Financial Planning Problems
1. If theinterest is compounded quarterly with 8% APR, which of the following statements is CORRECT?
a. The periodic rate of interest is 2% and the effective rate of interest is 4%.
b. The periodic rate of interest is 8% and the effective rate of interest is greater than 8%.
c. The periodic rate of interest is 4% and the effective rate of interest is less than 8%.
d. The periodic rate of interest is 2% and the effective rate of interest is greater than 8%.
e. The periodic rate of interest is 8% and the effective rate of interest is also 8%.
2. What is the coefficient of variation for security a?
3. You plan to save $6,400 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. How much will you have 4 years from today?
4. Which of the following investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.
a. Investment A pays $250 at the beginning of every year for the next 10 years (a total of 10 payments).
b. Investment B pays $125 at the end of every 6-month period for the next 10 years (a total of 20 payments).
c. Investment C pays $125 at the beginning of every 6-month period for the next 10 years (a total of 20 payments).
d. Investment D pays $2,500 at the end of 10 years (just one payment).
e. Investment E pays $250 at the end of every year for the next 10 years (a total of 10 payments).
5. Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, starting at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?
6. Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.
7. Which indenture provision may affect the price of the bond differently?
b. sinking fund
d. restrictions on dividends
8. Suppose 1-year Treasury bonds yield 4.00% while 2-year T-bonds yield 4.80%. Assuming the pure expectations theory is correct, what is the yield on a 1-year T-bond expected to be one year from now?
9. Which of the following factors would be most likely to lead to an increase in nominal interest rates?
a. Households reduce their consumption and increase their savings.
b. A new technology like the Internet has just been introduced, and it increases investment opportunities.
c. There is a decrease in expected inflation.
d. The economy falls into a recession.
e. The Federal Reserve decides to try to stimulate the economy.
10. You are comparing saving $100 every month for a year vis-à-vis $1,200 at the beginning of the year. How much extra will you have at the end of the year by saving $ 1,200 at the beginning of the year instead of saving $100 each month at the end of each month. Use 6% interest rate.
11. The real risk-free rate is 3.05%, inflation is expected to be 2.75% this year, and the maturity risk premium is zero. IBM stock has a risk premium of 0.9%. What is the equilibrium rate of return on a 1-year Treasury bond?
12. Suppose the real risk-free rate is 3.25%, the average future inflation rate is 4.35%, and a maturity risk premium of 0.07% per year to maturity applies to both corporate and T-bonds, i.e., MRP = 0.07%(t), where t is the years to maturity. Suppose also that a liquidity premium of 0.50% and a default risk premium of 0.90% apply to A-rated corporate bonds but not to T-bonds. How much higher would the rate of return be on a 10-year A-rated corporate bond than on a 5-year Treasury bond?
13. Dyl Inc.'s bonds currently sell for $1,180 and have a par value of $1,000. They pay a $65 annual coupon and have a 15-year maturity, but they can be called in 5 years at $1,100. What is their yield to maturity (YTM)?
14. Sadik Inc.'s bonds currently sell for $1,270 and have a par value of $1,000. They pay a $105 annual coupon and have a 15-year maturity, but they can be called in 5 years at $1,100. What is their yield to call (YTC)?
15. Bonds sell at a discount from par value when market rates for similar bonds are
a. Less than the bond’s coupon rate.
b. Greater than the bond’s coupon rate.
c. Equal to the bond’s coupon rate.
d. Both lower than and equal to the bond’s coupon rate.
e. Market rates are irrelevant in determining a bond’s price.
16. Which of the following bonds would have the greatest percentage increase in value if all interest rates in the economy fall by 1%?
a. 10-year, zero coupon bond.
b. 20-year, 10% coupon bond.
c. 20-year, 5% coupon bond.
d. 1-year, 10% coupon bond.
e. 20-year, zero coupon bond.
17. O'Brien Ltd.'s outstanding bonds have a $1,000 par value, and they mature in 25 years. Their nominal yield to maturity is 9.25%, they pay interest semiannually, and they sell at a price of $975. What is the bond's nominal coupon interest rate?
18. Cooley Company's stock has a beta of 1.32, the risk-free rate is4.25%, and the market risk premium is5.50%. What is the firm's required rate of return?
19. Porter Inc's stock has an expected return of 10.75%, a beta of 1.25, and is in equilibrium. If the risk-free rate is 5.00%, what is the market risk premium?
20. Consider the following information and then calculate the required rate of return for the Global Investment Fund, which holds 4 stocks. The market’s required rate of return is 9.50%, the risk-free rate is 7.00%, and the Fund's assets are as follows:
Stock Investment Beta
A $200,000 1.50
B $300,000 -0.50
C $500,000 1.25
D $1,000,000 0.75
21. Which of the following statements best describes what you should expect if you randomly select stocks and add them to your portfolio?
a. Adding more such stocks will reduce the portfolio's unsystematic, or diversifiable, risk.
b. Adding more such stocks will increase the portfolio's expected rate of return.
c. Adding more such stocks will reduce the portfolio's beta coefficient and thus its systematic risk.
d. Adding more such stocks will have no effect on the portfolio's risk.
e. Adding more such stocks will reduce the portfolio's market risk but not its unsystematic risk.
22. Stock A has a beta of 0.7, whereas Stock B has a beta of 1.3. Portfolio P has 50% invested in both A and B. Which of the following would occur if the market risk premium increased by 1% but the risk-free rate remained constant?
a. The required return on Portfolio P would increase by 1%.
b. The required return on both stocks would increase by 1%.
c. The required return on Portfolio P would remain unchanged.
d. The required return on Stock A would increase by more than 1%, while the return on Stock B would increase by less than 1%.
e. The required return for Stock A would fall, but the required return for Stock B would increase.
23. Assume that you manage a $10 million mutual fund that has a beta of 1.05 and a 9.50% required return. The risk-free rate is 4.20%. You now receive another $5 million, which you invest in stocks with an average beta of 0.65. What is the required rate of return on the new portfolio? (Hint: You must first find the market risk premium, then find the new portfolio beta.)
24. If the current one year CD rate is 3% and the best estimate of one year CD which will be available one year from today is 5%, what is the current two year CD rate with 1% liquidity premium?
25. How long approximately does it take to triple your investment at 6% per year?
a. 18.9 years
b. 19.5 years
c. 19.7 years
d. 20.0 years
e. 22.7 years