Chapter 4 Practice Problems - Conceptual

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Apr 3, 2024

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Chapter 4 Practice Problems Conceptual: 1. What are the 4 basic Time Value of Money variables? a. Present Value (PV), Future Value (FV), Interest Rate (Rate), and Time as Stated as the Number of Periods (Nper). 2. Define Compounding, and describe how it works. a. Compounding is the process whereby interest is credited to an existing principal amount as well as to interest already paid. Compounding thus can be construed as interest on interest—the effect of which is to magnify returns to interest over time. 3. Define Discounting, and describe how it works. a. Discounting is the process of determining the present value of a payment or a stream of payments that is to be received in the future. Given the time value of money, a dollar is worth more today than it would be worth tomorrow. Discounting is the primary factor used in pricing a stream of tomorrow's cash flows; Cash flow in the future is worth less today 4. What happens to the present value of a future cash flow as the time period increases? a. As time period increases, the present value decreases due to the more interest you are giving up 5. What happens to the future value of an amount invested today (PV) as the interest rate rises (PV perspective: solving for FV)? What happens to the present value of a future cash flow as the interest rate rises (FV perspective: solving for PV)? a. P2: As the interest rate rises on a future cashflow, the present value goes down  This is because with a higher interest rate, you don’t need to start with as much 6. Would you be willing to pay $10,000 today in exchange for $100,000 in 40 years? What would be the key considerations in answering yes or no? Would your answer depend on who is making the promise to pay? a. Important to calculate the time value of money; What is the interest rate required? ; Very important to know who is promising to pay Calculating: 7. First City Bank pays 9% simple interest annually on savings account balances, whereas Second City Bank pays 9% interest compounded annually. If you make a deposit of $10,000 at each bank, after 10 years how much more would you have in your Second City Bank account than your First City Bank account?

8. Assume the total cost of your child’s education will be $400,000 when your child enters university in 18 years. You presently have $20,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child’s college education? 9. At 6.1% annual interest, how long does it take to double your money? To quadruple it? 10. Company X has an unfunded pension liability of $400 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts need to discount this liability back to the present. If the firm has determined it can invest money indefinitely at a rate of 5%, what is the present value of this liability? 11. Your grandparents purchased $500 worth of government savings bonds in 1950, that they have decided to give to you as a gift. Assuming that they accrue interest at a rate of 3% per year, and assuming you have estimated that you will retire in the year 2067, how much will the bonds be worth when you are ready to retire? 12. In 1895, the first U.S. Open Golf Championship was held. The winner’s prize money was $150. In 2016, the winner’s check was $1,800,000. What was the percentage increase per year in the winner’s check over this period? If the winner’s prize increases at the same rate, what will it be in 2050? 13. An anonymous investor purchased a painting in 2015 for $4,500,000. Unfortunately it was not such a good purchase, and the price dropped to $4,000,000 by the end of 2020. What was the investor’s return on this investment? 14. According to the Census Bureau, in October 2016, the average house price in the United States was $354,900. In October 2000, the average price was $215,100. What was the annual increase in the average house price during this period? 15. You’re trying to save to buy a new $245,000 Ferrari. You have $50,000 that can be invested today. If you are able to achieve an annual return of 4.3%, how long will it be before you have enough to buy the car? 16. You intend to buy a cabin in northern Saskatchewan. You have estimated you will need $100,000 (USD). If you can earn 5.6% on investments annually, you have $2000 now to invest now and you don’t intend to add to the investment until it is worth $100,000, how long will it be before you can buy the cabin? How many years sooner will you be able to buy it if you start with $42,000? 17. Using the data from the question above, say you have decided that you want to buy the cabin in 9 years. How much do you need to start with?

18. 6 Years ago, you bought stock in Autonomous Tankers, Inc. for $10 per share. You just sold it for $200 per share. What rate of interest did you achieve on this investment? 19. A friend has an investment opportunity that she needs money for, and has promised to return $25,000 to you in 4 years. If you require a 20% return on anything of this sort that you invest in, what is the most you should be willing to give her today? 20. A very astute investor turned $10,000 into $30,000. Assuming it took 8 years to accomplish this, what rate of return did the investor achieve?

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