P4-23 Funding your retirement You plan to retire in exactly 20 years. Your goal is to create a fund that will allow you to receive $20,000 at the end of each year for the 30 years between retirement and death (a psychic told you would die exactly 30 years after you retire). You know that you will be able to earn 11% per year during the 30-year retirement period.
1.How large a fund will you need when you retire in 20 years to provide the 30-year, $20,000 retirement annuity?
2.How much will you need today as a single amount to provide the fund calculated in part a if you earn only 9% per year during the 20 years preceding retirement?
3.What effect would an increase in the rate you can earn both during and prior to retirement have on the values found in parts a and b? Explain.
P4-32 Funding budget shortfalls As part of your personal budgeting process, you have determined that in each of the next 5 years you will have budget shortfalls. In other words, you will need the amounts shown in the following table at the end of the given year to balance your budget—that is, to make inflows equal outflows. You expect to be able to earn 8% on your investments during the next 5 years and wish to fund the budget shortfalls over the next 5 years with a single amount.
End of year Budget shortfall
1 $ 5,000
1.How large must the single deposit today into an account paying 8% annual interest be to provide for full coverage of the anticipated budget shortfalls?
2.What effect would an increase in your earnings rate have on the amount calculated in part a? Explain.
P4-46 Loan amortization schedule Joan Messineo borrowed $15,000 at a 14% annual rate of interest to be repaid over 3 years. The loan is amortized into three equal, annual, end-of-year payments.
1.Calculate the annual, end-of-year loan payment.
2.Prepare a loan amortization schedule showing the interest and principal breakdown of each of the three loan payments.
3.Explain why the interest portion of each payment declines with the passage of time.
P4-48 Monthly loan payments Tim Smith is shopping for a used car. He has found one priced at $4,500. The dealer has told Tim that if he can come up with a down payment of $500, the dealer will finance the balance of the price at a 12% annual rate over 2 years (24 months).
1.Assuming that Tim accepts the dealer’s offer, what will his monthly (end-of-month) payment amount be?
2.Use a financial calculator or Equation 4.15a (found in footnote 9) to help you figure out what Tim’s monthly payment would be if the dealer were willing to finance the balance of the car price at a 9% annual rate.
P6-3 Real and nominal rates interest Zane Perelli currently has $100 that he can spend today on polo shirts costing $25 each. Alternatively, he could invest the $100 in a risk-free U.S. Treasury security that is expected to earn a 9% nominal rate of interest. The consensus forecast of leading economists is a 5% rate of inflation over the coming year.
1.How many polo shirts can Zane purchase today?
2.How much money will Zane have at the end of 1 year if he forgoes purchasing the polo shirts today?
3.How much would you expect the polo shirts to cost at the end of 1 year in light of the expected inflation?
4.Use your findings in parts b and c to determine how many polo shirts (fractions are okay) Zane can purchase at the end of 1 year. In percentage terms, how many more or fewer polo shirts can Zane buy at the end of 1 year?
5.What is Zane’s real rate of return over the year? How is it related to the percentage change in Zane’s buying power found in part d? Explain.
P6-11 Bond prices and yields Assume that the Financial Management Corporation’s $1,000-par-value bond had a 5.700% coupon, matured on May 15, 2017, had a current price quote of 97.708, and had a yield to maturity (YTM) of 6.034%. Given this information, answer the following questions.
1.What was the dollar price of the bond?
2.What is the bond’s current yield?
3.Is the bond selling at par, at a discount, or at a premium? Why?
4.Compare the bond’s current yield calculated in part b to its YTM and explain why they differ.
P7.6 Common stock valuation—Zero growth Scotto Manufacturing is a mature firm in the machine tool component industry. The firm’s most recent common stock dividend was $2.40 per share. Because of its maturity as well as its stable sales and earnings, the firm’s management feels that dividends will remain at the current level for the foreseeable future.
1.If the required return is 12%, what will be the value of Scotto’s common stock?
2.If the firm’s risk as perceived by market participants suddenly increases, causing the required return to rise to 20%, what will be the common stock value?
3.Judging on the basis of your findings in parts a and b, what impact does risk have on value? Explain.