Principles of Finance

There are two options to choose from option 1 or option 2. Please be detailed and demonstrate work. Thank you
Option #1
Question 1: Future and Present Values
If you invest $100 at an interest rate of 15%, how much will you have at the end of eight years?
The cost of an automobile is $10,000. If the interest rate is 5%, how much would you have to set aside now to provide this sum in five years?
If the cost of capital is 9%, what is the PV of $374 paid in year 9?
If the PV of $10 a year for three years is $24.65, what is the three-year annuity factor?
Question 2: Compounding
You are quoted an interest rate of 6% on an investment of $10 million. What is the value of your investment after four years if interest is compounded: Annually?
Monthly?
Continuously?

Which would you prefer? (Work out the value of each investment after 1, 5, and 20 years)An investment paying interest of 12% compounded annually.
An investment paying interest of 11.7% compounded semiannually.
An investment paying 11.5% compounded continuously.

Question 3: IRR Rule
Mr. Clotz, the president of Mega Enterprises, has to make a choice between two possible investments:
ProjectC0C1C2IRR (%)A-400 250 30023B-200 140 17936The opportunity cost of capital is 9%. Mr. Clotz is tempted to take B, which has the higher IRR.
Explain to Mr. Clotz why this is not the correct procedure.
Show him how to adapt the IRR rule to choose the best project.
Show him that this project also has the higher NPV.
Question 4: Capital Rationing
Consider the following capital rationing problem:
ProjectC0C1C2NPVW-10,000-10,0000 6,700X0-20,000 5,000 9,000Y-10,000 5,000 5,000 0Z-15,000 5,000 4,000-1,500Financing Available20,00020,00020,000 Set up this problem as a linear program and solve it.
Note: You can allow partial investments, that is, ” 0 ≤ x ≤ 1.” Calculate and interpret the shadow prices on the capital constraints.
Your paper should be one to two pages in length (excluding cover page and references). Be sure to discuss and reference concepts taken from the assigned textbook reading and relevant research. Review the grading rubric to see how you will be graded for this assignment.
Option #2
Question 1: Present Values
Your firm’s geologists have discovered a small oil field in New York’s Westchester County. The field is forecasted to produce a cash flow of C 1 = $2 million in the first year. You estimate that you could earn an expected return of r = 12% from investing in stocks with a similar degree of risk to your oil field. Therefore, 12% is the opportunity cost of capital. What is the present value? The answer, of course, depends on what happens to the cash flows after the first year.
Calculate present value for the following cases:
The cash flows are forecasted to continue forever, with no expected growth or decline.
The cash flows are forecasted to continue for 20 years only, with no expected growth or decline during that period.
The cash flows are forecasted to continue forever, increasing by 3% per year because of inflation.
The cash flows are forecasted to continue for 20 years only, increasing by 3% per year because of inflation.
Question 2: Continuous Compounding
How much will you have at the end of 20 years if you invest $100 today at 15% annually compounded? How much will you have if you invest at 15% continuously compounded?
Question 3: IRR Rule
Cash Flows ($ thousands)
ProjectC0C1C2C3A-100 60 600B-10000 140Calculate the NPV of each project for discount rates of 0%, 10%, and 20%. Plot these on a graph with NPV on the vertical axis and discount rate on the horizontal axis.
What is the approximate IRR for each project?
In what circumstances should the company accept project A?
Calculate the NPV of the incremental investment (B- A) for discount rates of 0%, 10%, and 20%. Plot these on your graph. Show that the circumstances in which you would accept A are also those in which the IRR on the incremental investment is less than the opportunity cost of capital.
Question 4: Capital Rationing
Suppose you have the following investment opportunities, but only $90,000 available for investment. Which projects should you take?
ProjectNPVInvestment15,00010,00025,0005,000310,00090,000415,00060,000515,00075,00063,00015,000Your paper should be one to two pages in length (excluding cover page and references). Be sure to discuss and reference concepts taken from the assigned textbook reading and relevant research. Review the grading rubric to see how you will be graded for this assignment.