# Principles of Corporate Finance A Tale of Value

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## Principles of Corporate Finance A Tale of Value

## Offered By ”Moscow Institute of Physics and Technology”

**Week- 1**

**1 – The power of PV calculations**

1.

Question 1

Capital budgeting is the choice of:

1 point

**The real assets the firm will purchase**- The securities the firm will issue
- The firm’s overall financial plan
- The loans the firm will take

2.

Question 2

The opportunity cost of capital is 15 percent for all four investments.

Project Initial Cash Flow, C0 ($) Cash Flow in Year 1, C1 ($)

1 –4,000 6,000

2 –2,000 3,000

3 –5,000 9,000

4 –2,000 4,500

Which

project has the highest rate of return?

1 point

- Project 3
**Project 4**- Project 1
- Project 2

3.

Question 3

Suppose that in terms of Question 2, each investment would require the use of the same parcel of land. Therefore you can take only one. Which one?

1 point

**Project 3**- Project 2
- Project 4
- Project 1

4.

Question 4

If the 4-year annuity factor is 2.855 and the 3-year annuity factor is 2.283, what is the present value of $1 received in year 4?

1 point

- $0.658
- $0.879
**$0.572**- Can’t say

5.

Question 5

A factory is put for sale at $1 million. You believe that starting from the end of year 1, it will produce an inflow after operating costs of $180,000 a year for 10 years. What is the NPV of the purchase of the factory, if the opportunity cost of capital is 12 percent?

1 point

- $12,567
**$17,040**- $19,123
- $20,712

6.

Question 6

In terms of Question 5, how much will the factory be worth just before the end of year 8?

1 point

- $432,330
- $304,209
- Nothing
**$484,209**

7.

Question 7

Suppose now that the factory from Question 5 is expected to produce an inflow after operating costs of $180,000 a year forever. The factory’s value at the end of year 5 and at the end of year 10 will be:

1 point

- Positive, different
- Can’t say
**Positive, the same**- Nothing in both cases

8.

Question 8

Suppose you just won the lottery and must choose one of the following (guaranteed) payoffs. Which one would you choose? The interest rate is 7%; ignore tax consequences.

1 point

- $140,000 paid 5 years from today
- $50,000 paid 1 year from today and $68,000 paid 4 years from today
**$14,000 paid per year for 10 years, with the first year’s payment made today**- $100,000 paid today

9.

Question 9

Consider the example of a fixed-rate mortgage (see Handout 1.2). If the price of the house is $450,000, and your bank would give you a mortgage with the 20% down payment for 30 years at a 6% annual rate, what will be the monthly payment?

1 point

- $2,198.33
**$2,158.38**- $2,233.11
- $1,986.22

10.

Question 10

You are planning to provide a gift for you newborn nephew in the form of a life insurance contract. You will make 21 installment payments of $1,000 at the beginning of each year starting now. All the accumulated proceeds will be reinvested at the annual market rate of 6%. How much will you nephew receive when he reaches 21?

1 point

- $38,992.73
- $33,996.64
- Can’t say
**$42,392.29**

**Week- 2**

**2 – PV of bonds and stocks – models and market values**

1.

Question 1

What will be the value of a just issued 6½ percent 5-year Treasury note if the market rate of interest is 3 percent? (Assume annual coupon payments).

1 point

$1,044.76

$1,120.67

$1,083.14

**$1,160.29**

2.

Question 2

Calculate the value on January 1, 2018, of the 3½ percent U.S. Treasury bond maturing on December 31, 2036, assuming that the rate of interest is 2.5 percent compounded semiannually. (Do not forget to recognize that coupon payments occur semiannually).

1 point

$1,067.17

$1,078.56

**$1,150.51**

$1,211.34

3.

Question 3

You have estimated the following annual spot rates:

Year Spot Rate, Percent

1 r1 = 5.00

2 r2 = 5.40

3 r3 = 5.70

4 r4 = 5.90

5 r5 = 6.00

What would be the fair price of a newly issued 10-percent 5-year Treasury note? Assume annual coupon payments.

1 point

**$1,171.48**

$ 989.17

$1,098.23

$1,154.89

4.

Question 4

In terms of Question 3, what will be the yield to maturity of the Treasury note?

1 point

6.00%

5.54%

**5.94%**

5.87%

5.

Question 5

Let r1 = 6%. What is the minimum r2 to prevent the arbitrage opportunities?

1 point

2.43%

2.00%

**2.96%**

2.79%

6.

Question 6

Next year ABC will pay a dividend of $2.4. Then the dividends are expected to grow at 3% a year. If you require a return of 14%, how much would you pay for the ABC stock?

1 point

$80.00

$14.11

**$21.82**

$17.14

7.

Question 7

The XYZ Company is not paying a dividend to its common stockholders this year because of the cumulative preferred dividend in arrears. However, in years 2 and 3 it will pay the common dividends of $1 and $3 respectively. Then the common dividends would grow at a rate of 2% a year.

The XYZ stock price is $20 per share. Your investment guidelines force you to avoid investments in similar stocks if returned less than 14% annually. Would you buy the XYZ stock at this price?

1 point

You just break even

Yes

Can’t say

**No**

8.

Question 8

Your investment guidelines require that you valued your investment in stocks in the following way. You take the 5-year horizon and discount the expected dividends in years 1 through 5 at the market rate. In valuing “the tail” you take DIV6, expect the dividends to flat out thereafter and use a conservative rate of 20% to discount the tail.

Suppose the dividends of the TYU Company for the first five years are forecasted to be $2, $3, $4, $5, and $6. DIV6 is estimated at $6.5. What would be your estimated return if the market price of the stock is $28?

1 point

16.26%

15.87%

15.61%

**16.77%**

9.

Question 9

Suppose for the TYU Company from Question 8 instead of the simplified formula from the investment guidelines you would use the correct DCF formula. For the same forecast of dividends, what would be now your estimated return if the stock price is still $28?

1 point

15.61%

**17.62%**

18.01%

16.53%

10.

Question 10

Suppose that the FGH Company is expected to generate an EPS1 of $10 and is not expected to grow. However, starting this year, the firm could invest in a 3-year long project that would require the investment of 60% of the EPS each year.

Each investment is expected to generate a permanent 25 percent return. In year 4, however, the project will be completed, and FGH will come back to the no growth case.

What will be the expected immediate increase in the FGH stock price after the announcement that it takes the project assuming that investors require a 15 percent rate of return on equivalent investments?

1 point

$ 6.91

The stock price will not change

$ 3.56

**$10.43**

**Week- 3**

**3 – The problems of IRR and the power of EAC**

1.

Question 1

The projects’ cash flows (in $) now and in Years 2 and 3 are as follows:

C0 C1 C2

– 400 2,000 -2,000

What is (approximately) the project’s IRR?

1 point

a. 38%

b. 261%

**c. Both “a” and “b”**

d. Can’t say

2.

Question 2

In terms of Question 1, what would be the project’s NPV if the opportunity cost of capital is 10% a year?

1 point

$0

$235

– $511

**– $235**

3.

Question 3

In terms of Question 1, at what opportunity cost of capital r would you take the project?

1 point

**38% < r < 261%**

r > 261%

Can’t say

0 < r < 38%

4.

Question 4

The projects’ cash flows (in $) now and in years 2 and 3 are as follows:

C0 C1 C2

-7,500 5,000 20,000

What would be the project’s NPV if the opportunity cost of capital is 30% a year?

1 point

$17,500

**$ 8,180**

$13,574

$10,555

5.

Question 5

The projects’ cash flows (in $) now and in Years 2 and 3 are as follows:

C0 C1 C2

2,000 2,000 – 5,000

What is (approximately) the project’s IRR?

1 point

13.7%

14.3%

**15.8%**

11.9%

6.

Question 6

In terms of Question 5, would you take the project if the opportunity cost of capital is 10% a year?

1 point

**No**

Can’t say

Yes

You are indifferent because the project’s NPV is 0

7.

Question 7

In our case of comparing the costs of the electric and the gas heating systems (see Lecture 3.11 and Handout 3.2) suppose that the cost of installation of the electric system increased to $1.4 million. Which system is now preferred?

1 point

Can’t say

We are indifferent

**The gas system**

The electric system

8.

Question 8

Suppose in our case of comparing the costs of the electric and the gas heating systems (see Lecture 3.11 and Handout 3.2) the cost of installation of the electric system stays at $1.2 million. At what the cost of installation of the gas system will we become indifferent between the two systems?

1 point

**$1.823m**

$1.798m

$1.752m

$1.842m

9.

Question 9

In our case of comparing the costs of the electric and the gas heating systems (see Lecture 3.11 and Handout 3.2) suppose that we use the accelerated depreciation system so that the annual depreciation charges as a percentage of the cost are as follows:

Year Depreciation (%)

1 20

2 40

3 15

4 15

5 10

On the basis of EAC, which system is now preferred?

1 point

Can’t say

**The electric system**

The gas system

We are indifferent

10.

Question 10

In terms of Question 9, at what the cost of installation of the gas system will we become indifferent between the two systems?

1 point

$1.798m

$1.817m

$1.842m

**$1.889m**

**Week- 4**

**4 – Returns, betas, and the cost of capital**

1.

Question 1

You believe that there is a 40% chance that stock A will decline by 10% and a 60% chance that it will rise by 20%. Correspondingly, there is a 30% chance that stock B will decline by 10% and a 70% chance that it will rise by 20%. The correlation coefficient between the two stocks is 0.7. If the portfolio consists of these two stocks equally weighted, what is the standard deviation of the portfolio returns?

1 point

**13.1%**

14.7%

13.7%

11.8%

2.

Question 2

An individual invests 60 percent of her funds in stock I and the balance in stock J. The standard deviation of returns on I is 10 percent, and on J is 20 percent. Calculate the standard deviation of portfolio returns if the correlation between the returns is –0.2.

1 point

10.92%

9.51%

10.47%

**8.99%**

3.

Question 3

Joan Smart has invested two-thirds of her money in General Mills stock and the remainder in Holly Sugar. On past evidence, the standard deviation is 20 percent for General Mills and 40 percent for Holly Sugar. Suppose the correlation between General Mills and Holly Sugar was –1.0. What is the standard deviation of Ms. Smart’s portfolio?

1 point

30.0%

26.6%

15.2%

**0%**

4.

Question 4

What is the standard deviation of a poorly diversified portfolio of stocks with an average β of 0.8?

1 point

Less than 0.8 times the standard deviation of RM

Can’t say

**More than 0.8 times the standard deviation of RM**

The same as the standard deviation of RM

5.

Question 5

The TYU Company has the following capital structure:

Security β Total Market Value, $ million

Debt 0 100

Preferred Stock 0.20 40

Common Stock 1.20 200

What is the firm’s asset β (i.e., the β of a portfolio of all the firm’s securities)?

1 point

0.45

0.62

**0.73**

0.56

6.

Question 6

In terms of Question 5, how will the asset β change if TYU issued an additional $140m of common stock and used the cash to repurchase all the debt and preferred stock?

1 point

**β will not change**

β will decrease

Can’t say

β will increase

7.

Question 7

In terms of Question 5, what discount rate should TYU set for investments that expand the scale of its operations without changing its asset β? Assume CAPM holds, any new investment is all equity-financed, RF = 7%, RM = 15%.

1 point

13.3%

13.0%

13.7%

**12.8%**

8.

Question 8

Portfolio C has an expected return of 12% and a standard deviation of 18%. Portfolio D has an expected return of 14% and a standard deviation of 20%. What should investors do, if they can borrow and lend at an interest rate of 8%?

1 point

Be indifferent between portfolios C and D

Can’t say without knowing investors’ degree of risk aversion

**Prefer portfolio D to portfolio C**

Prefer portfolio C to portfolio D

9.

Question 9

Which of these strategies will offer the same expected return as a stock with a β of 1.5?

1 point

Investing a third of money in Treasury bills and the rest in the market portfolio

Borrowing an amount equal to one-third of the own resources and investing everything in the market portfolio

**Borrowing an amount equal to one-half of the own resources and investing everything in the market portfolio**

None of the above

10.

Question 10

If a company uses the same company cost of capital for evaluating all projects, which of the following results is likely?

1 point

a. Accepting poor low risk projects

b. Rejecting good high risk projects

c. Both “a” and “b”

**d. Neither “a” nor “b”**

**Week- 5**

**5 – The many different faces of option valuation**

1.

Question 1

The current price of a share of stock is $40. The price of a 6-month European put option with the strike K = $60 is $22. What would be the price of the 6-month European call with the same strike if the riskless interest rate is 6% a year?

1 point

$1.00

**$3.77**

$5.54

$2.63

2.

Question 2

In our analysis of option valuation with the use of replication (see Lectures 5.3 – 5.4, Handout 5.2) suppose that SH = $130 and SL = $77 while the risk-free rate is 6% a year. What would be the delta of a one-year European put with the strike price of $105?

1 point

0.67

0.35

**0.53**

0.86

3.

Question 3

In our analysis of option valuation with the use of risk neutrality (see Lectures 5.3 – 5.4, Handout 5.2) suppose that SH = $125 and SL = $80 while the risk-free rate is 6% a year. What would be the implied volatility of the stock price movements?

1 point

25.0%

20.1%

**22.3%**

19.2%

4.

Question 4

In studying options in real investment projects, the most challenging task is:

1 point

**Identifying options**

Interpreting the options’ parameters

Using the Black–Scholes formula

All of the above

5.

Question 5

The Black–Scholes approach is poorly fit for valuing bond options because:

1 point

It assumes the constant risk-free rate

It assumes the constant price volatility

It works for European options only

**All of the above**

6.

Question 6

What is the yield to call for an 11% coupon bond, callable in 6 years at a call price of $1,055.00 and selling for $1,233.64?

1 point

7.1%

**6.9%**

6.6%

7.4%

7.

Question 7

The bond’s coupon rate is 7%. It yields 7% and has the maturity of 5 years. What will the bond’s price be if the interest rates went up by 100 basis points?

1 point

**$959.44**

$947.57

$955.12

$952.40

8.

Question 8

The bond’s coupon rate is 6%. It yields 7% and has the maturity of 3 years. What is the bond’s modified duration (in years)?

1 point

2.53

**2.69**

2.79

2.85

9.

Question 9

In terms of Question 8, what is the bond’s convexity (in years)?

1 point

20.96

83.84

35.51

**8.88**

10.

Question 10

What is the range of call option-adjusted duration (OAD) for a callable bond (DNCB is the duration of the corresponding non-callable bond)?

1 point

– ∞ < OAD < DNCB

**0 < OAD < DNCB**

DNCB < OAD < + ∞

– DNCB < OAD < DNCB

**Final Test**

1.

Question 1

The annual club membership costs $40,000 and is expected to increase by 3% a year. A life membership is $500,000 and the discount rate is 8%. In order to justify paying for the life membership, what is your minimum life expectancy?

2 points

10 years

15 years

25 years

**20 years**

2.

Question 2

The price of a Treasury bill maturing in six months is 95.23% of face value. The price of a Treasury note paying a coupon of 8% and maturing in one year is 97.25% of face value. What is a forecast of the 6-month rate 6 months from now?

3 points

5.5%

5.0%

**6.0%**

4.5%

3.

Question 3

How can one invest today at the 2-year forward rate of interest?

2 points

By buying a 1-year bond and selling a 2-year bond with the same coupon

**By buying a 2-year bond and selling a 1-year bond with the same coupon**

Can’t say

By buying a 1-year bond, then at t = 1 reinvesting in a further 1-year bond

4.

Question 4

Which of these strategies will offer the investor the same expected return as a stock with a β of 2.0?

2 points

Investing a third of his money in Treasury bills and investing the remainder in the market portfolio

Borrowing an amount equal to his own resources and investing everything in the market portfolio

**Borrowing an amount equal to one-half of his own resources and investing everything in the market portfolio**

None of the above

5.

Question 5

Consider the following market-value balance sheet:

Assets 200 50 Debt (D)

150 Equity (E)

200 200 Market Value (V)

βequity = 0.8 and the debt is risk-free. Now suppose this firm announces an issue of $120 of additional debt. All the proceeds of the debt issue are paid out as a special dividend. After the change, the market value of old debt falls to $40 and βdebt = 0.3. What is the new βequity?

2 points

2.0

**1.8**

2.4

0.9

6.

Question 6

Assume that “the market” consists of two stocks equally weighted. The expected returns, variances and covariances are:

Expected Return (%) Variance Covariance

11 15 5

19 18

What is the expected return on the market portfolio?

2 points

13%

14%

12%

**15%**

7.

Question 7

In terms of Question 6, what is the standard deviation of the market portfolio?

2 points

3.28

4.06

**3.08**

4.64

8.

Question 8

In terms of Question 6, assume that the risk-free rate is 6%. What portfolio mix of the market portfolio and riskless T-bills will provide an expected return of 12%?

2 points

**1/3 invested in T-bills and 2/3 invested in the market portfolio**

Can’t say

2/3 invested in T-bills and 1/3 invested in the market portfolio

1/2 invested in T-bills and 1/2 invested in the market portfolio

9.

Question 9

What is the β of the portfolio formed in Question 8?

2 points

**0.67**

0.50

1.00

0.33

10.

Question 10

The FEC Company has three different divisions:

Division Percentage of Firm Value

Food 30

Electronics 20

Chemicals 50

To estimate the cost of capital for each division, FEC has identified the following three principal competitors (assume that their debt is riskless):

Competitor Estimated: Equity β Debt: Debt + Equity

United Foods 0.8 0.4

General Electronics 1.6 0.3

Associated Chemicals 1.2 0.2

Assume risk-free rate of 6% and the expected return on the market portfolio of 15%.

What is the required rate of return for an across-the board expansion by FEC?

2 points

12.9%

13.6%

**14.2%**

12.1%

11.

Question 11

In terms of Question 10, if FEC’s debt-to-equity ratio is 0.6, and βdebt = 0.2, what is the β of FEC’s equity?

2 points

1.17

1.12

**1.24**

1.08

12.

Question 12

In terms of Question 10, FEC is contemplating a diversification into cosmetics. The analysis of a project in the cosmetics industry with an initial investment of $1 million that generated expected payoffs of $110,000 per year in perpetuity indicated that this project earned a fair rate of return. What is the β of projects in the cosmetics industry?

2 points

**0.55**

0.67

Can’t say

0.72

13.

Question 13

The Global Groceries has just dispatched a year’s supply of soft drinks to the Government of the Central Antarctic Republic. Payment of $100,000 will be made one year after. Unfortunately, there is a good chance of a coup d’etat, in which case the new government will not pay. Global’s controller decides to discount the payment at 40%, rather than at the company’s 12% cost of capital. How much is the $100,000 payment really worth if the chances of a coup d’etat are 25%?

2 points

**$66,964**

$71,429

$62,500

$89,285

14.

Question 14

The call option for a callable bond is worth $40 if the bond price is $1,050. If the bond price rises to $1,070, the value of the call option grows to $45. If the duration of the non-callable bond is 6.5 years, what is the call-adjusted duration?

3 points

5.6 years

5.0 years

5.2 years

**5.4 years**

**Peer-graded Assignment: The valuation of a real investment project – analyzing inputs, scenarios, sensitivity, and timing**