Corporate Finance

Question 1– True or False (20 points) 

Part A (2.5 points): Adding risk-free bonds to the risky portfolio increases its Sharpe ratio, because they add zero volatility, while bringing positive returns at the same time.

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True

False

 

Explain your answer.

 

Part B (2.5 points): If two stocks have the same volatility, but one of them has a higher expected rate of return, that would be a violation of CAPM.

True

False

 

Explain your answer:

 

Part C (2.5 points): An upward sloping yield curve presents clear arbitrage opportunities and mispricing of the bonds; one can exploit it by investing in high yield long-term bonds, while borrowing at the lower short term interest rate.

 

True

False

 

Explain your answer:

 

Part D (2.5 points): The average annual inflation-adjusted return on gold is historically only 1.1%, while being 7.4% for equities. The volatility of gold is also 50% higher than that of stocks. Gold is dominated in both risk and return by stocks, and therefore, should never be a part of an optimal portfolio.

 

True

False

 

Explain your answer:

 

Part E (2.5 points): Choosing a project with the highest Internal Rate of Return always implies going for the investment that creates most value for shareholders.

 

True

False

 

Explain your answer:

 

Part F (2.5 points): Investing in a specific company stock is riskier than investing in an index mutual fund.

 

True

False

 

Explain your answer:

 

Part G (2.5 points): When interest rates increase, bond prices tend to go up as well.

 

True

False

 

Explain your answer:

Part H (2.5 points): Other things being equal, growing Net Working Capital tends to increase Free Cash Flows and the overall value of the firm.

 

True

False

 

Explain your answer:

 

Question 3– Annuities (40 points)

 

Morton Gage (his best friends call him Mort) is a loan officer at a large bank in Kent.  He has been discussing the terms of a twenty-year mortgage his bank is prepared to offer to Savi Baurer. Morton is offering Savi a 20 year mortgage having a 5.5% APR (with monthly compounding) and monthly payments equal to £4,471.27. According to the mortgage contract, Savi would need to make 240 monthly payments, each equal to £4,471.27.

 

 

Part A (5 Points): Given that the twenty-year loan has a 5.5% APR with monthly compounding and the monthly payments are £4,471.27, what is the amount Morton’s bank is loaning Savi? In other words, what is the loan value?

 

The loan value is:

_______________________________________________________________

 

Show all your work:

 

Part B (5 Points): Savi tells Morton that she would like to make higher monthly payments in the first ten years so that she can make lower payments in the last ten. She is proposing that her first 120 payments be set at £5,200 and is asking Morton what this will mean for the level of her last 120 payments.  To be precise, she is proposing that her first 120 payments be set at £5,200 and her last 120 be set at £X. She wants to know what £X will be, so that making 120 payments at £5,200 followed by 120 payments at £X is the same as making 240 payments at £4,471. The APR is still 5.5%.  What is the monthly payment level Savi must make in the last ten years if she pays £5,200 in the first ten?

 

 

Savi’s monthly payment for the last ten years will be: __________________________________

 

Show all your work:

 

Question 4– CAPM (10 points)

 

Suppose you know the following information from the financial markets:

 

Asset Expected return Volatility
Risk-free bonds 2% 0
Market portfolio 8% 15%
Orion stock 10.4% 30%

 

 

Part A (5 points): What is the beta of Orion?

 

The beta of the company is _____________________________________.

 

Show your work.

 

 

 

 

Part B (5 points): What is the correlation between the return of Orion shares and that of the market portfolio?

 

The correlation is ____________________________________.

 

Show your work.

 

 

 

 

Question 5– Portfolio optimization (20 points)

 

The CEO of MiM Inc., I.C. Pearl, has a portfolio (“goodR”) that she expects to generate returns of 12% with a standard deviation of 15%. She has the opportunity to move a fraction of her wealth into a new investment (“highVol”) that she expects to generate returns of 20% with a standard deviation of 35%.  The risk free rate is 5%, and the correlation between the returns in “goodR” and “highVol” is 0.30.  Assume that she can borrow and lend at the risk free rate.

 

 

Part A (4 points): Find the Sharpe ratios of the current portfolio and suggested investment.

 

The Sharpe Ratio of the portfolio “goodR” is ________________________.

The Sharpe Ratio of the portfolio “highVol” is _______________________.

Show all your work.

 

Part B (5 points): What is the expected return, volatility and Sharpe ratio of the portfolio that is equally split between “goodR” and “highVol” (50/50)?

 

The expected return of this portfolio is _________%, its volatility is _________%, and

 

its Sharpe ratio is _______________________.

 

Show all your work.

 

Part C (5 points): What is the optimal allocation between the current portfolio (“goodR”) and this new investment (“highVol”)?

 

The optimal weight on the current portfolio is  ______________________________.

The optimal weight on the new investment is _______________________________.

Sharpe Ratio of such a portfolio is _______________________________________ .

Explain your answer.

 

Part D (6 points): CEO wants to mix this optimal portfolio with risk-free bonds such that the standard deviation of her new investment was 5%. How much should she invest in “goodR”, “highVol”, and risk-free bonds?  Risk-free bonds have no risk (volatility or correlation with other assets).

 

She would invest   __________ in risk-free bonds, __________ in portfolio “goodR,” and _______________ in portfolio “highVol.”

Explain your answer.

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