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IEEN 5329 Homework 10 12

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IEEN 5329 Homework 10

12.7, 12.17, 12.20

Understanding the Capital Rationing

Problem

12(1) Write a short paragraph that explains the problem of rationing investment capital among several projects that are independent of one another.

12.2 State the reinvestment assumption about project cash flows that 1s made when one is solving the capital budgeting problem.

12.3 Four independent projects (1, 2, 3, and 4) are to be evaluated for investment by Perfect Manufacturing. Develop all the acceptable mutually exclusive bundles based on the following selection restrictions developed by the department of engineering production:

Project 2 can be selected only if project 3 is selected.

Projects 1 and 4 should not both be selected; they are essentially duplicates.

12.4 Develop all acceptable mutually exclusive bundles for the four independent projects described below if the investment limit is $400 and the following project selection restriction applies: Project 1 can be selected only if both projects 3 and 4 are selected.

Project	Initial Investment, $
1	-250
2	-150
3	-75
4	-235

 

Selection from Independent Projects

12.5 (a) Determine which of the following independent projects should be selected for investment if $325,000 is available and the MARR is 10% per year. Use the PW method to evaluate mutually exclusive bundles to make the selection.

Project	Initial Investment, $	Net cash Flow, $/year	Life, Years
A	-100,000	50,000	8
B	-125,000	24,000	8
C	-120,000	75,000	8
D	-220,000	39,000	8
E	-200,000	82,000	8

 

(b) If the five projects are mutually exclusive alternatives, perform the present worth analysis and select the best alternative.

12.6 Work Problem 12.5(q@), using a spread-sheet.

12.7 The engineering department at General Tire has a total of $900,000 for no more than two projects in capital improvement for the year. Use a spreadsheet-based PW analysis and a minimum 12% per year return to answer the following.

(a) Which projects are acceptable from the three described below?

(b) What is the minimum required annual net cash flow necessary to select the bundle that expends as much as possible without violating either the budget limit or the two-project maximum restriction?

Project	Initial Investment, $	Estimated NCF, $/Year	Life, Years	Salvage Value, $
A	-400,000	120,000	4	40,000
B	-200,000	90,000	4	30,000
C	-700,000	200,000	4	20,000

 

12.8 Jesse wants to choose exactly two independent projects from four opportunities.

Each project has an initial investment of $300,000 and a life of 5 years. The annual NCF estimates for the first three projects are available, but a detailed estimate for the fourth is not yet prepared and time has run out for the selection.

Using MARR = 9% per year, determine the minimum NCEF for the fourth project (Z) that will guarantee that it is part of the selected twosome.

Project	Annual NCF, $/year
W	90,000
X	50,000
Y	130,000
Z	At least 50,000

 

12.9 The engineer at Clean Water Engineering has established a capital investment limit of $800,000 for next year for projects that target improved recovery of highly brackish groundwater. Select any or all of the following projects, using a MARR of 10% per year. Present your solution by hand calculations, not Excel.

Project	Initial Investment, $	Annual NCF, $/Year	Life, Years	Salvage Value, $
A	-250,000	50,000	4	45,000
B	-300,000	90,000	4	-10,000
C	-550,000	150,000	4	100,000

 

12.10 Develop an Excel spreadsheet for the three projects in Problem 12.9. Assume that the engineer wants project C to be the only one selected. Considering the viable project options and & = $800,000, determine (a) the largest initial investment for C and (b) the largest MARR allowed to guarantee that C is selected.

12.11 Eight projects are available for selection at HumVee Motors. The listed PW values are determined at the corporate MARR of 10% per year and rounded to the nearest $1000. Project lives vary from 5 to 15 years.

Project	Initial Investment, $	PW value at 10%, $
1	-1,500,000	-50,000
2	-300,000	+35,000
3	-95,000	-9,000
4	-400,000	+75,000
5	-195,000	+125,000
6	-175,000	-27,000
7	-100,000	+62,000
8	-400,000	+110,000

 

Project selection guidelines:

1. No more than $400,000 in investment capital is available.

2. No negative PW project may be selected.

3. At least one project, but no more than three, must be selected.

4. The following selection restrictions apply Lo specific projects:

• Project 4 can be selected only if project 1 is selected.
• Projects 1 and 2 are duplicative; don't select both.
• Projects 8 and 4 are also duplicative.
• Project 7 requires that project 2 also be selected.

(a) Identify the viable project bundles and select the best economically justified projects. What is the investment assumption for any remaining capital funds?

(b) If as much of the $400,000 as possible must be invested, use the same restrictions and determine the project(s) to select. Is this a viable second choice for investing the $400,000? Why?

12.12 Use the analysis below of five independent projects to select the best, if the capital limitation is (a) $30.000. (4) $60,000, and (c) unlimited.

Project	Initial Investment, $	Life, Years	PW at 12% per Year, $
S	-15,000	6	8,540
A	-25,000	8	12,325
M	-10,000	6	3,000
E	-25,000	4	10
H	-40,000	12	15,350

12.13 The independent project estimates below have been developed by the engineering and finance managers. The corporate MARR 1s 15% per year, and the capital investment limit is $4 million.

(a) Use the PW method and hand solution to select the economically best projects.

(b) Use the PW method and computer solution to select the economically best projects.

Project	Project Cost, $ Millions	Life, Years	NCF, $/Year
1	-1.5	8	360,000
2	-3.0	10	600,000
3	-1.8	5	520,000
4	-2.0	4	820,000

 

12.14 The following capital rationing problem is defined. Three projects are to be evaluated at a MARR of 12.5% per year. No more than $3.0 million can be invested.

(a) Use a spreadsheet to select from the independent projects.

(b) Use SOLVER to determine the minimum year | NCF for project 3 alone to have the same PW as the best bundle in part (a) if project 3 life can be increased to 10 years for the same $1 million investment. All other estimates remain the same. With this increased NCF and life. What are the best projects for investment?

Project	Investment, $ Millions	Life, Years	Estimated NCF, $/Year
			Year 1	Gradient after Year 1
1	-0.9	6	250,000	-5000
2	-2.1	10	485,000	+5000
3	-1.0	5	200,000	+10%

 

12.15 Use the PW method to evaluate four independent projects. Select as many as three of the four projects. The MARR is 12% per year, and an available capital investment limit is $16,000.

12.16 Work Problem 12.15, using a spreadsheet.

12.17 Using the NCF estimates in Problem 12.15 for projects 3 and 4. Demonstrate the reinvestment assumption made when the capital budgeting problem is solved for the four projects by using the PW method. (Hint: Refer to Equation [12.2].)

Linear Programming and Capital Budgeting

12.18 Formulate the linear programming model, develop a spreadsheet, and solve the capital rationing problem in Example 12.1 (a) as presented and (4) using an investment limit of $13 million.

12.19 For Problem 12.5, use Excel and SOLVER to (a) answer the question in part (a) and (b) select the projects if MARR = 12% per year and the investment limit is increased to $500,000.

 

12.20 Use SOLVER to work Problem 12.10.

12.21 Use SOLVER to find the minimum NCF required for project Z as detailed by Jesse in Problem 12.13.

 

12.22 Use linear programming and a spreadsheet-based solution technique to select from the independent unequal-life projects in Problem 12.13.

12.23 Solve the capital budgeting problem in Problem 12.14(a), using the linear programming model and Excel.

12.24 Solve the capital budgeting problem in Problem 12.15, using the linear programming model and Excel.

12.25 Using the data in Problem 12.15 and Excel solutions of the capital rationing problem for capital budget limits ranging from b = $ 5000 to b = $25,000, develop an Excel chart that plots b versus the value of Z.