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Example 15.7 Capital Budgeting at the Tatham Company

Example 15.7 Capital Budgeting at the Tatham Company. Integer Programming Models. Objective. To use IP to find the set of investments that maximizes NPV while staying within budget. Background Information. The Tatham Company is considering four investments.

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Example 15.7 Capital Budgeting at the Tatham Company

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  1. Example 15.7Capital Budgeting at the Tatham Company Integer Programming Models

  2. Objective To use IP to find the set of investments that maximizes NPV while staying within budget.

  3. Background Information • The Tatham Company is considering four investments. • The cash required for each investment and the net present value (NPV) each investment adds to the firm are given in the table below.

  4. Background Information -- continued • The cash available for investment is $14,000. • Tatham wants to find the investment policy that maximizes its NPV. • The crucial assumption here is that if Tatham wishes to take part in any of these investments, it must go “all the way”. It can’t, for example, go halfway in investment 1, by investing $2500 and realizing an NPV of $8000. (If partial investments were allowed we wouldn’t need IP, we could use LP.)

  5. Solution • The solution of this problem is quite straightforward. • Tatham must keep track of the following: • investments chosen • total cash required for the chosen investments • total NPV from the chosen investments

  6. Developing the Model • To keep track of which investments are chosen, we use a 0-1 variable for each investment. This is a variable that must equal 0 or 1. Usually it corresponds to activity that is or is not undertaken. It is also called a binary variable. • If a particular investment is chosen, the 0-1 variable for this investment will equal 1; if it is not chosen, the 0-1 variable will equal 0.

  7. TATHAM.XLS • This file provides the setup to develop the model seen below.

  8. Developing the Model -- continued • To develop the model proceed as follows: • Inputs. Enter the NPVs, the investment costs, and the budget amount in the appropriate shaded cells. • 0-1 values for investments. Enter any trial 0-1 values for the investments in the Invest range. • NPV contributions. Calculate the NPV contributed by the investments in to TotNPV cell with the formula =SUMPRODUCT(Invest,B7:E7). Observe the formula “picks up” the NPV only for those investments with 0-1 variables equal to 1.

  9. Developing the Model -- continued • Cash invested. Calculate the total cash invested in the TotCost cell with the formula =SUMPRODUCT(Invest,B9:E9) Again, this picks up only the cost of the investments with 0-1 variables equal to 1.

  10. Using Solver • The Solver dialog box is shown here. • We want to maximize the total NPV, subject to staying within budget. However, we also need to constrain the changing cells to be 0-1. This is simple, as we show here.

  11. Solution • The optimal solution indicates that a maximum NPV of $42,000 can be obtained by selecting investments 2, 3, and 4. These three investments use up all of the available budget. • If we rank Tatham’s investments on the basis of NPV per dollar invested, then investment 1 yields $3.20 per dollar invested, investment 2 yields $3.14, investment 3 yields $3.00, and investment 4 yields $2.67. Investment 1 might be considered the best investment but our optimal solution doesn’t include it!

  12. Solution -- continued • The reason investment 1 is not included is because choosing investment 1 forces Tatham to forego investing at least $2000 of its total budget. • On the other hand, the optimal investment combination allows Tatham to invest all $14,000 of its budget. • This enables Tatham to achieve a higher NPV than it could with any other combination that includes investment 1.

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