### Sample Questions for Chapters 6  9

Multiple Choice

1. Bob has a \$50,000 stock portfolio with a beta of 1.2, an expected return of 10.8 percent, and a standard deviation of 25 percent. Becky has a \$50,000 portfolio with a beta of 0.8, an expected return of 9.2 percent, and a standard deviation of 25 percent. The correlation coefficient, r, between Bob's and Becky's portfolios is 0. Bob and Becky are engaged to be married. Which of the following best describes their combined \$100,000 portfolio?

a. The combined portfolio's expected return is a simple average of the expected returns of the two individual portfolios (10%).

b. The combined portfolio's beta is a simple average of the betas of the two individual portfolios (1.0).

c. The combined portfolio's standard deviation is less than a simple average of the two portfolios' standard deviations (25%), even though there is no correlation between the returns of the two portfolios.

d. Statements a and b are correct.

e. All of the statements above are correct.

2. You hold a diversified portfolio consisting of a \$10,000 investment in each of 20 different common stocks (that is, your total investment is \$200,000). The portfolio beta is equal to 1.2. You have decided to sell one of your stocks that has a beta equal to 0.7 for \$10,000. You plan to use the proceeds to purchase another stock that has a beta equal to 1.4. What will be the beta of the new portfolio?

a. 1.165

b. 1.235

c. 1.250

d. 1.284

e. 1.333

3. At an inflation rate of 9 percent, the purchasing power of \$1 would be cut in half in 8.04 years. How long to the nearest year would it take the purchasing power of \$1 to be cut in half if the inflation rate were only 4 percent?

a. 12 years

b. 15 years

c. 18 years

d. 20 years

e. 23 years

Financial Calculator Section

4. You want to borrow \$1,000 from a friend for one year, and you propose to pay her \$1,120 at the end of the year. She agrees to lend you the \$1,000, but she wants you to pay her \$10 of interest at the end of each of the first 11 months plus \$1,010 at the end of the 12th month. How much higher is the effective annual rate under your friend's proposal than under your proposal?

a. 0.00%

b. 0.45%

c. 0.68%

d. 0.89%

e. 1.00%

5. You just bought a house and have a \$150,000 mortgage. The mortgage is for 30 years and has a nominal rate of 8 percent (compounded monthly). After 36 payments (3 years) what will be the remaining balance on your mortgage?

a. \$110,376.71

b. \$124,565.82

c. \$144,953.86

d. \$145,920.12

e. \$148,746.95

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6. You are considering two Treasury bonds. Bond A has a 9 percent annual coupon, and Bond B has a 6 percent annual coupon. Both bonds have a yield to maturity of 7 percent. Assume that the yield to maturity is expected to remain at 7 percent. Which of the following statements is most correct?

a. If the yield to maturity remains at 7 percent, the price of both bonds will increase by 7 percent per year.

b. If the yield to maturity remains at 7 percent, the price of both bonds will increase over time, but the price of Bond A will increase by more.

c. If the yield to maturity remains at 7 percent, the price of both bonds will remain unchanged.

d. If the yield to maturity remains at 7 percent, the price of Bond A will decrease over time, but the price of Bond B will increase over time.

e. If the yield to maturity remains at 7 percent, the price of Bond B will decrease over time, but the price of Bond A will increase over time.

Financial Calculator Section

7. A 15-year bond with a 10 percent semiannual coupon has a par value of \$1,000. The bond may be called after 10 years at a call price of \$1,050. The bond has a nominal yield to call of 6.5 percent. What is the bond's yield to maturity, stated on a nominal, or annual basis?

a. 5.97%

b. 6.30%

c. 6.75%

d. 6.95%

e. 7.10%

8. Stock X has a required return of 12 percent, a dividend yield of 5 percent, and its dividend will grow at a constant rate forever. Stock Y has a required return of 10 percent, a dividend yield of 3 percent, and its dividend will grow at a constant rate forever. Both stocks currently sell for \$25 per share. Which of the following statements is most correct?

a. Stock X pays a higher dividend per share than Stock Y.

b. Stock X has a lower expected growth rate than Stock Y.

c. One year from now, the two stocks are expected to trade at the same price.

d. Statements a and b are correct.

e. Statements a and c are correct.

9. NOPREM Inc. is a firm whose shareholders don't possess the preemptive right. The firm currently has 1,000 shares of stock outstanding; the price is \$100 per share. The firm plans to issue an additional 1,000 shares at \$90.00 per share. Since the shares will be offered to the public at large, what is the amount per share that old shareholders will lose if they are excluded from purchasing new shares?

a. \$90.00

b. \$ 5.00

c. \$10.00

d. \$    0

e. \$ 2.50

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ANSWER KEY FOR TEST - SU02_T2S

1. e

Portfolio risk and return

Chapter:6       QUESTION:  9

2. b

Portfolio beta

1.2 = 1/20(0.7) + (9/20)b

b is average beta for other 19 stocks.

1.165 = (19/20)b.

New Beta = 1.165 + 1/20(1.4) = 1.235.

Chapter:6       QUESTION: 59

3. c

Effect of inflation

Time Line:

0            1                  n = ?  Years

4%

³ÄÄÄÄÄÄÄÄÄÄÄÄāÄÄÄÄÄÄ ś ś ś ÄÄÄÄÄÄÄ³

-1.00                              0.50

Tabular solution:

0.5 = \$1(PVIF4%,n)

PVIF4%,n = 0.5

PVIF4%,18 = 0.4936; PVIF4%,17 = 0.5134

n ÷ 18 years.

Although a financial calculator or interpolation might be used to solve precisely, statement c is clearly the closest and best answer of those given.

Financial calculator solution:

Inputs: I = 4; PV = -1; PMT = 0; FV = 0.50.

Output: N = -17.67 ÷ 18 years.

Chapter:7       QUESTION: 27

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4. c

Effective annual rate

EAR1 = \$120/\$1,000

EAR1 = 12%.

Interest is being paid each month (\$10/\$1,000 = 1% per month), so it compounds, and the EAR is higher than kNom = 12%:

.           0.12Ć12

.EAR2 = ³1 + ÄÄÄÄ³   - 1 = 12.68%.

     12 Å

Difference = 12.68% - 12.00% = 0.68%.

You could also visualize your friend's proposal in a time line format:

0           1          2                   11         12

i = ?

³ÄÄÄÄÄÄÄÄÄÄÄāÄÄÄÄÄÄÄÄÄÄāÄÄÄÄÄ ś ś ś ÄÄÄÄÄÄÄÄāÄÄÄÄÄÄÄÄÄÄ³

1,000       -10        -10                  -10       -1,010

Insert those cash flows in the cash flow register of a calculator and solve for IRR. The answer is 1%, but this is a monthly rate. The nominal rate is 12(1%) = 12%, which converts to an EAR of 12.68% as follows:

Input into a financial calculator the following:

P/YR = 12; NOM% = 12; and then solve for EFF% = 12.68%.

Chapter:7       QUESTION: 54

5. d

Remaining mortgage balance

Solve for the monthly payment as follows:

N = 30 š 12 = 360; I = 8/12 = 0.667; PV = -150,000; FV = 0; and then solve for PMT = \$1,100.65/month.

Use the calculator's amortization feature to find the remaining principal balance:

3 š 12 = 36 payments

1 INPUT 36 ” AMORT

= displays Int: \$35,543.52

= displays Prin: \$4,079.88

= displays Bal: \$145,920.12.

Chapter:7       QUESTION: 63

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6. d

Bond yields and prices

If the YTM is 7 percent, this is the market interest rate. Therefore, Bond A's coupon rate is higher than the market rate, so it must be selling above par (at a premium). Bond B's coupon rate is lower than the market rate, so it must be selling below par (at a discount).

Statement a is false. If the YTM remains the same, the price of Bond A will fall, and the price of bond B will rise. The total yield of 7 percent on both bonds will consist of a capital gains yield and a current yield. The sum of these two yields will be 7 percent. Statements b, c, and e are false for the reason mentioned above. Therefore, the correct answer is statement d.

Chapter:8       QUESTION: 20

7. d

Yield to maturity - semiannual bond

Step 1: First determine what the bond is selling for today based on

the information given about its call feature:

N = 10(2) = 20; I = 6.5/2 = 3.25; PMT = 100/2 = 50; FV =

1,050; and then solve for PV = -\$1,280.81. VB = \$1,280.81.

Step 2: Use this current price solution to solve for the YTM:

N = 15(2) = 30; PV = -1,280.81; PMT = 100/2 = 50; FV = 1,000;

and then solve for I = 3.4775%.

Step 3: Since this is a semiannual rate, multiply it by 2 to solve for

the nominal, annual YTM:

YTM = 3.4775%(2) = 6.955% ÷ 6.95%.

Chapter:8       QUESTION:101

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8. e

Constant growth stock

If Stock X has a required return of 12 percent and a dividend yield of 5 percent, we can calculate its growth rate:

ks = D1/P0 + g

12% = 5% + g

7% = g.

If Stock Y has a required return of 10 percent and a dividend yield of 3 percent, we can calculate its growth rate:

ks = D1/P0 + g

10% = 3% + g

7% = g.

Since both stocks have the same price and Stock X has a higher dividend yield than Stock Y, its dividend per share must be higher. Therefore, statement a is true. We just showed above, that both stocks have the same growth rate, so statement b must be false. One year from now, the stocks will both trade at the same price. They are starting at the same price today, and will be growing at the same rate this year, so they will end up with the same stock price one year from now. Therefore, statement c must also be true. Since both statements a and c are true, the correct choice is statement e.

Chapter:9       QUESTION: 24

9. b

New issues and dilution

Calculate current and new market value of firm after new stock issue

1,000 shares š \$100 per share    =   \$100,000

Plus 1,000 new shares @ \$90 each   +   90,000

New firm market value              \$190,000

ĶĶĶĶĶĶĶĶ

Calculate new market share price

\$190,000/2,000 shares = \$95.00 per share

Dilution  Old shareholders lose \$100 - \$95 = \$5.00 per share.

Chapter:9       QUESTION: 54