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Real Estate Investments/AnalysisSpring 2009

Professor HarrisonQuiz #1 -- Time Value of Money Review

The following problems are designed to provide a review of many of the basic calculations you learned to perform in your previous finance curriculum which will come in useful/necessary throughout this semester. If you are unable to accurately answer these questions, please review these concepts immediately. Good-luck!

1. Which amount is worth more at 8.50% compounded annually: $1,000 in hand today or $2,000 due in 8 years?

2. What is the present value of a perpetuity of $1,500 per year if the appropriate discount rate is 7.25%?

3. Your company is planning to borrow $100,000 on a 7-year, 11.00%, annual payment, fully amortized term loan. What fraction of the payment made

at the end of the third year will represent repayment of principal?

4. As manager of Gotham Jewelry, you want to sell on credit, giving customers 3 months in which to pay. However, you will have to borrow from the bank

to carry the accounts payable. The bank will charge a nominal 14 percent, but with monthly compounding. You want to quote a nominal rate to your customers (all of whom are expected to pay on time) which will exactly cover your financing costs. What nominal annual rate should you quote to your customers?

5. To the closest year, how long will it take $35,000 to double if it is deposited and earns 6.25% compounded annually?

6. What is the present value of $75,000 to be received 10 years from today if the interest rate is 7.35% compounded continuously?

7. What is the future value, in 25 years, of a $1,000 deposit invested at 9.50%, compounded continuously?

8. Suppose your Professor currently has no savings, but wants to retire in 30 years as a millionaire. If he can earn 8.75%, compounded annually on his investments,

how much should he set aside in equal installments (beginning one year from today) to reach his goal?

9. Lawson Lawn and Garden invests $5 million to clear a tract of land and to set out some young pine trees. The trees will mature in 10 years, at which time

Lawson plans to sell the forest at an expected price of $15.5 million. What is Lawson's expected rate of return?

10. You are planning to retire in 38 years. You currently have $25,000, and would like to have $5 million when you retire. What annual rate of interest

would you have to receive on your money in order to reach your goal, assuming you save no more money?

11. What is the present value of a cash flow stream, given an interest rate of 7.85%, compounded annually, which offers the following end of year payments:

Year 1, $100; Year 2, $200; Year 3, $300; Year 4, $400; and Year 5, $500?

12. What is the future value (at the end of year 5) of a cash flow stream, given an interest rate of 7.85%, compounded annually, which offers the following

end of year payments: Year 1, $100; Year 2, $200; Year 3, $300; Year 4, $400; and Year 5, $500?

13. What is the effective annual rate on a security offering a 12.25% nominal rate, compounded monthly?

14. What is the stated (nominal) annual rate on a loan which charges an effective rate of 16.65%, with interest compounded quarterly?

15. First City Savings pays 7.5% interest, compounded annually. Second City Savings pays 7.35% interest, compounded quarterly. Based on

effective, or equivalent, interest rates, in which bank would you prefer to deposit your money?

16. A 15-year security has a price of $340.4689. The security pays $50 at the end of each of the next 5 years, and then it pays a different fixed cash flow

amount at the end of each of the following 10 years. Interest rates are 8.00%. What is the annual cash flow amount between years 6 and 15?

17. Suppose you borrow $15,000 to purchase a new car. You take advantage of the manufacturer's special financing offer, and obtain a loan rate of 4.9%.

You sign a note requiring you to make 60 equal monthly payments to fully repay the loan. How much is each monthly payment?

18. What is the present value of a cash flow stream, given an interest rate of 6.75%, compounded annually, which offers the following end of year payments:

Year 1, $500; Year 2, $400; Year 3, $300; Year 4, $200; and Year 5, $100?

19. What is the future value (at the end of year 5) of a cash flow stream, given an interest rate of 6.75%, compounded annually, which offers the following

end of year payments: Year 1, $500; Year 2, $400; Year 3, $300; Year 4, $200; and Year 5, $100?

20. Consider an investor with a 3 asset portfolio. 25% of the investor’s portfolio is invested in AT&T stock with an expected return of 14%, an additional

25% of the investor’s portfolio is invested in Kellogg’s Corporation stock with an expected return of 13%, while the remaining 50% of the portfolio is invested in IBM stock with an expected return of 12%. The standard deviation of expected returns for the three individual assets is 25%, 15%, and 10% respectively. The correlation coefficent between the AT&T and Kellogg’s stock returns is 0.40, the correlation coefficient between the Kellogg’s and IBM stock returns is 0.50, and the correlation coefficient between the AT&T and IBM stock returns is 0.60. What is the standard deviation of expected return for this portfolio?

Answers1. $2,000 in 8 years2. $20,689.663. 59.35%4. 14.16%5. 11 years6. $35,962.917. $10,751.018. $7,685.909. 11.98%10. 14.96%11. $1,142.1312. $1,666.5413. 12.96%14. 15.70%15. Second City Savings16. $30.8417. $282.3818. $1,292.1619. $1,791.2520. 12.41%