Hart Venture Capital

HART Venture Capital

Capital Allocation Plan for Security System and Market Analysis for three years

Table of Content

Abstract I

List of Table II-VIII

State of Problem 1

Constraints 2

Analysis of the ProblemObjective Function 3

Solutions and Results

Graphical Solutions 4

Extreme Points and Optimal Point 5

Slack and Surplus 6

Dual Price 6-7

Range of Optimality 8

Range of R.H.S Value 9-11

DiscussionExcel Summary 12Managerial Report 13-16

Conclusion 17Work Contribution 18Reference Cited 19

AbstractHart Venture Capital (HVC) is a company of providing venture capital for software development and Internet application. Currently, there are two companies: Security Systems and Market Analysis need additional capital. Security package needs additional capital to develop an Internet security software package; Market Analysis needs additional capital to develop a software package for conducting customer satisfaction surveys. The company is trying to find the optimal percentage of each project that HVC should fund in order to yield the maximum net present value of the total investment.

To solve this problem, linear programming will be used. The problem the firms faces is a maximization problem. The net present value generated by the sum of the net present value multiplied by the recommended percentage of two investments will be the objective function. The answer will be the optimal point of the feasible region within the constraints of the amount of capital available.

Capital availability will be the key role in determining how much capital should be allocated to the two companies over three years. The recommended percentages for the two companies will remain unchanged over three years. This paper will solve the problems that the firm faces and look into the change in objective function if additional capital is provided.

I

LIST OF TABLESPage 3

Security Systems Market Analysis

Net Present Value (100 Percent funding) $ 1,800,000 $ 1,600,000

Page 4

　 Investment Opportunities 　Years Security System Stock Market Analysis Maximum Investment each year

1 $ 600,000 $ 500,000 $ 800,000 2 $ 600,000 $ 350,000 $ 700,000 3 $ 250,000 $ 400,000 $ 500,000

Page 6

Page 8

Total Investment in Year 1 S*600,000 M*500,000 = 800,000



　

ecurity System Stock

Market Analysis

　 Algebra Slope Intercept 　　　

　　　　　　 Security System Stock Market AnalysisOptimal Solution 61% 87% Maximization

-1600000/1800000 -0.888888889 Algebra S Algebra M

Constrain 1 600000 500000 <= 800000 -500000600000

-0.833333333 800000/600000 1.333333333 800000/500000 1.6

Constrain 2 600000 350000 <= 700000 -350000/600000 -0.6 700000/600000 1.166666667 700000/350000 2

Constrain 3 250000 400000 <= 500000 -400000/250000 -1.6 500000/250000 2 500000/400000 1.3

Constrain 4 1 　 >= 0 Undefined 　　　　　

Constrain 5 　 1 >= 0 0 　　　　　

Slope of a line = y = -mx + b 　　　　

II

Page 16

　Security

System StockMarket

Analysis total

Investment in Year 1 $ 365,217.39 $ 434,782.61 $ 800,000.00



Figures

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VIII

Statement of Problem and Process

I dentification of the problem The problem is what percentage of each project that HVC should fund to generate the

maximum net present value of the total investment in Security System and Market Analysis. Using an 8% rate of return, HVC’s financial analysis team estimate that 100 percent funding of the Security Systems project has a net present value of $1,800,000 and 100 percent funding of the Market Analysis project has a net percent value of $1,600,000. HVC has the option to fund

any percentage of the Security Systems and Market Analysis project. Therefore, let the S be the recommended percentage of Security Systems that HVC should fund; let the M be the recommended percentage of Market Analysis that HVC should fund, the net percent value of the Security Systems would be S*($1,800,000); the net percent value of the Market Analysis would be M*($1,600,000).

Security Systems Market Analysis

Net Present Value (100 Percent funding) $ 1,800,000 $ 1,600,000

1

ConstraintsThe constraints are each year’s investment amount on both projects that HVC commit at

most. In year 1, in exchange for Security Systems stock, the firm has asked HVC to provide $600,000; in exchange for Market Analysis, the firm has asked for $500,000; HVC are willing to commit at most $800,000 for both projects in the first year.

In year 2, Security Systems has asked for $600,000 and Market Analysis has asked for $350,000; the most investment by HVC in year 2 is $700,000.

In year 3, Security System has asked for $250,000, while the Market Analysis has asked for $400,000; the maximum investment by HVC is $500,000.

　 Investment Opportunities 　

Years Security System Stock Market Analysis Maximum Investment each year1 $ 600,000 $ 500,000 $ 800,000 2 $ 600,000 $ 350,000 $ 700,000 3 $ 250,000 $ 400,000 $ 500,000

2

Analysis of the problem

Objective function Max 1,800,000 (S) + 1,600,000 (M)

S.T.

600,000 (S) + 500,000 (M) 800,000

600,000 (S) + 350,000 (M) 700,000

250,000 (S) + 400,000 (M) 500,000

S 0

M 0

3

Solutions and Results

Graphical Solution

There are three extreme points (A, B, C, D) and the optimal point at point C. The reason is that C is the farthest point from the origin. Point C is on the intersection of Constrain 1 and 3.

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Extreme Points and Optimal PointTherefore:

　Security System Stock

Market Analysis

　 Algebra Slope Intercept 　　　

　　　　　　 Security System Stock Market AnalysisOptimal Solution 61% 87% Maximization

-1600000/1800000 -0.888888889 Algebra S Algebra M

Constrain 1 600000 500000 <= 800000 -500000/600000 -0.833333333 800000/600000 1.333333333 800000/500000 1.6

Constrain 2 600000 350000 <= 700000 -350000/600000 -0.6 700000/600000 1.166666667 700000/350000 2

Constrain 3 250000 400000 <= 500000 -400000/250000 -1.6 500000/250000 2 500000/400000 1.3

Constrain 4 1 　 >= 0 Undefined 　　　　　

Constrain 5 　 1 >= 0 0 　　　　　

Slope of a line = y = -mx + b 　　　　

600,000 (S) + 500,000 (M) = 800,000 = 6S + 5M =8

250,000 (S) + 400,000 (M) = 500,000 2.5S + 4M =5

S= 60.86956% M= 86.95652%

At the optimal point (point c), HVC should fund 61% of the Security Systems project and 87% of the Market Analysis. The total net present value will be:

$ 2,486,956.52 Point A Refer to the graph S=133%

M =0

At Point A 133% S and 0% M will fund. The total net present value will be:

$ 2,394,000.00

Point B

600,000 (S) + 500,000 (M) = 800,000 = 6S+5M=8

600,000 (S) + 350,000 (M) = 700,000 6S+3.5M=7

M= 66.66666%

S= 77.77777%

At the Point B, 67% S and 77% M will fund. The total net present value will be:

$ 2,466666.67

Point D Refer to the graph

S= 0%

M = 125%

At the Point B, 69% S and 82% M will fund. The total net present value will be:

$ 2,000,000.00 5

Slack and SurplusTotal Investment in Year 1 S*600,000 M*500,000 800,000

=



To find the slack determine the percentage funded and subtract that from the total allowable investment that HVC is willing to commit.

The result is that there are slacks in the non-binding constrains. There is still $ 30,435.00 that could invest in the second year.

Dual PriceThe dual price is calculated by adding one additional unit to the right hand side of a binding constraint. After plugging the results back into the optimal solution and then subtract the previous optimal solution from the answer.

Constraint 1

600,000 (S) + 500,000 (M) = 800,000 = 600,000 (S) + 500,000 (M) = 800,001

250,000 (S) + 400,000 (M) = 500,000 250,000 (S) + 400,000 (M) = 500,000

M= 86.95630%

S = 60.86991%

1,800,000*(60.86991%) + 1,600,000*(86.95630%) - 2,486,956.52 = 2.78 = Dual Price for Constrain 1

Constraint 3

600,000 (S) + 500,000 (M) = 800,000 = 600,000 (S) + 500,000 (M) = 800,000

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250,000 (S) + 400,000 (M) = 500,000 250,000 (S) + 400,000 (M) = 500,001

M = 86.95704%

S = 60.86913%

1,800,000*(60.86913%) + 1,600,000*(86.95704%) - 2,486,956.52 = 0.52 = Dual Price for Constrain 3

If the total investment in year 1 is increase by $1, the net present value will increase by $ 2.78. If $1 was added to the investment amount of year 3, the net present value will increase by $ 0.52.

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Range of Optimality

The range of optimality is how much the optimal solution variable can change until the extreme point is changed. To calculate this set the slope of the optimal solution between the two binding solutions.

S

-1.6 - S/M -5/6 = -1.6 -S/1,600,000 -5/6

1.6 S/1,600,000 5/6

1,333,333.33 S 2,560,000

M

-1.6 - S/M -5/6 = -1.6 - 1,800,000/M -5/6

5/6 1,800,000/M 1.6

1,125,000 M 2,160,000

8

Range of RHS values

To determine the RHS values, move one of the constraints up or down until it hits an extreme point or an optimal point. Afterwards plug the coordinates of the point into the constraint that was moved. Then subtract the number from the original RHS.

Constraint 1

Point D

600,000 (0) + 500,000 (1.25) = 625,000 - 800,000 = -175,000 = maximum allowable decrease

Point E

600,000 (S) + 350,000 (M) = 700,000 = 6S + 3.5M = 7

250,000 (S) + 400,000 (M) = 500,000 2.5S + 4M =5

S = 68.852459%

M = 81.9672131%

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600,000 (68.852459%) + 500,000 (81.9672131%) – 800,000 = 22,950.81967 = maximum allowable increase

Constraint 2

Point C

600,000 (60.86956%) + 350,000 (86.95652%) = 669,565.18 - 700,000 = -30,434.82 = maximum allowable decrease

= maximum allowable increase

Constraint 3

10

Point B

600,000 (S) + 500,000 (M) = 800,000 = 6S + 5M = 8

600,000 (S) + 350,000 (M) = 700,000 6S + 3.5M = 7

M= 66.6666666%

S = 77.7777777%

250,000 (77.7777777%) + 400,000 (66.6666666%) = 461,111.1107 - 500,000 = - 38888.88935 = maximum allowable decrease

Point F

250,000 (0) + 400,000 (1.6) = 640,000 – 500,000 = 140,000 = maximum allowable increase

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Discussion

Excel Summary

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Managerial Report1. The recommended numbers for HVC are 61% of Security Systems stock and 87% of Market

Analysis. The net present value is $ 2,486,956.52.

2. In the first year, HVC should invest $ 365,217.39 in Security Systems Stock and $ 434,782.61 in Market Analysis, the total investment amount is $800,000. In the second year, this company will spend the same amount of money on the Security Systems Stock as the first year and $ 304,347.83 on Market Analysis, the total investment is $ 669,565.22; in the last year, HVC can commit $ 152,173.91 for Security System Stock and $ 347,826.09, the total is $500,000.

　Security

System StockMarket

Analysis total




3. If HVC is willing to commit an additional $100,000 during the first year, the recommend percentage of the Security System Stock will increase to 69% and the number of Market Analysis will decrease to 82%; the net present value will change to $2,550,819.67. In this case, the bindings will change from constraint 1 and 3 to constraint 2 and 3.

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4. There are four situations to consider:

Case (1) Adding all $100,000 to constraint 1

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Case (4) According to the optimal solution, adding $22,950.8197 of allowable increase to constraint 1; the remaining $100,000-22950.8197=$77,049.1803 which within the allowable increase of constraint 3 is added to the R.H.S of constraint 3.

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To sum up:

CaseDifferent O.F

Value　 Original

O.F Value　

Increase in Present Value

1 2550819.67 -2486956.5

2= 63863.15

2 2539130.43 -2486956.5

2= 52173.91

3 2486956.52 -2486956.5

2= 0.00

4 2591019.24 -2486956.5

2= 104062.72

Case 4 generates the largest increase in Present Value.

5. $22,950.8197 out of the additional $100,000 should be allocated to the first year.

Capital allowed to Security Systems in 1st year= 600,000*0.35=$210,000

Capital allowed to Markey Analysis in 1st year=500,000*1.22=$610,000

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ConclusionHart Venture Capital should allocate the available capital as below for Security Systems and Market Analysis over 3 years:

　Security

System StockMarket

Analysis total




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Reference citedAnderson, David R., Dennis J. Sweeney, Thomas A, and Kipp Martin. An Introduction to Management Science: Quantitative Approaches to Decision Making. 12 ed. Ohio: Thomas South-Western, 2008

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