Final Practice Problems

Question 1

If you were told the risk free rate was 4%, the market return was 14% and the beta of a stock was 0.2, what is the expected (required) return on that stock?

Answer 1

CAPM: re = 0.04 + .2(0.14 - 0.04) = 6%

Question 2

What is the WACC for a firm with 50% debt and 50% equity that pays 12% on its debt, 20% on its equity, and has a 40% tax rate?

Answer 2

WACC = [.5 x ((1-.4) x .12)] + (.5 x .2)
= .036 + .10
= .1360
= 13.60%

Question 3

Find the required rate of return for equity investors of a firm with a beta of 1.3 when the risk free rate is 5%, and the return on the market is 10%.

Answer 3

CAPM: re = 0.05 + 1.30(0.10 - 0.05)
= 11.5%

Question 4

What is the weighted-average cost of capital for a firm with the following sources of funds and corresponding required rates of return: $5 million common stock at 16%, $500,000 preferred stock at 10%, and $3 million debt at 9%. All amounts are listed at market values and the firm’s tax rate is 35%.

Answer 4

12.07%

Question 5

You are considering a new investment. The rate on T-bills is 3.3% and the return on the S&P 500 is 8.5%. You have measured the non-diversifiable risk of the investment you are considering to be .5. What rate of return will you require on the investment?

Answer 5

CAPM: re = 0.033 + .5(0.085 - 0.033) = .0590 = 5.9%

Question 6

What return on equity do investors expect for a firm with a $25 share price, an expected dividend in year 1 of $3.00, a beta of .6 and a constant growth rate of 2.5%?

Answer 6

re = (div1 / P0) +g
= (3.00/25) + .025 = .1450 = 14.5%

Question 7

What is a firm’s weighted-average cost of capital if the stock has a beta of 1.45, Treasury bills yield 5%, and the market portfolio offers an expected return of 14%? In addition to equity, the firm finances 30% of its assets with debt that has a yield to maturity of 9%. The firm is in the 35% marginal tax bracket.

Answer 7

re = .05 + 1.45 (.14 - .05) rd = YTM=9%
= .05 + .1305
= 18.05%

	WACC = (.3 × (1-.35) × .09) + (.7 × .1805)
	= .01755 + .12635	= 14.39%

Question 8

Be SPECIFIC and DETAILED in answering the following questions:
a. Give one example of systematic risk and one example of unsystematic risk.
b. Which type of risk can a portfolio help you avoid? How?
c. Which type of risk are you rewarded for bearing? Why?

Answer 8

A. There are many possible answers here. Systematic risk is things like interest rates, war, and recessions. Unsystematic risk is anything firm-specific like a fire, or death of the CEO etc.

B. Portfolios help you avoid unsystematic risk. By holding stocks in a portfolio which are not perfectly positively correlated, you can diversify away unsystematic risk. Diversification lowers standard deviation.

C. You are rewarded for bearing systematic risk only because it cannot be avoided. You are not compensated for bearing unsystematic risk because it can be diversified away.

Question 9

Why does risk matter in valuing projects, stocks, or any cash flows?

Answer 9

Risk matters because people are risk averse. Therefore if risk increases, required returns are going to increase as well.

Question 10

What does the beta of a stock measure?

Answer 10

Systematic risk.

Question 11

You hold one stock (A) with a standard deviation of 20%. You are thinking about buying another stock (B) with a standard deviation of 30%. You will hold these two stocks in a portfolio with 50% of your money invested in each. Stock B has a correlation coefficient of –0.2 with stock A. Calculate the standard deviation of the portfolio.

Answer 11

16.28%

Question 12

You are considering purchasing a stock. You know that the rate on T-bills is 3.5% and the market return is 13%. The beta of the stock you are considering is 0.6. What is the expected return (required return) on the stock?

Answer 12

9.2%

Question 13

You own a portfolio that is 50% invested in stock X, 30% in stock Y, and 20% in stock Z. The expected returns on these three stocks are 11%, 17%, and 14%, respectively. What is the expected return on the portfolio?

Answer 13

13.4%

Question 14

You are considering investing in two stocks to form a portfolio. You are very risk averse (you do not like risk). Which one of the following stock combinations will you choose for your portfolio (these are your only options)? (Choose only one)

a. Stocks A & B which are in the same industry.
b. Stocks C & D have zero correlation with each other.
c. Stocks E & F which are negatively correlated.
d. Stocks G & H which are positively correlated.

Answer 14

c. Stocks E & F which are negatively correlated.

Question 15

Your company is considering a project with the following cash flows: an immediate investment of $150 million, cash inflows of $60 million for 6 years (starting next year). If your discount rate for this project is 12%, what is the project’s NPV? Should you accept the project?

Answer 15

You should get 96.68 and because it is positive you accept the project. (Solution is in millions.)

Question 16

What does the NPV calculation tell us? Why do we use it?

Answer 16

NPV tells us the dollar amount by which a project increases value. We use it because it focuses on cash flow and therefore tells us how much we are increasing shareholder value, the ultimate goal of the company.

Question 17

You are considering starting a natural food store. You own a piece of real estate on Hilyard St. that you believe would be a good location for your shop. You bought the land 4 years ago for $75,000; the market value of the land today is $100,000. To start the business you will need to initially invest $150,000 in long term assets, such as the building, as well as fixtures, computers etc. You plan on depreciating these assets (not the land) straight line to zero over a 3-year period. You also figure you will need $5,000 each year, beginning in year zero, in working capital to run the business. Your working capital will be recovered in the last year. US Bank has offered to lend you the $155,000 as a 4 year loan at an interest rate of 7%. Forecasted revenues for each year are $200,000 while costs will be $60,000. The tax rate for businesses in Lane County is 35%. You estimate your cost of capital to be 15%. Should you build your natural food store? Why or why not?

Answer 17

Year 0 Year 1 Year 2 Year 3
+ Revenues 200,000 200,000 200,000
-Costs 60,000 60,000 60,000
- Deprec 50,000 50,000 50,000
= EBIT 90,000 90,000 90,000
- Taxes 31,500 31,500 31,500
=Net Income 58,500 58,500 58,500
+ Deprec 50,000 50,000 50,000
= Oper. CF 108,500 108,500 108,500
-  in NWC 5,000 -5,000
- Capital Ex. 150,000
- Opp. Costs 100,000
= Net CF -255,000 108,500 108,500 113,500

You must then find the NPV of the calculated cash flows:

-255,000 + 108500 [ (1- (1/1.15)2) / .15] + 113500/(1.153) = -3983 (note: I valued the 108,500 cash flows as a 2 year annuity. You could also value these as multiple cash flows)

NPV = -3983 and therefore it is a bad investment because it decreases value, reject.

Question 18

You purchased land 3 years ago for $50,000 and believe its market value is now $60,000. You are considering building a hotel on this land instead of selling it. To build the hotel, it will initially cost you $75,000, an expense that you plan to depreciate straight line over the next three years. Wells Fargo offered you a loan for $60,000 at an 8% interest rate to be repaid over the next 4 years. You anticipate that the hotel will earn revenues of $140,000 each year, while expenses will be a mere $30,000 each year. The initial working capital requirement will be $7,000. The tax rate is 35%. Your estimated cost of capital is 11%. Assume the project terminates after year 3. Is the hotel a good investment? Why or why not?

Answer 18

Year 0 Year 1 Year 2 Year 3
+ Revenues 140,000 140,000 140,000
-Costs 30,000 30,000 30,000
- Deprec 25,000 25,000 25,000
= EBIT 85,000 85,000 85,000
- Taxes 29,750 29,750 29,750
=Net Income 55,250 55,250 55,250
+ Deprec 25,000 25,000 25,000
= Oper. CF 80,250 80,250 80,250
-  in NWC 7,000 -7,000
- Capital Ex. 75,000
- Opp. Costs 60,000
= Net CF -142,000 80,250 80,250 87,250

You must then take NPV of the calculated cash flows:

-142,000 + 80250 [ (1- (1/1.11)2) / .11] + 87250/(1.113) = 59,226

NPV = 59,226 and therefore it is a good investment because it increases value.

Question 19

Your company is considering expanding its retail outlet. Currently, inventory levels are $5,000. With the expansion, it is expected that inventory levels will need to be $9,500. It is expected that account’s receivable will increase by $4,000 and account payable will decrease by $10,000. The expansion of the building will cost $120,000.

A.  What change in net working capital is this expansion causing?   
B.  This will result in: (Choose one)

A. a net source of cash.
B. a net use of cash.
C. no impact on cash.
D. positive net present value.

Answer 19

CHANGE NWC = CHANGE current assets – CHANGE current liabilities

\+4500 inv		-10,000
\+4000 a/r			
8500		-	-10,000 = +18,500

B. a net use of cash.

Question 20

Net present value analysis is how we typically make investment decisions in the capital budgeting process. The payback method is an alternative method to NPV. The problem with this alternative is that: (choose one)

a. The time value of money is not taken into consideration.
b. It takes into consideration all future cash flows.
c. It provides a dollar measure of a projects impact on firm value and good decisions can only be made from rates of return.
d. It uses historical accounting numbers.

Answer 20

a. The time value of money is not taken into consideration.

Question 21

A firm is considering a project which would decrease accounts receivable by $10,000, decrease accounts payable by $50,000, and increase inventory by $25,000. Which of the following is true? (choose one)

a. Net working capital has decreased.
b. Sales will increase.
c. Net working capital has increased.
d. This is a net source of cash.

Answer 21

c. Net working capital has increased.

Question 22

What is the after tax cost of debt for a $1,000,000 loan with a 5% interest rate for a firm in the 35% tax bracket?

Answer 22

r_D * (1-T_c)
.05 * (1-.35) = .0325 = 3.25%

Question 23

What is the present value of the interest tax shield for a firm with $3 million in debt that pays 12% interest if the firm is in the 35% tax bracket?

Answer 23

PV of Interest tax shield = Tc x debt
= $3,000,000 x .35
= $1,050,000

Question 24

Theory on capital structure, such as the M&M proposition, indicates that:
A. There is a single capital structure that is optimal for all firms
B. The tax shield on debt positively affects firm value
C. Firms should finance themselves solely through debt
D. Firms should finance themselves solely through equity

Answer 24

B. The tax shield on debt positively affects firm value

Question 25

Tia Lupita Foods has forecasted its operating cash flow and capital expenditures for the next three years. This forecast is summarized in the table below:

Year 0	Year 1	Year 2	Year 3 Operating cash flow	-	$14 million	$36 million	$44 million Capital expenditure	$8 million	$8 million	$10 million	$12 million

After year 3, Tia Lupita expects operating cash flows and capital expenditures to grow at a constant rate of 3% per year. The cost of capital is 8.5%. What is Tia Lupita’s terminal value in year 3? What is the NPV of the business?

Answer 25

Find FCF 0-3: -8M, 6M, 26M, 32M
Find TV3 = CF3(1+g)/r-g = 32(1.03) / .085-.03 = 599.27
Bring all cash flows back to present value
-8
6/(1.085)^1
26/*1.085^2
(32+599.27)/(1.085)^3
Sum all of those =
$513.84 NPV of business

Question 26

What is beta?
A. A rate of return measure
B. The return on a stock relative to the overall market
C. The rate of dividend growth
D. The percentage of net income paid out as a dividend
E. A measure of a stock’s risk relative to the stock market average

Answer 26

E. A measure of a stock’s risk relative to the stock market average