Question

How much money would you have in a year if you put $1,000 in the bank at an annual interest rate of 3 percent? How much would you have if you left all of that money in the bank for another year and annual interest rates increased to 4 percent in the second year?

How much would you loan your brother-in-law if he said he could repay you $100 in six months, $200 in a year, and $500 in two years if you can get 2 percent interest from the bank on a six month CD? Show that you are in fact indifferent between the loan and putting your money in the bank for the next two years.

What is the present value of an asset that pays $10,000 per year at the end of the next four years if the appropriate discount rate is 5 percent? What total return would you earn if you bought this asset and it paid its expected cash flows on time each year for the next four years? Prove that you earned the same return that you would have, had you put your money in the bank for four years at 5 percent per year.

What is the net present value of a project that has upfront costs of $5 million and pays end of the year cash flows of $1 million in one year, $2 million in two years, and $3 million in three years if the annual discount rate for the project is 3 percent? Show how much money you would have at the end of three years if you bought the project and what you would have instead if you banked your $5 million for three years at 3 percent.

Your agency is competing with another agency for $15 million in government money. Only one of you will get the $15 million. Your agency will use the $15 million for vocational training that will increase the skills and earning power of 100 people in about two years when they finish the program. The other agency will use the $15 million to study how floods affect homeowners’ insurance costs. Their study will take four years but it will create twice as much value as your agency’s project at the end of that time. The government uses a 4 percent discount rate for both projects. Who will get the $15 million?

Calculate the Net Present Value of a project that has upfront costs of $124,000 and end-of-year annual cash flows of $30,000 for five years, if the appropriate discount rate is 6.5 percent. Suppose that discount rate is the borrowing cost for the project. Show that this project’s cash flows can pay off a loan with an annual interest rate of 6.5 percent over the next five years.

Would you suggest your firm invest in a new machine that costs $450,000 and generates cash flows of $60,000 per year at the end of each of the next ten years if the appropriate discount rate for the machine is 8 percent? What is the present value of the annuity generated by this machine’s cash flows?

Calculate the internal rate of return for a project that has upfront costs of $6 million and cash flows of $2 million per year for each of the next four years. Suppose the risk adjusted borrowing cost of this project is 15 per-cent. Using IRR analysis, would you undertake this project? Confirm your answer by calculating the project’s NPV.

Answer 1

As per guidelines I am answering 1st question I.e.

How much money would you have in a year if you put $1,000 in the bank at an annual interest rate of 3 percent? How much would you have if you left all of that money in the bank for another year and annual interest rates increased to 4 percent in the second year?

FV = PV (1+r)^n

= 1000(1+0.03)^1

= 1000(1.03)

Therefore money we have in a year = $1030

If we left the money for another year earning 4% interest

FV = 1030(1+0.04)^1

= 1030(1.04)

Therefore money we have after year 2 = $1071.20