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Finance Problems: Required Rate of Return

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2. Required Rate of Return
AA Industries stock has a beta of 0.8. The risk-free rate is 4% and the expected return on the market is 12%. What is the required rate of return on AA's stock?

10. Portfolio Required Return
Suppose you manage a $4 million fund that consists of four stocks with the following investments:
Stock Investment Beta______________
A $ 400,000 1.50
B 600,000 -0.50
C 1,000,000 1.25
D 2,000,000 0.75
If the market's required rate of return is 14% and the risk-free rate is 6%, what is the fund's required rate of return?

13. Historical Realized Rates of Return
You are considering an investment in either individual stocks or a portfolio of stocks. The two stocks you are researching, stock A and B, have the following historical returns:

Year rA rB_________
2009 -20.00% -5.00%
2010 42.00% 15.00%
2011 20.00% -13.00%
2012 -8.00% 50.00%
2013 25.00% 12.00%
a. Calculate the average rate of return for each stock during the 5-year period.
b. Suppose you had held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return o the portfolio during this period?
c. Calculate the standard deviation of returns for each stock and for the portfolio.
d. If you are a risk-averse investor, then, assuming these are your only choices, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

14. Historical Returns: Expected and Required Rates of Return
You have observed the following returns over time:

Year Stock X Stock Y Market_____
2009 14% 13% 12%
2010 19 7 10
2011 -16 -5 -12
2012 3 1 1
2013 20 11 15
Assume that the risk-free rate is 6% and the market risk premium is 5%.
a. What are the betas of Stocks X and Y?
b. What are the required rates of return on Stock X and Y?
c. What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?

3. Two-Asset Portfolio
Stock A has an expected return of 12% and a standard deviation of 40%. Stock B has an expected return of 18% and a standard deviation of 60%. The correlation coefficient between Stock A and B is 0.2. What are the expected return and standard deviation of a portfolio invested 30% in Stock A and 70% in Stock B?

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This solution provides calculations for the required rate of return in Excel.

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Finance Test Review


1. The money market is usually thought of as dealing with long-term debt instruments issued by firms with excellent credit ratings.

2. For a firm to have its securities listed on an exchange, it must meet certain requirements.
These usually include measures of profitability, size, market value, and public ownership.

3. When fixed expenses increase relative to sales, it indicates that there is not enough productive
capacity to absorb an increase in sales.

4. The more frequent the compounding periods in a year, the higher the future value.

5. In measuring cash flows we are interested only in the incremental or differential after-tax cash flows that are attributed to the investment proposal being evaluated.

6. Additional cash needed to fill increased working capital requirements should be included in the initial cost of a product when analyzing an investment.

7. The weighted average cost of capital is the minimum required return that must be earned on additional investment if firm value is to remain unchanged.

8. The weighted cost of capital assumes that the company maintains a constant dividend payout ratio.

9. In most instances, as the amount of debt rises, the common stockholders will decrease their required rate of return.

10. The objective of hedging strategy is to have a zero net asset position in a foreign currency.

Multiple Choice

11. Which of the following is not an advantage of a private placement (as compared to a public offering)?
a. Greater financing flexibility
b. Lower flotation costs
c. Lower interest costs
d. Quicker availability of funds

12. The demand for funds by the federal government puts upward pressure on interest rates causing private investors to be pushed out of the financial markets. This is called:
a. the big squeeze.
b. the efficient market hypothesis.
c. the crowding out effect.
d. liquidity preference.
e. government intervention.

13. The opportunity cost is defined as the:
a. rate of return based on historical costs.
b. rate of return available to an investor for a given level of risk.
c. cost associated with the acquisition of investments.
d. future value of the purchase price.

14. The percent-of-sales method can be used to forecast:
a. expenses.
b. assets.
c. liabilities.
d. all of the above.

15. Which of the following statements about the percent-of-sales method of financial forecasting is true?
a. It is the least commonly used method of financial forecasting.
b. It is a much more precise method of financial forecasting than a cash budget would be.
c. It involves estimating the level of an expense, asset, or liability for a future period as a percent of the forecast for sales revenues.
d. It projects all liabilities as a fixed percentage of sales.

16. Which of the following will increase cumulative borrowing in the cash budget?
a. Decreasing the average collection period
b. Increasing purchases
c. Decreasing depreciation expense
d. Both a and c
e. All of the above

17. A company collects 60% of its sales during the month of the sale, 30% one month after the sale, and 10% two months after the sale. The company expects sales of $10,000 in August, $20,000 in September, $30,000 in October, and $40,000 in November. How much money is expected to be collected in October?
a. $25,000
b. $15,000
c. $35,000
d. None of the above

18. The present value of a perpetuity decreases when the _______ decreases.
a. number of investment periods
b. annual discount rate
c. perpetuity payment
d. both b and c

19. Which of the following would decrease free cash flows? A decrease in:
a. depreciation expense.
b. interest expense.
c. incremental sales.
d. both a & c.
e. all of the above.

20. Exchange rate risk:
a. arises from the fact that the spot exchange rate on a future date is a random variable.
b. applies only to certain types of international businesses.
c. has been phased out due to recent international legislation.
d. both a and b.

Problems (Please remember to show your calculations)

21. The treasurer for Brookdale Clothing must decide how much money the company needs to borrow in July. The balance sheet for June 30, 2004 is presented below:

Brookdale Clothing Balance Sheet
June 30, 2004
Cash $75,000 Accounts payable $ 400,000
Marketable securities 100,000 Long-term debt 300,000
Accounts receivable 300,000 Common stock 100,000
Inventory 250,000 Retained earnings 200,000
Total current assets 725,000 Total liabilities and
Fixed assets 275,000 stockholder's equity $1,000,000
Total assets $1,000,000

The company expects sales of $250,000 for July. The company has observed that 25% of its sales is for cash and that the remaining 75% is collected in the following month. The company plans to purchase $400,000 of new clothing. Usually 40% of purchases is for cash and the remaining 60% of purchases is paid in the following month. Salaries are $100,000 per month, lease payments are $50,000 per month, and depreciation charges are $20,000 per month. The company plans to purchase a new building for $200,000 in July and sell its marketable securities for $100,000. If the company must maintain a minimum cash balance of $50,000, how much money must the company borrow in July?

22. How does the risk-return tradeoff relate to the time value of money and the multinational firm?

23. You are planning to deposit $10,000 today into a bank account. Five years from today you expect to withdraw $7,500. If the account pays 5% interest per year, how much will remain in the account eight years from today?

24. What is the value (price) of a bond that pays $400 semiannually for 10 years and returns $10,000 at the end of 10 years? The market discount rate is 10% paid semiannually.

25. Frank Zanca is considering three different investments that his broker has offered to him. The different cash flows are as follows:

End of Year A B C
1 300 400
2 300
3 300
4 300 300 600
5 300
6 300
7 300
8 300 600

Because Frank has enough savings for only one investment, his broker has proposed the third alternative to be, according to his expertise, the best in town. However, Frank questions his broker and wants to eliminate the present value of each investment. Assuming a 15% discount rate, what is Frank's best alternative?

26. Combs, Inc. is issuing new common stock at a market price of $22. Dividends last year were $1.15 per share and are expected to grow at a rate of 7%. Flotation costs will be 5% of the market price. What is Combs, Inc.'s cost of external equity?

27. Company K is considering two mutually exclusive projects. The cash flows of the projects are as follows:
Year Project A Project B
0 -$2,000 -$2,000
1 $500
2 $500
3 $500
4 $500
5 $500
6 $500
7 $500 $5,650
a. Compute the NPV and IRR for the above two projects, assuming a 13%
required rate of return.
b. Discuss the ranking conflict.
c. Which of these two projects should be chosen?

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