Question

Alyeska Salmon Inc., a large salmon canning firm operating out of Valdez, Alaska, has a new automated production line project it is considering. The project has a cost of $300,000 and is expected to provide after-tax annual cash flows of $80,000 for seven years. The cost of capital for the firm is 15 percent.

1. What is the payback period of the project?

   		3.33 years
   		3.75 years
   		4.25 years
   		4.82 years
   		5.33 years

1 points   

1. What is the NPV of the project?

   		29,625
   		32,834
   		39,158
   		43,238
   		61,157

1. What is the EAA (Equivalent Annual Annuity) cash flow of the project?

   		6,372
   		7,131
   		7,892
   		9,335
   		10,341

1. What is the IRR of the project?

   		13.34%
   		15.76%
   		16.93%
   		17.51%
   		18.58%

1. What is the profitability index (PI) of the project?

   		1.08
   		1.11
   		1.25
   		1.32
   		1.45

1. The firm's management is uncomfortable with the IRR reinvestment assumption and prefers the modified IRR approach. What is the project's MIRR?

   		15.13%
   		15.75%
   		16.72%
   		17.35%
   		19.18%

Answer 1

Project
Year	Cash flow stream	Cumulative cash flow
0	-300000	-300000
1	80000	-220000
2	80000	-140000
3	80000	-60000
4	80000	20000
5	80000	100000
6	80000	180000
7	80000	260000

Payback period is the time by which undiscounted cashflow cover the intial investment outlay

this is happening between year 3 and 4

therefore by interpolation payback period = 3 + (0-(-60000))/(20000-(-60000))

3.75 Years

Project
Discount rate	15.000%
Year	0	1	2	3	4	5	6	7
Cash flow stream	-300000	80000	80000	80000	80000	80000	80000	80000
Discounting factor	1.000	1.150	1.323	1.521	1.749	2.011	2.313	2.660
Discounted cash flows project	-300000.000	69565.217	60491.493	52601.299	45740.260	39774.139	34586.208	30074.963
NPV = Sum of discounted cash flows
NPV Project =	32833.58
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project
Discount rate	15.000%
Year	0	1	2	3	4	5	6	7
Cash flow stream	-300000.000	80000.000	80000.000	80000.000	80000.000	80000.000	80000.000	80000.000
Discounting factor	1.000	1.150	1.323	1.521	1.749	2.011	2.313	2.660
Discounted cash flows project	-300000.000	69565.217	60491.493	52601.299	45740.260	39774.139	34586.208	30074.963
NPV = Sum of discounted cash flows
NPV Project =	32833.58
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Equvalent annuity(EAA)=	7891.89
Required rate =	15.000%
Year	0	1	2	3	4	5	6	7
Cash flow stream	0.00	7891.89	7891.89	7891.89	7891.89	7891.89	7891.89	7891.89
Discounting factor	1.000	1.150	1.323	1.521	1.749	2.011	2.313	2.660
Discounted cash flows project	0.000	6862.514	5967.404	5189.047	4512.214	3923.665	3411.882	2966.854
Sum of discounted future cashflows =	32833.58
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor

Project
IRR is the rate at which NPV =0
IRR	18.58%
Year	0	1	2	3	4	5	6	7
Cash flow stream	-300000.000	80000.000	80000.000	80000.000	80000.000	80000.000	80000.000	80000.000
Discounting factor	1.000	1.186	1.406	1.667	1.977	2.344	2.780	3.296
Discounted cash flows project	-300000.000	67467.417	56898.155	47984.645	40467.501	34127.972	28781.577	24272.733
NPV = Sum of discounted cash flows
NPV Project =	0.000
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	18.58%

PI= (NPV+initial inv.)/initial inv.

=(32833.58+300000)/300000

1.11

Reinvestment Approach
All cash flows except the first are compounded to the last time period and IRR is calculated
Thus year 7 modified cash flow=(185044.86)+(160908.58)+(139920.5)+(121670)+(105800)+(92000)+(80000)
=885343.94
Discount rate	15.000%
Year	0	1	2	3	4	5	6	7
Cash flow stream	-300000.000	80000.000	80000.000	80000.000	80000.000	80000.000	80000.000	80000.000
Compound factor	1.000	2.313	2.011	1.749	1.521	1.323	1.150	1.000
Compounded cash flows	-300000.000	185044.86	160908.58	139920.5	121670	105800	92000	80000
Modified cash flow	-300000.000	0	0	0	0	0	0	885343.940
Discounting factor (using MIRR)	1.000	1.167	1.362	1.590	1.856	2.166	2.528	2.951
Discounted cash flows	-300000.000	0.000	0.000	0.000	0.000	0.000	0.000	300000.000
NPV = Sum of discounted cash flows
NPV Discount rate =	0.00
MIRR is the rate at which NPV = 0
MIRR=	16.72%
Where
Compounding factor =	(1 + reinvestment rate)^(time of last CF-Corresponding period in years)
compounded Cashflow=	Cash flow stream*compounding factor