840	0.706	0.593	0.499
Discounted Cashflow (Cash flow * PVF)	(364,000.00)	38,655.46	48,019.21	40,352.28	228,390.29

NPV2 = (38655.46+48019.21+40352.28+228390.29)-364000

= 355417.23-364000

= -8582.77

IRR = R1 + ((NPV1 * (R2 - R1)) / (NPV1 - NPV2))

= 18+((1437.80*(19-18)) / (1437.80+8582.77)

= 18+(1437.80/10020.57)

= 18+0.14348485166v

= 18.14%

Project B

Lets find NPV at say 25%

Year	0	1	2	3	4
Cashflow(in $)	(52,000)	25,000	22,000	21,500	17,500
PVF @25%	1	0.800	0.640	0.512	0.410
Discounted Cashflow (Cash flow * PVF)	(52,000.00)	20,000.00	14,080.00	11,008.00	7,168.00

NPV = (20000+14080+11008+7168)-52000

= 52256-52000

= 256

Since NPV is positive, Take a higher rate say 26%

Year	0	1	2	3	4
Cashflow(in $)	(52,000)	25,000	22,000	21,500	17,500
PVF @26%	1	0.794	0.630	0.500	0.397
Discounted Cashflow (Cash flow * PVF)	(52,000.00)	19,841.27	13,857.39	10,747.98	6,943.14

NPV = (19841.27+13857.39+10747.98+6943.14)-52000

= 51389.79-52000

= -610.22

IRR = R1 + ((NPV1 * (R2 - R1)) / (NPV1 - NPV2))

= 25 + ((256*(26-25)) / (256+610.22))

= 25 + (256/866.22)

= 25+0.29553693057

= 25.30%

d-2. If you apply the IRR criterion, which investment will you choose?

A project is acceptable when IRR is greater than required rate of return. Project B as this has higher IRR.

e-1. What is the profitability index for each project?

Project A

Profitability index = PV of future Cash Flows / Initial Investment

= 448051.57/364000

= 1.231

Project B

Profitability index = PV of future Cash Flows / Initial Investment

= 67626.62/52000

= 1.301

e-2. If you apply the profitability index criterion, which investment will you choose?

Project B as it has Higher Profitability index.

f. Based on your answers in (a) through (e), which project will you finally choose?

Project A as it has higher NPV as NPV supercedes all other evaluation technique.