Unit06 Sample Homework Problems CHAPTER 10. …

Unit06 Sample Homework Problems CHAPTER 10. INVESTMENT RETURNS AND AGGREGATE MEASURES OF STOCK MARKETS

1. You buy a stock for $40. After a year the price rises to $50 but falls back to $40 at the end of the second year. What was the average percentage return?

Since the beginning and closing prices are the same, the return has to be 0%. The percentage changes for each year are 25% and 20%, so the average percentage change is 2.5%.

3. You make an investment and the annual return are as follows:

Year 1 2 3 4 5

Return 15% 13% -8% 0% 5%

The average annual return is 3 percent. What is the geometric time-weighted return?

The geometric time-weighted average return is

[(1.15)(1.13)(0.92)(1)(1.05)]^(1/5)-1 = 4.65%

4. Given the following information concerning four stocks,

---

Price

Number of Shares

Stock A

$20

100,000

Stock B

34

50,000

Stock C

26

150,000

Stock D

40

200,000

a. Construct a simple price-weighted average, a value-weighted average, and a geometric average.

1

a. Simple price-weighted average: ($20 + 34 + 26 + 40)/4 = $30

Value-weighted average:

Stock A B C D

Price $20 34 26 40

Number of Shares 100,000 50,000 150,000 200,000 500,000

Total Value $2,000,000 1,700,000 3,900,000 8,000,000 $15,600,000

Average value per share: $15,600,000/500,000 = $31.20

Geometric average: [($20)(34)(26)(40)]^(1/4)=707200^(0.25)=$29

b. What is the percentage change in a value-weighted average if the stocks' prices become $10, $17, $13, $40?

The new Value-weighted average:

Stock A B C D

Price $10 17 13 40

Number of Shares 100,000 50,000 150,000 200,000 500,000

Total Value $1,000,000 850,000 1,950,000 8,000,000

$11,800,000

Average value per share: $11,800,000/500,000 = $23.60

% Change =23.60/31.2-1=-24.36%

6. An investor buys a stock for $10 and sells it for $15 after five years. There is no dividend income. (a)What is the holding period return on an annual basis? (b) What is the true annual rate of return?

a. The holding period return: 15/10-1 = 50%. On an annual basis: 50%/5 = 10%

b. The true annual rate of return: $10(1 + r)^5 =15

Solving for r: r=(15/10)^(1/5)-1=8.45%

2

13. You purchase a stock for $30 and sell it for $40 after holding it for five years. During this period you collected an annual dividend of $1. Did you earn more than 10 percent annual internal rate of return on your investment? What was the annual dollar-weighted rate of return?

Price = div + ... + div + sales price

(1 + r)

(1 + r)n

(1 + r)n

In this case: 30=$1*(PVFS, r=?, n=5)+40 (PVF r=?, n=5)

PVFS=present value factor sum PVF=present value factor

30=1*(1-(1/(1+r)^5))/r)+40/(1+r)^5

For a given rate to be the correct return, the two sides of the equation must be equal. At 10 percent, the right-hand side of the equation equals to $1(3.790787) + 40(.620921) = $28.63.

(3.790787 is the PVFS when r=10% and n=5. 0.620921 is the PVF when r=10% and n=5.) The present value of the cash flows ($28.63) does not equal the cost of the investment ($40), so the rate of return is less than 10 percent.

The actual dollar-weighted return is 8.92 percent. (PV = -40; N = 5; PMT = 1; FV = 40; I = ? = 8.92%.)

You can use Excel to solve this problem by trying different r's until the equation 30=1*(1-(1/(1+r)^5))/r)+40/(1+r)^5 holds.

18. You believe that QED stock may be a good investment and decide to buy 100 shares at $30. You subsequently buy an additional $3,000 worth of the stock every time the stock's price declines by an additional $3. (That means you bought $3000 when the price went down to $27, and another $3000 when the price went down to $24). If the stock's price declines to $22 and rebounds to $32, at which time you sell your holdings, what is your profit? (Assume that no fractional shares may be purchased so you may spend a little less than 3,000 each time.)

3

This problem illustrates dollar cost averaging.

Price of the

Number of Shares

Cost of Stock

Stock

Purchased

$30

100

$3,000

27

111

2,997

24

125

3,000

336

$8,997

Average cost per share: $8,997/336 = $26.78 Proceeds of the sale: 336 X $32 = $10,752 Profit: $10,752 ? 8,997 = $1,775

19. On January 31, 2001, you bought 10 shares of AVAYA (AV) for $7 a share. Subsequent prices of AV were: January 1, 2002, $5; January 1, 2003, $2; January 1, 2004, $15. You owned the stock for three years (2001 through 2004). What was your holding period return? What was the average percentage return? What was your true return on this investment?

Holding period return: $15/$7-1 =114.29%

Yearly percentage returns: First year: $5/7-1 = -28.57% Second year: 2/5-1 = -60% Third year: 15/2-1 = 650%

Average percentage return for three years: [(-28.57%) + (-60%) + 650%]/3 = 187.14%

True return: $7(1 + r)3 = $15

r=(15/7)^(1/3)-1=28.92%

Averaging percentage returns can produce very misleading results.

4

Teaching Guides for the Financial Advisor's Case: The Calculation of Returns

1. Return on the market: (1.12)(1.17)(1.02)(0.97)(1.14).2 = 1.0813 = 8.13%

Return on the stock:

Annual returns

Year 1:

Amount invested $10

Yearly cash inflow $10.50 + 0.30

Percentage return

8%

Year 2: Amount invested $10.50 Yearly cash inflow $12 + 1 Percentage return 23.8%

Year 3:

Amount invested $12

Yearly cash inflow $11.25 + 0.50

Percentage return

-2.1%

Year 4 Amount invested $11.25 Yearly cash inflow $12.50 + 1 Percentage return 20.0%

Year 5 Amount invested $12.50 Yearly cash inflow $14.00 + 1.25 Percentage return 22.2%

(1.08)(1.238)(0.979)(1.20)(1.22).2 = 1.1389 = 13.89%

2. Questions 2 and 3 require considering the beta of the stock and the standard deviations of the returns. The standard deviation of the returns is 8.5%, and the standard deviation of the stock returns is 11.1%. The beta coefficient is 0.491 with the coefficient of determination of 0.142. Based on this information, the stock is less volatile than the market because the beta is less than 1.0. These investors bear less systematic risk, but the low coefficient of determination

5

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download