Finance 445, Sections 2, 3 and 4 - University of Kentucky



Finance 445

Capital Investment and Financing Decisions

Computer Problem Set #4

Due: March 28, 2002

U.S. Resorts, Inc. is considering investment in three non-mutually exclusive projects (Projects X, Y and Z). All three projects require an initial investment of $1,000. After extensive analysis and research, time 1 project cash flows in three different states of the economy were calculated. (Each project terminates at time 1.) For comparison purposes, time 1 cash flows for a one-year, $1,000 investment in the risk-free asset and the market are also provided.

Time 1 Cash Flows

|State |1 |2 |3 |

|Economy |Boom |Normal |Recession |

|Probability |20% |60% |20% |

|Risk-Free |$1,050 |$1,050 |$1,050 |

|Market |$1,430 |$1,160 |$760 |

|Project X |$825 |$1,050 |$1,150 |

|Project Y |$1,030 |$1,070 |$1,010 |

|Project Z (extra credit) |$2,800 |$1,200 |$200 |

One-year returns based on the $1,000 initial investment.

|State |1 |2 |3 |

|Economy |Boom |Normal |Recession |

|Probability |20% |60% |20% |

|Risk-Free |5% |5% |5% |

|Market |43% |16% |-24% |

|Project X |-17.5% |5% |15% |

|Project Y |3% |7% |1% |

|Project Z (extra credit) |180% |20% |-80% |

The present values of the time 1 cash flows are:

Present value of the time 1 risk-free cash flows = $1,000

Present value of the time 1 market cash flows = $1,000

Present value of the time 1 Project X cash flows = $1,012.440040

Present value of the time 1 Project Y cash flows = $996.305333

Present value of the time 1 Project Z cash flows = not provided (solve by iteration)

1. Calculate the expected time 1 cash flows for Project X and Project Y. (1 point)

2. Calculate the returns in each economic state for Project X and Project Y based on the present value of their time 1 cash flows. (1 point)

3. Calculate the expected return (based on the initial investment) for Project X and Project Y. (1/2 point)

4. Calculate the expected return (based on the present values) for Project X and Project Y. (1/2 point)

5. Calculate the standard deviation of Project X’s and Project Y’s returns (based on present values). (1 point)

6. Calculate the correlation coefficient between Project X's returns and the Market's returns. Also, calculate the correlation coefficient between Project Y's returns and the Market's returns. (Returns are calculated based on present values). (1 point)

7. Calculate the beta of Project X’s returns and the beta of Project Y’s returns. (1 point)

8. Using a risk-free rate of 5% and a market risk premium of 8.4% (and the CAPM), what discount rates should you use to calculate the NPVs for Project X and Project Y? (1 point)

9. What is the NPV for Project X? What is the NPV Project Y? (1 point)

10. Optional 1 point extra credit. Calculate the above figures for Project Z. (With Project Z, you will need to start the calculations with the $1,000 initial investment (instead of the present value of the project cash flows) and iterate until you converge on the present value of the project cash flows. I will explain the iteration technique to interested students. In order to receive the 1 point of extra credit, you must provide correct figures for all the analysis required for Projects X and Y.

Use the following to determine if your program is working (the risk-free investment, market investment, and Project Sample require a time 0 initial investment of $1,000):

Time 1 Cash Flows

|State |1 |2 |3 |

|Economy |Boom |Normal |Recession |

|Probability |20% |60% |20% |

|Risk-Free |$1,050 |$1,050 |$1,050 |

|Market |$1,430 |$1,160 |$760 |

|Project Sample |$1,250 |$1,075 |$1,005 |

One-year returns based on the $1,000 initial investment.

|State |1 |2 |3 |

|Economy |Boom |Normal |Recession |

|Probability |20% |60% |20% |

|Risk-Free |5% |5% |5% |

|Market |43% |16% |-24% |

|Project Sample |25% |7.5% |0.5% |

The present values of the time 1 cash flows are:

Present value of the time 1 risk-free cash flows = $1,000

Present value of the time 1 market cash flows = $1,000

Present value of the time 1 Project Sample cash flows = $1,016.629322

1. Expected time 1 cash flow = $1,096.0000

2. Returns in each economic state based on the present value (22.9553%, 5.7416%, -1.1439%)

3. Expected return (based on the initial investment) = 9.6000%

4. Expected return (based on the present value) = 7.8072%

5. Standard deviation of returns (based on present value) = 0.0803

6. Correlation coefficient between Project Sample’s returns and the Market’s returns (based on present value) = 0.8917

7. Beta of Project Sample’s returns = 0.3342

8. Discount rate (using the CAPM, a risk-free rate of 5%, and a market risk premium of 8.4%) = 7.8072%

9. NPV for Project Sample = $16.629322

Instructions

1. This problem set is worth 10 points. You are expected to turn in a professionally written solution to the problem set, including an executive summary (1 – 2 pages) of the problem, your main findings, and recommendations. Supporting analysis should be attached to the executive summary. Two of the ten points are used to grade your presentation. Incorrect conclusions, faulty reasoning, spelling errors, grammatical errors, or poor presentation will result in a reduction in this portion of your score. Eight points are allocated to your numerical solutions and recommendations for project acceptance or rejection. Grading is outlined above. Warning: If you get an “early” answer wrong, it could cause all of your other answers to be incorrect.

2. You must get the answer exactly correct (to two decimal places) to receive credit. For instance, for any answer given in dollars (expected cash flows, NPVs), show the solution to the penny (e.g., $12.34). For any answer given in returns (returns in each economic state, expected returns, discount rates), show the solution to two decimal places (e.g., 12.34%). For your solutions to standard deviation, correlation coefficient, and beta, show your solution to two decimal places (e.g., 0.12). An answer rounded to too few decimal places is also wrong. For instance, $12 will be marked as wrong if the correct answer is $12.34.

3. You can turn your assignment one day late without penalty, as long as it is turned in before March 29, 2002, 5 p.m. After that time, your score will be reduced by 2 points. Another 2 points will be taken off your score for each additional “school” day the assignment is turned in late. (See syllabus for more details.)

4. Remember you can work together in groups of four, and compare your answers with other groups.

5. Your solutions must be printed on a computer printer or typed.

6. You will be given an opportunity to repeat the assignment for one-half credit (5 points maximum). Of course, this option will only help you if your score is less than 5 points. The makeup assignment will have the same type of problems, but with different assumptions. This opportunity is not available if you turn in the assignment later than 5 p.m., March 29, 2002.

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