Finance 445, Sections 1 and 2
Capital Investment and Financing Decisions
Computer Problem Set #1
Due: February 6, 2002
U.S Resorts Inc. owns twenty golf resorts throughout the United States. In recent years, it has been thinking about diversifying its operations by purchasing an existing (or developing a new) ski resort. Its first venture into the ski resort business has just started as the president of the company (Fred Jones) and chairman of the board of directors (Mary Smith) signed a perpetual lease for 2,500 acres of land on Black Mountain. Black Mountain is the highest mountain in Kentucky with an elevation of 4,139 feet. In the past, logging and coal mining companies have used Black Mountain. But Governor Paul Patton has indicated that he would like to see the development of Black Mountain’s recreational opportunities. He enthusiastically supports this project as a way to achieve this goal and as a way to improve the economy in the state of Kentucky.
You have been recently hired as a financial analyst for U.S. Resorts, Inc. Your first real job as a financial analyst for U.S. Resorts is to put together an analysis of four mutually exclusive projects and to make a banking recommendation for the firm.
It is current company policy that all projects will be selected or rejected based on the project’s IRR. In other words, if the project IRR is greater than the opportunity cost of capital (equal to 12% for all projects), then the project is accepted. If the project IRR is less than the opportunity cost of capital, the project is rejected. When considering mutually exclusive projects, the firm picks the project will the highest IRR (assuming the IRR is greater than the opportunity cost of capital).
You remember from your corporate finance class that the project IRR isn’t always a reliable measure in deciding whether to accept or reject a project. The project NPV is the best number to use when evaluating projects. All positive NPV projects should be accepted and all negative NPV projects should be rejected. When faced with mutually exclusive projects, the project with the highest NPV should be selected (assuming NPV > $0).
You have gone back and found several of the company’s past projects that have been evaluated using the IRR rule. You have decided to put together a presentation for your boss that shows the NPV for each project. This will show your boss instances when using the IRR led to correct or incorrect decisions. You also plan to show your boss the modified internal rate of return (MIRR) for each of these old projects. The MIRR corrects many (but not all) of the problems associated with the IRR. Even though you prefer to use the NPV method, you will give your boss the MIRR of each project to show its advantage over the IRR. (Use a 12% opportunity cost of capital to evaluate each of these projects)
In your analysis of each project, you will:
· Calculate the project IRR (If there are two IRRs, report the second IRR.)
· Calculate the project NPV.
· Calculate the project MIRR.
· Using the project NPV, show whether each project should have been accepted or rejected.
The following are the project cash flows for the old projects. Pine Golf Course A and B are mutually exclusive projects. Forest Golf Course A and B are also mutually exclusive projects. Using the IRR method, the company accepted the Alpine, Pine A, and Forest B projects.
Golf Course / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10Alpine / -2000.00 / 0.00 / 0.00 / 525.00 / 525.00 / 525.00 / 525.00 / 525.00 / 525.00 / 525.00 / 525.00
Meadow / -3000.00 / 2500.00 / 500.00 / 500.00 / 500.00 / 500.00 / 500.00 / 500.00 / 500.00 / 500.00 / -4000.00
Pine A / -3800.00 / 750.00 / 750.00 / 750.00 / 750.00 / 750.00 / 750.00 / 750.00 / 750.00 / 750.00 / 750.00
Pine B / -5000.00 / 975.00 / 975.00 / 975.00 / 975.00 / 975.00 / 975.00 / 975.00 / 975.00 / 975.00 / 975.00
Forest A / -4000.00 / 0.00 / 0.00 / 0.00 / 0.00 / 0.00 / 0.00 / 0.00 / 0.00 / 0.00 / 15000.00
Forest B / -4000.00 / 570.00 / 10% more / 10% more / 10% more / 10% more / 10% more / 10% more / 10% more / 10% more / 10% more
In addition to your evaluation of the old projects outlined above (all of which last 10 years), the company is considering the following four mutually exclusive perpetual projects. Calculate the NPV for each of these perpetual projects and recommend to your boss which of these four projects the firm should accept. (Do not calculate the IRR or MIRR.)
0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / →Ski Project A / -5000 / 680 / 680 / 680 / 680 / 680 / 680 / 680 / 680 / 680 / 680 / 680
Ski Project B / -5000 / 0 / 0 / 0 / 675 / 5% more / 5% more / 5% more / 5% more / 5% more
Ski Project C / -5000 / 135 / 45% more / 45% more / 45% more / 45% more / 4% more / 4% more / 4% more / 4% more / 4% more / 4% more
Ski Project D / -5000 / 0 / 0 / 0 / 230 / 50% more / 50% more / 50% more / 4% more / 4% more / 4% more / 4% more
Finally, for your last assignment, your boss has asked you to recommend where to deposit $750,000 in excess cash for 5 years. Assume each bank offers the same services and are equally risky. Therefore, pick the best bank based on which will pay the greatest interest to the firm over the five-year period.
Bank A: Annual nominal interest rate = 3.50%, annual compounding
Bank B: Annual nominal interest rate = 3.46%, semi-annual compounding
Bank C: Annual nominal interest rate = 3.45%, monthly compounding
Bank D: Annual nominal interest rate = 3.44%, continuous compounding
Directions
- 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. Each numerical error (or error in recommendation) will result in a reduction of one-half point (down to a score of zero).
- You can turn your assignment one day late without penalty, as long as it is turned in before February 7, 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.)
- You must get the answer exactly correct (to two decimal places) to receive credit (i.e., $12.34, 12.34%). For instance, if the correct answer is 12.34% and you give 12.36% as an answer, it will be marked as wrong. Also, an answer rounded to too few decimal places is also wrong. For instance, 12% or 12.3% will also be marked as wrong in the above example.
- Remember you can work together in groups of four, and compare your answers with other groups.
- I have provided a set of similar practice questions and answers for your review. Also, look at the Chapter 3 notes on my web site for further assistance.
- Your solutions must be printed on a computer printer or typed.
- 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., February 7, 2002.
Practice problem #1. (The following projects have been evaluated using a 15% opportunity cost of capital.)
Project A / -$400,000 / $110,000 / $110,000 / $110,000 / $110,000 / $110,000 / $110,000 / $110,000 / $110,000
Project B / -$300,000 / $700,000 / $10,000 / $10,000 / $10,000 / $10,000 / $10,000 / $10,000 / -$400,000
Project C / $500,000 / $0 / $0 / $0 / $0 / $0 / $0 / $0 / -$1,100,000
Project D1 / -$100,000 / $25,000 / $25,000 / $25,000 / $25,000 / $25,000 / $25,000 / $25,000 / $25,000
Project D2 / -$500,000 / $115,000 / $115,000 / $115,000 / $115,000 / $115,000 / $115,000 / $115,000 / $115,000
Project E1 / -$250,000 / $20,000 / $40,000 / $60,000 / $80,000 / $100,000 / $120,000 / $140,000 / $160,000
Project E2 / -$250,000 / $100,000 / $90,000 / $80,000 / $70,000 / $60,000 / $50,000 / $40,000 / $30,000
Solutions to practice problem #1 (Projects D1 and D2 are mutually exclusive. Projects E1 and E2 are mutually exclusive.)
NPV / IRR #1 / IRR #2 / MIRR / Correct DecisionProject A / $93,605.37 / 21.84% / None / 18.06% / Accept
Project B / $210,843.49 / 135.45% / -2.35% / 20.87% / Accept
Project C / $140,408.05 / 10.36% / None / 19.84% / Accept
Project D1 / $12,183.04 / 18.62% / None / 16.66% / Reject
Project D2 / $16,041.97 / 15.97% / None / 15.45% / Accept
Project E1 / $89,360.74 / 22.32% / None / 19.48% / Accept
Project E2 / $73,925.00 / 25.61% / None / 18.78% / Reject
Practice Problem #2. Using a 15% discount and interest rate, what is the present value (at time 0) of the following perpetual cash flow streams?
0 / 1 / 2 / 3 / 4 / 5 / 6 / ®A. / $0 / $100 / 10% more / 10% more / 10% more / 10% more / 2% more / 2% more
B. / $100 / 10% more / 10% more / 10% more / 10% more / 2% more / 2% more / 2% more
C. / $0 / $0 / $100 / 10% more / 10% more / 10% more / 10% more / 2% more
Solutions to practice problem #2
A. $969.72
B. $1,115.18
C. $843.23
Practice Problem #3. ABC Inc. has $500,000 that it will deposit in a bank account. Calculate the future value (in four years) if the money is deposited in each of the following four banks.
A. Bank A: Annual nominal interest rate = 5%, annual compounding
B. Bank B: Annual nominal interest rate = 4.95%, semi-annual compounding
C. Bank C: Annual nominal interest rate = 4.92%, monthly compounding
D. Bank D: Annual nominal interest rate = 4.89%, continuous compounding
Solutions to practice problem #3
A. $607,753.13
B. $608,013.78
C. $608,505.38
D. $608,020.20