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# Finance Problems: Risk Free Rate of Return

Find attached finance problems I appreciate helping and solving in advance.

1. The risk free rate of return is 8 percent; the expected rate of return on the market is 12 percent. Stock X has a beta coefficient of 1.3, an earnings and dividend growth rate of 7 percent, and a current dividend of \$2.40. If the stock is selling for \$35, what should you do?
2. Presently, Stock A pays a dividend of \$2.00 a share, and you expect the dividend to grow rapidly for the next four years at 20 percent. Thus the dividend payments will be:

Year Dividend
1 \$1.20
2 1.44
3 1.73
4 2.07

After this initial period of super growth, the rate of increase in the dividend should decline to 8 percent. If you want to earn 12 percent on investments in common stock, what is the maximum you should pay for this stock?
3. You are hurt in a car accident and your lawyer wins a RM100,000 settlement to be distributed as follows:
? RM20,000 immediate payment
? RM5,000 a year for ten years starting now
? RM30,000 after ten years.
If the lawyer's fee is RM10,000, what is the value of this settlement if the interest rate is
10 percent?
4. A state lotto awarded a prize of RM560,000 a year for the next 20 years starting today. If the state sold RM21,900,000 in lotto tickets, what proportion of the sales will the state distribute if it earns 8% annually on invested funds?

5. A firm has a RM1,000,000 debt (e.g., a bond) outstanding that matures after 10 years.
The sinking fund requires the firm to set aside annually an amount so the debt may be
retired at maturity. If the firm can earn 10% annually on these funds, how much must it
invest annually to meet the sinking fund?

Describe the relationship between following variables:
i) future value and interest rate;
ii) future value and time period;
iii) present value and interest rate; and
iv) present value and time period

6. The risk-free rate of return is 8 percent; the expected rate of return on the market is 12
percent. Stock X has a beta coefficient of 1.3, an earnings and dividend-growth rate of 7
percent, and a current dividend of RM2.40. If the stock is selling for RM35, what should
you do?
7. Two stocks each pay a RM1 dividend that is growing annually at 8 percent. Stock A has
a beta of 1.3; stock B's beta is 0.8.
i) Which stock is more volatile?
ii) If treasury bills yield 6 percent and you expect the market to rise by 12 percent, what
iii) Using the dividend-growth model, what is the maximum amount you would be willing
to pay for each stock?
iv) Why are your valuations different
8. Presently, Stock A pays a dividend of \$2.00 a share, and you expect the dividend to
grow rapidly for the next four years at 20 percent. Thus the dividend payments will be:
Year Dividend
1 RM1.20
2 1.44
3 1.73
4 2.07

After this initial period of super growth, the rate of increase in the dividend should decline
to 8 percent. If you want to earn 12 percent on investments in common stock, what is the
maximum you should pay for this stock?
9. As an investor you have a required rate of return of 14 percent for investments in risky
stocks. You have analyzed three risky firms and must decide which (if any) to purchase.
Firm A B C
Current dividends RM1.00 RM3.00 RM7.50
Expected annual growth
rate in dividends 7% 2% (-1%)
Current market price RM23 RM47 RM60
i) What is the maximum price? Which (if any) should you buy?
ii) If you bought Stock A, what is your implied rate of return?
iii) If your required rate of return were 10 percent, what should be the price necessary to
induce you to buy Stock A?
10. What does an inventory turnover of 3.0 suggest? If inventory is sold for cash instead of
on credit, how will this affect the inventory turnover? If a firm's inventory turnover is 4.0
and its receivables turnover is 6.0, how long will it take for the company to generate cash
from the newly acquired inventory?
11. The inventory turnover for an industry is 6 (every two months) but Silauan Cahaya Bhd.
turns over its inventory 4 times a year (every three months). If annual sales are
RM1,000,000 and the interest cost to carry inventory is 12 percent, what is the potential
savings in interest expense if the firm achieves the industry for the turnover of its
inventory?
12. A homeowner has been offered three alternative mortgage loans to finance the purchase of a RM300,000 house. The interest rate on the first alternative is 8 percent for twenty-five years, and the loan requires a 20 percent down payment. The second mortgage loan is also for twenty-five years with an interest rate of 7 percent but requires a down payment of a third of the cost of the house. The third loan also requires a third down but is for 20 years at 6 percent. What are the annual mortgage payments required by each loan?

13. If you purchase a RM5 preferred stock for RM40 a share, what is the current yield? If you anticipate that yields will decline to 10 percent, what will be the anticipated capital gain on this investment?

14. What is the value of a RM1,000 zero coupon government bond that matures after eight years, if comparable yields are 7%?

Reference Book
1. Financial Management-Theory and practice by Eugene F. Brigham, Michael C. ehrhardt 11 Edition.

#### Solution Preview

1. The risk free rate of return is 8 percent; the expected rate of return on the market is 12 percent. Stock X has a beta coefficient of 1.3, an earnings and dividend growth rate of 7 percent, and a current dividend of \$2.40. If the stock is selling for \$35, what should you do?
2. Presently, Stock A pays a dividend of \$2.00 a share, and you expect the dividend to grow rapidly for the next four years at 20 percent. Thus the dividend payments will be:

Year Dividend
1 \$1.20
2 1.44
3 1.73
4 2.07

After this initial period of super growth, the rate of increase in the dividend should decline to 8 percent. If you want to earn 12 percent on investments in common stock, what is the maximum you should pay for this stock?
3. You are hurt in a car accident and your lawyer wins a RM100,000 settlement to be distributed as follows:
? RM20,000 immediate payment
? RM5,000 a year for ten years starting now
? RM30,000 after ten years.
If the lawyer's fee is RM10,000, what is the value of this settlement if the interest rate is
10 percent?
4. A state lotto awarded a prize of RM560,000 a year for the next 20 years starting today. If the state sold RM21,900,000 in lotto tickets, what proportion of the sales will the state distribute if it earns 8% annually on invested funds?

5. A firm has a RM1,000,000 debt (e.g., a bond) ...

#### Solution Summary

The solution determines the risk free rate of return.

\$2.19