$ 65.00

Problem 2 [10 points]

Company Miami just paid annual dividend of $25 today. The dividend is expected to grow at 8%

for the next 3 years, then it will grow at 3% in perpetuity. If stocks of similar company earn 12%

annual return, what is the price of a share of Company Miami stock?

2

Problem 3 [10 points]

Table below shows the historical returns for Companies A, B and C

1. If one investor has a portfolio consisting of 70% Company A and 30% Company B, what

are the average portfolio return and standard deviation? What is Sharpe ratio if the riskfree

rate is 3.5%?

2. If another investor has a portfolio consisting of 1/3 Company A, 1/3 Company B and 1/3

Company C, what are the average portfolio return and standard deviation? What is

Sharpe ratio if the risk-free rate is 3.5%?

Year Company A Company B Company C

1 30% 26% 47%

2 7% 15% -54%

3 18% -14% 15%

4 -22% -15% 7%

5 -14% 2% -28%

6 10% -18% 40%

7 26% 42% 17%

8 -10% 30% -23%

9 -3% -32% -4%

10 38% 28% 75%

11 27.0% 23.4% 42.3%

12 6.3% 13.5% -48.6%

13 16.2% -12.6% 13.5%

14 -19.8% -13.5% 6.3%

15 -12.6% 1.8% -25.2%

16 9.0% -16.2% 36.0%

17 23.4% 37.8% 15.3%

18 -9.0% 27.0% -20.7%

19 -2.7% -28.8% -3.6%

20 34.2% 25.2% 67.5%

3

Problem 4 [15 points]

You currently have $1,000,000. You want to invest it in the following three assets: 10-year US

Treasury bond with coupon rate 4.5%, Blandy and Gourmange stocks, which have the following

historical annual returns:

Your goal is to have the expected annual return of 7.6% with a minimum portfolio risk. How

much money should you allocate to these three assets? What is the minimum portfolio risk (i.e.,

the standard deviation)?

Year Blandy Gourmange

1 26.0% 47.0%

2 15.0% -54.0%

3 -14.0% 15.0%

4 -15.0% 7.0%

5 2.0% -28.0%

6 -10.0% 40.0%

7 22.0% 17.0%

8 30.0% -23.0%

9 -32.0% -4.0%

10 28.0% 75.0%

11 28.6% 51.7%

12 16.5% -59.4%

13 -15.4% 16.5%

14 -16.5% 7.7%

15 2.2% -30.8%

16 -11.0% 44.0%

17 62.2% 18.7%

18 33.0% -25.3%

19 -35.2% -4.4%

20 50.8% 82.5%

21 23.4% 42.3%

22 13.5% -48.6%

23 -12.6% 13.5%

24 -13.5% 6.3%

25 1.8% -25.2%

26 -9.0% 36.0%

27 18.8% 15.3%

28 27.0% -20.7%

29 -28.8% -3.6%

30 25.2% 67.5%

4

Problem 5 [25 points]

A real estate investor has the following information on an office building:

• Purchase price is $1,250,000 with acquisition costs of $60,000

• 45,000 leasable square feet

• Initial rent of $10/sq. ft. per year and will increase 1.0 percent per year

• Vacancy rate of 8% of gross rent per year

• Operating expenses are 42% of effective gross income

• Three financing choices:

1. All equity without any financing;

2. Mortgage with 75% LTV ratio, 15 years, annual payments and 3.5% contract

rate;

3. Mortgage with 95% LTV ratio, 15 years, annual payments and 6.0% contract

rate;

• Expected increase in value is 3.0% per year. Holding period is 15 years, and 5%

selling expenses

• For simplicity, assuming that no capital improvement over the entire holding period

• 75% depreciable

• Investor’s tax rate is 28%, and capital gain tax rate is 15%.

Questions:

1. What is the equity after-tax return (internal rate of return) for each financing

choice?

2. How much percentage of the IRR comes from cash flows and how much from

capital gain for each financing choice?

3. Which financing choice is the best and why?

5

Problem 6 [10 points]

We currently have the once-in-a-generation low interest rate environment, and the rates are

likely to increase in the next decade. If you recently graduated from college and have a

decent job, you have decided to purchase a relative expansive house to your income.

Suppose that a bank offers you three types of mortgages: adjusted rate mortgage (ARM),

fixed-rate mortgage with constant payments (FRM) and graduated payment mortgage

(GPM). Which type of mortgage should you choose and why?

Problem 7 [10 points]

Consider the following average annual returns for Stocks A and B and the Market. Which of

the possible answers best describes the historical betas for A and B and why?

Years Market Stock A Stock B

1 0.03 0.16 0.05

2 -0.05 0.20 0.05

3 0.01 0.18 0.05

4 -0.10 0.25 0.05

5 0.06 0.14 0.05

a. bA > +1; bB = 0.

b. bA = 0; bB = -1.

c. bA < 0; bB = 0.

d. bA < -1; bB = 1.

Problem 8 [10 points]

Suppose that Federal Reserve actions have caused an increase in the risk-free rate, rRF.

Meanwhile, investors are afraid of a recession, so the market risk premium, (rM – rRF), has

increased. Under these conditions, with other things held constant, which of the following

statements is most correct and why?

a. The required return on all stocks would increase, but the increase would be

greatest for stocks with betas of less than 1.0.

b. The prices of all stocks would decline, but the decline would be greatest for the

highest-beta stocks.

c. The prices of all stocks would increase, but the increase would be greatest for the

highest-beta stocks.

d. The required return on all stocks would increase by the same amount