(a) Formulate and solve Titan's investment decision problem as a lincar program (use AMPL). (b) Provide an interpretation of the shadow prices in the specific context of the Titan investment problem, e.g., how might the shadow prices be used to determine hurdle rates consistent with Titan's available investments? Note: I know that most of you are not Finance specialists, nonetheless, I am asking you to provide thoughtful commentary on how the shadow prices can support decision- making in this context. (c) How might you determine how sensitive the investment decision is to changes in the projects' final payouts? In particular consider Projects D and E. Would the portfolio change if E pays only $1.34 per dollar invested? if D pays only $1.70 per dollar invested? Can you determine this without re-running your model? (d) How might you use results to determine whether new projects should be included in the portfolio? In particular, consider the two projects, F and G depicted in Table 4, which return $1.25 per dollar invested. Would you recommend that the portfolio be changed if F were available? if G were available? if both were available? Table 4: New investment options Project Year F G 2021 (1.00) (1.00) 2022 0.80 1.10 2023 0.45 0.00 0.15 2024 0.00 (e) Assuming that Project F is available, use the computer output to consider the sensitivity of the portfolio decision to the changes in projects D and E considered in question (c). Would the portfolio change if Project E pays only $1.34 per dollar invested? How? Does that make sense? Would the portfolio change if D pays only $1.70 per dollar invested (and E retains original payout)? How? Does that make sense? Mr. Lee asked me to prepare a list of typical investment projects for us to consider in our next meeting. The table below depicts five projects that might compete for our investment dollar. The table details the cash flow resulting from investing a single dollar. Project Year A B с D E 2021 (1.00) 0.00 (1.00) (1.00) 0.00 2022 0.30 (1.00) 1.10 0.00 0.00 2023 1.00 0.30 0.00 0.00 (1.00) 2024 0.00 1.00 0.00 1.75 1.40 Limit $500,000 $500,000 N/A N/A $750,000 Project A is a two-year investment available at the beginning of 2021, which pays 30 cents per dollar invested at the end of the first year and returns an additional dollar per dollar invested at the end of the second. At most $500,000 can be invested in Project A. • Project B is identical to A except that it is available a year later. • Project C is a one-year investment available only at the beginning of 2021, which pays $1.10 per dollar invested at the end of that year. • Project D is a three-year investment available at the beginning of 2021, which pays $1.75 per dollar invested at the beginning of 2024. Project E will become available at the beginning of 2023 and will, after a year, pay $1.40 per dollar invested. Project E is limited to a maximum of $750,000. Of course, the cash we receive from any of these projects may be reinvested in others that are available at the time. In addition, we could obtain 6% via short-term bank accounts for any money not invested in a given year. For purpose of discussion, let's assume we want to invest $1,000,000 into some mix of these projects at the beginning of 2021 but no more thereafter, although we will reinvest throw-offs. All cash received at the beginning of 2024 will be withdrawn. The table below gives the results of the discounting these projects as we had previously considered. Project Value @ 10%* IRR A or B $0.099 16.1% с $0.000 10.0% D $0.315 20.5% E $0.273 40.0% *A hypothetical hurdle rate similar to ones we have seen used in the past. NPV's are calculated to the beginning of the year in which the outflow occurs.

(a) Formulate and solve Titan's investment decision problem as a lincar program (use AMPL). (b) Provide an interpretation of the shadow prices in the specific context of the Titan investment problem, e.g., how might the shadow prices be used to determine hurdle rates consistent with Titan's available investments? Note: I know that most of you are not Finance specialists, nonetheless, I am asking you to provide thoughtful commentary on how the shadow prices can support decision- making in this context. (c) How might you determine how sensitive the investment decision is to changes in the projects' final payouts? In particular consider Projects D and E. Would the portfolio change if E pays only $1.34 per dollar invested? if D pays only $1.70 per dollar invested? Can you determine this without re-running your model? (d) How might you use results to determine whether new projects should be included in the portfolio? In particular, consider the two projects, F and G depicted in Table 4, which return $1.25 per dollar invested. Would you recommend that the portfolio be changed if F were available? if G were available? if both were available? Table 4: New investment options Project Year F G 2021 (1.00) (1.00) 2022 0.80 1.10 2023 0.45 0.00 0.15 2024 0.00 (e) Assuming that Project F is available, use the computer output to consider the sensitivity of the portfolio decision to the changes in projects D and E considered in question (c). Would the portfolio change if Project E pays only $1.34 per dollar invested? How? Does that make sense? Would the portfolio change if D pays only $1.70 per dollar invested (and E retains original payout)? How? Does that make sense? Mr. Lee asked me to prepare a list of typical investment projects for us to consider in our next meeting. The table below depicts five projects that might compete for our investment dollar. The table details the cash flow resulting from investing a single dollar. Project Year A B с D E 2021 (1.00) 0.00 (1.00) (1.00) 0.00 2022 0.30 (1.00) 1.10 0.00 0.00 2023 1.00 0.30 0.00 0.00 (1.00) 2024 0.00 1.00 0.00 1.75 1.40 Limit $500,000 $500,000 N/A N/A $750,000 Project A is a two-year investment available at the beginning of 2021, which pays 30 cents per dollar invested at the end of the first year and returns an additional dollar per dollar invested at the end of the second. At most $500,000 can be invested in Project A. • Project B is identical to A except that it is available a year later. • Project C is a one-year investment available only at the beginning of 2021, which pays $1.10 per dollar invested at the end of that year. • Project D is a three-year investment available at the beginning of 2021, which pays $1.75 per dollar invested at the beginning of 2024. Project E will become available at the beginning of 2023 and will, after a year, pay $1.40 per dollar invested. Project E is limited to a maximum of $750,000. Of course, the cash we receive from any of these projects may be reinvested in others that are available at the time. In addition, we could obtain 6% via short-term bank accounts for any money not invested in a given year. For purpose of discussion, let's assume we want to invest $1,000,000 into some mix of these projects at the beginning of 2021 but no more thereafter, although we will reinvest throw-offs. All cash received at the beginning of 2024 will be withdrawn. The table below gives the results of the discounting these projects as we had previously considered. Project Value @ 10%* IRR A or B $0.099 16.1% с $0.000 10.0% D $0.315 20.5% E $0.273 40.0% *A hypothetical hurdle rate similar to ones we have seen used in the past. NPV's are calculated to the beginning of the year in which the outflow occurs.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter7: Exponents And Exponential Functions

Section: Chapter Questions

Problem 68SGR

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