Exam 4: The Time Value of Money Part 2

Edward wishes to save enough money to purchase a retirement lake cabin. He is willing to spend $500,000 for the cabin and he can save $25,000 per year and invest the money into an account earning 8.00% per year. If Edward's investments come in the form of equal annual end-of-the-year cash flows and the first cash flow is in exactly one year, how long will it take him to save enough money to buy the lake cabin?

Your department at work places $10,000 every year-end into an account earning 5%. The money is used when the corporate office fails to fully finance your profitable projects. The money has not been touched since a deposit was made exactly five years ago. If the most recent deposit was made today, how much money is currently in the account?

Your company just sold a product with the following payment plan: $50,000 today, $25,000 next year, and $10,000 the following year. If your firm places the payments into an account earning 10% per year, how much money will be in the account after collecting the last payment?

When solving for present value, we use the term compounding of cash flows rather than the term discounting of cash flows.

Johnson has an annuity due that pays $600 per year for 15 years. (Note: There are 15 annual cash flows with the first cash flow occurring today.) What is the value of the cash flows 14 years from today (immediately after the last deposit is made) if they are placed in an account that earns 7.50%?

Given the following cash flows, what is the future value at year ten when compounded at an interest rate of 12.0%?

You have just won the Reader's Digest lottery of $5,000 per year for twenty years, with the first payment today followed by nineteen more start-of-the-year cash flows. At an interest rate of 5%, what is the present value of your winnings?

What is the present value today of an ordinary annuity cash flow of $3,000 per year for forty years at an interest rate of 6.0% per year?

When you pay off the principal and all of the interest at one time at the maturity date of the loan, we call this type of loan a(n) ________.

Amy Plisko is 23 years old and plans to retire in 32 years when she is 55 years old. Amy just graduated from a university in the West. Upon graduation, she took a job with a starting annual salary of $50,000. Amy asks you to answer the following two questions: 1. If her salary increases at a rate roughly equal to the U.S. long-run average annual rate of inflation over the past 80 years (about 3% per year), how large will her annual salary be in her last year before retirement? (Use 32 years.) 2. If her salary increases at a rate roughly equal to the U.S. long-run average annual rate of return on common stocks over the past 80 years (about 10.5% per year), how large will her annual salary be in her last year before retirement? (Use 32 years.) After hearing your answers, Amy says, "WOW ! That's quite a difference." She decides that she would like an income of $500,000 per year each year in retirement, provided in equal annual end-of-the-year cash flows. These cash flows need to last for 40 years, and her investments would earn an annual rate of return of 7% during her retirement. Amy's final question to you is how much money must she save in equal annual end-of-the-year cash flows for the next 32 years to provide for her desired retirement, if her investments earn roughly the same rate of return as those earned by U.S. small stocks over the last 80 years (geometric average is about 12% per year). Use a calculator to determine the answers to the different parts of the problem.

You have decided to endow the insert your name here Chair in Finance at the State University. How much money must you deposit into the endowment account today if the Chair pays $125,000 per year forever (first payment one year from today) and is invested at a rate that pays out 4.50% per year forever?

Given a positive interest rate and a positive cash flow, an ordinary annuity always has a greater present value than an annuity due of the same size and number of cash flows.

Amounts of money can be added or subtracted only if they are at the same point in time.

Johnson has an annuity due that pays $600 per year for 15 years. What is the value of the cash flows 15 years from today if they are placed in an account that earns 7.50%? Note: You are asked to find the FV one year after the last cash flow is realized.

Once you begin making payments on an amortization schedule for a loan such as a mortgage or car loan, most contracts clearly state that you may NOT pay off the loan early.

If you borrow $5,000 at an annual interest rate of 9.0% for six years, what will your repayment(s) be if this is a discount loan?

You just won a lottery - CONGRATULATIONS! Your parents have always told you to plan for the future, so since you already have a well-paying job you decide to invest rather than spend your lottery winnings. The payment schedule from the lottery commission is $100,000 after taxes at end of year one and 19 more payments of exactly $100,000 after taxes in equal annual end-of-the-year deposits (i.e., the first of the next 19 deposits is one year from today) into your account paying 7% compounded annually. How much money will be in your account after the last deposit is made?

Eastinghome Inc. just agreed to pay $8,000 today, $10,000 in one year, and $15,000 in two years to a landowner to explore for but not extract valuable minerals. If the landowner invests the money at a rate of 5.5% compounded annually, what is the investment worth two years from today?

Your firm intends to finance the purchase of a new construction crane. The cost is $1,500,000. How large is the payment at the end of year ten if the crane is financed at a rate of 8.50% as a discount loan?

Present value calculations do which of the following?