Exam 3: The Time Value of Money Part 1

The Present Value Interest Factor (PVIF) is the reciprocal of the Future Value Interest Factor (FVIF).

You have just won the university lottery. If you graduate, you will receive a refund equal to the amount of tuition you paid in your first four years of school. However, you need money now and a firm that specializes in buying expected future cash flows has offered to discount the lottery winnings at a rate of 8% and pay you cash today in exchange for your future lottery winnings. Since you have studied finance, you insist that they discount the cash flows at 12% instead of 8% because there is some risk as to the certainty of your graduating. If the firm agrees to your demand, then this means they will increase the present value of what they will pay you today.

To determine the present value of a future amount, one should ________ the future cash flows.

An investment promises a payoff of $195 two and one-half years from today. At a discount rate of 7.5% per year, what is the present value of this investment?

Write the equation for present value. How are prices and interest rates related? Refer to your equation when answering the first part of this question. Give an example of a real-world situation in which knowing the relationship between prices and interest rates would be valuable.

You know that regular tax-deferred investments are a popular investment choice for many people preparing for retirement. Did you know that if you invest $2,000 today and at the end of every year for 40 years at an annual rate of 10% that you will have grown your portfolio to a value of $975,704 at the end of that time? How much of that future value dollar amount comes from the $2,000 investment you made today?

You made your first $3,000 deposit today into a retirement account earning an average annual rate of 6%. How long will it take your deposit to reach a value of $50,000? How long will it take if instead you invest the money into an account earning 10% per year? After making your calculations, how does this information affect your decision-making regarding long-term investments?

Your firm has sold a fleet of 100 cars to a local firm at a discounted price of $20,000 each (a total of $2,000,000) due in six months. You are willing to discount the purchase price at an annual rate of 4% if the firm pays cash today. What is the least amount of money you will accept if the firm pays your company today?

Which of the following will result in a future value greater than $100?

Even if you are given a present value, a single future value, and a time period, solving for the rate of return, r, is still a trial-and-error process.

You intend to buy a vacation home in seven years and plan to have saved $50,000 for a down payment. How much money would you have to place today into an investment that earns 8% per year to have enough for your desired down payment?

A plant nursery pays $2,000 for 800 one-gallon flowering trees, plants them, and forgets them. Five years later, the nursery is able to sell each of the 100 trees that survived for $50 each. What is the rate of return on its total investment?

Your father spent all of his adult life working in a small T-shirt making firm. His first year of sales was $118,000 and his last year of sales was $450,000. If the firm grew at an average rate of 3.15% per year, how many years did your father sell T-shirts in his firm?

Your university is running a special offer on tuition. This year's tuition cost is $18,000. Next year's tuition cost is scheduled to be $19,080. The university offers to discount next year's tuition at a rate of 6% if you agree to pay both years' tuition in full today. How much is the total tuition bill today if you take the offer?

Your production manager informs you that currently the firm is producing 1,438 heating units per month but has plans to increase production at a rate of 5% per month until the firm is producing 3,000 units per month. How many months will this take?

Even if you are given a present value, a future value, and an interest rate, solving for the time period "n" is still a trial-and-error process.

$5,000 invested at an annual rate of 6% for 3 years has a smaller future value than $5,000 invested at an annual rate of 3% for 6 years.

A two-year investment of $200 is made today at an annual interest rate of 6%. Which of the following statements is true?

The Millville School District had 3,071 students enrolled five years ago. Today, the district enrollment is 2,418 students. What has been the annual rate of change of student enrollment in the Millville School District over this time period?

Compare and contrast the discount rate with the compound (or growth) rate.