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# Stock Valuation, Annuities, Fixed Income Securities(Bonds)

7. Delbert Harris has just retired at age 60. His Roth retirement savings account currently has a value of \$2,000,000. Delbert expects to live for thirty more years. During that time, Delbert wishes to withdraw money from his retirement account every 6 months. Delbert's financial advisor is confident that Delbert can earn a semiannually compounded after-tax return of 5 percent per year on his retirement savings. Unfortunately, prices are expected to increase at a semiannually compounded rate of 8 percent per year due to inflation. Assuming that Delbert wants the purchasing power of his semiannual withdrawals/income to remain constant during his retirement, determine the maximum amount that Delbert can withdraw from the fund, assuming that Delbert makes one withdrawal from the fund every 6 months.

13. Harold's Electronic Superstores is a young start-up company that expects to earn 2.00 per share next year. Since the firm is currently retaining 100 percent of its earnings to finance future growth, no dividends will be paid on the stock during the next four years. Exactly five years from today, the firm expects to pay a dividend of \$4.00 per share from earnings of \$5.00 per share. The firm expects to reinvest earnings retained in the firm at a return on assets (ROA) of 25 percent. The required rate of return on the company's stock is 17.5 percent. Assuming that Harold's will retain the same fraction of earnings and reinvest at the same return on assets from the end of year five onwards, determine
a. the current price of shares in Harold?s computer store and,
b. explain whether and why the price earnings ratio for shares in Harold?s computer store will increase or decrease over the next four years.

14. On February 8, 2007 KC Kincaid paid \$1000 for a U.S. Government bond having a yield to maturity of 6 percent, a par value of \$1000, and exactly 10 years to maturity. Assume that on February 9, 2007 (?the day after?) the required yield to maturity for KC?s bond increases to 6.5 percent and remains constant, so that all future coupon payments for the bond will be reinvested at 6.5 percent compounded semiannually. Determine
a. the price of KC?s bond on February 8, 2008,
b. the future amount to which KC?s \$1000 will have grown by February 8, 2017 (the maturity date for the bond), assuming that each of the coupon payments that KC receives are reinvested at 6.5 percent compounded semiannually.

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7. Delbert Harris has just retired at age 60. His Roth retirement savings account currently has a value of \$2,000,000. Delbert expects to live for thirty more years. During that time, Delbert wishes to withdraw money from his retirement account every 6 months. Delbert's financial advisor is confident that Delbert can earn a semiannually compounded after-tax return of 5 percent per year on his retirement savings. Unfortunately, prices are expected to increase at a semiannually compounded rate of 8 percent per year due to inflation. Assuming that Delbert wants the purchasing power of his semiannual withdrawals/income to remain constant during his retirement, determine the maximum amount that Delbert can withdraw from the fund, assuming that Delbert makes one withdrawal from the fund every 6 months.

r= 2.50% 2.50%
g= 4% =8%/2 (Growth rate of annuity to beat inflation)
number of years = 30 years
For semiannual payments the number of periods= n= 60
Let the first semiannual payment be A and let it increase by g=4% every period (semiannual ) for 30 years
The discount rate per period =r=2.5%

The PV of this annuity ={ A / (r-g)} x { 1- (1+g)^n / (1+r)^n}

We have to equate this value to the amount in retirement saving account
{ A / (r-g)} x { 1- (1+g)^n / (1+r)^n} = \$2,000,000
{ 1- (1+g)^n / (1+r)^n} / (r-g) = 92.7292 (1-(1+0.04)^60/(1+0.025)^60) / (0.025-0.04)
Therefore, A= \$21,568.18 =2000000/92.7292

Therefore Dilbert can withdraw \$21,568.18 in the first 6 month after retirement.
Thereafter he can withdraw amounts that are growing at 4% every half year

13. Harold's Electronic Superstores is a young start-up company that expects to earn 2.00 per share next year. Since the firm is currently retaining 100 percent of its earnings to finance future growth, no dividends will be paid on the stock during the next four years. Exactly five years from today, the firm expects to pay a ...

#### Solution Summary

Answers questions on calculation of annuity, share price and bond price.

\$2.19