# Hart Venture Capital

Topics: Investment, Limit of a function, Optimization Pages: 5 (808 words) Published: November 6, 2011
Hart Venture Capital Case Problem 3

After performing an analysis of HVC’s investment problem, I found that the company’s objective was to maximize the net present value of the total investment in Security Systems and Market Analysis. To find the maximum net present value and analyze the numbers, I set up the model shown below.

Max1,800,000*SS + 1,600,000*MA

s.t.600,000*SS + 500,000*MA ≤ 800,000
600,000*SS + 350,000*MA ≤ 700,000
250,000*SS + 400,000*MA ≤ 500,000
SS,MA ≥ 0

After solving the above model for an optimal solution, I found that HVC should invest in 60.9% of the Security Systems project and 87% of the Market Analysis project. These recommended percentages give an optimal solution of \$2,486,957 for the net present value of the total investment. A capital allocation plan for the coming three-year period is shown below. When using Management Scientist, a rounding error occurred with the optimal percentages for each project. You can see this error in the Year 1 and Year 3 totals for HVC Investment. The totals for these 2 years are a little bit above what the constraints should hold them at.

| SS| MA| HVC Investment|
Year 1| 365,400 | 435,000 | 800,400 |
Year 2| 365,400 | 304,500 | 669,900 |
Year 3| 152,250 | 348,000 | 500,250 |

If HVC were willing to commit an additional \$100,000 during the first year, the optimal solution and percentages would change. This increase in investment would result in a recommendation of funding 68.9% of the Security Systems project and 82% of the Market Analysis project. This slight change in percentages gives an optimal solution of \$2,550,820 for the net present value of total investment, an increase of \$63,863. A capital allocation plan for the coming three-year period with an additional \$100,000 during the first year is shown below.

| SS| MA| HVC Investment|
Year 1| 413,400 | 410,000 | 823,400 |
Year 2| 413,400 | 287,000 | 700,400 |
Year 3| 172,250 | 328,000 | 500,250 |

When considering whether to recommend committing the additional \$100,000 in the first year, I had to consider the change in the optimal solution along with the amount of slack funds that HVC did not use in their investments. Without the additional \$100,000 in the first year, HVC has a net present value of the total investment of \$2,486,957. They also have slack of \$30,435 in constraint 2, shown in Appendix 1. This means that they have \$30,435 that they could be investing elsewhere. However, with the additional \$100,000, HVC has a net present value of the total investment of \$2,550,820. HVC also has slack of \$77,049 in constraint 1, shown in Appendix 2. This means that HVC has an additional \$77,049 that they could be investing elsewhere. With this information, it is clear that the additional \$100,000 in the first year should be committed. The extra cash would result in a greater net present value of the total investment and would also give HVC more extra cash to invest elsewhere if they wish. With this greater amount of extra capital, HVC could potentially make a greater return.

Appendix 1

MAX 1800000SS + 1600000MA

S.T.

1) 600000SS +500000MA < 800000

2) 600000SS + 350000MA < 700000

3) 250000SS + 400000MA < 500000

OPTIMAL SOLUTION

Objective Function Value = 2486956.522

Variable Value Reduced Costs

-------------- --------------- ------------------

SS 0.609 0.000

MA 0.870 0.000

Constraint Slack/Surplus Dual Prices

-------------- --------------- ------------------

1 0.000 2.783

2 30434.783 0.000

3 0.000 0.522...