Mathematic Finance


Problem 3
Joyful Smiles asks you to estimate its weighted average cost of capital. She is taxed
at the rate of 40%. You have the following information regarding its various funding
sources :
1) The company has a bank debt of $ 5,000,000 which it repays with annual
payments at an effective annual rate of 12%.
2) The company has just issued bonds with a maturity of 15 years that pay halfyearly
coupons. The total nominal value of these bonds is 25 million dollars. They
are currently selling for $ 1,200. Bonds of the same maturity could be issued at par
with a coupon rate capitalized semi-annually 14%. To issue these new obligations,
net issuance costs should be incurred tax of 4% of the nominal value ($ 1000).
3) The company has a total of 2 million preferred shares outstanding. These shares
are currently selling for $ 7 each and pay a quarterly dividend of $ 0.20. To issue
new preferred shares, issue fees should be $ 0.50 per share. These expenses would
qualify as a taxable expense.
4) The company has 4 million common shares outstanding. Their current price is $
15. Dividends on common shares are paid annually and grow at a rate constant of
10% annual workforce. The last dividend paid was $ 1 per share. Fees $ 0.40 per
share should be paid to issue new common shares. They would qualify as a taxable
1) What are the market values of each of the funding sources of the company?
2) What are the weights of each of the company’s sources of financing? (round
to three digits after the decimal point)?
3) What are the costs of each of the company’s sources of financing?
4) What is the weighted average cost of the company’s capital? (4 points)
Problem 4
You have a capital of $ 100,000. You want to build a portfolio from securities A and
B, both ordinary shares. You have the following information’s on these titles:
Possible Scenarios pro
probability of
title A
title B
Expansion 40% 40% 30%
Stability 35% 8% 15%
Recession 25% -10% -5%
1) What is the expected rate of return for each of the two stocks?
2) What is the standard deviation of returns for each security?
3) What is the covariance between titles A and B? You form a portfolio in
which you place $ 75,000 in Title A and $ 25,000 in the title B.
4) What is the expected return of this portfolio?
5) What is the standard deviation of this portfolio?
Problem 5
You are interested in the common shares of JBM, a company specialized in the
extraction and the sale of gold. A financial analyst gives you the following
Possible Scenarios Probability of
JMB title
Portfolio of M market
Expansion 55% 5% 15%
recession 45% 25% 5%
Rate of return on treasury bills
Standard deviation of the market
JBM standard deviation 9.950%
1) What is the covariance between the JBM stock and the market portfolio?
2) What is the correlation coefficient of the JBM stock with the market
3) What is the beta of the JBM title?
4) Calculate the expected return of the JBM security according to the
theoretical formula of the CAPM (CAPM).
Compare it to the expected performance observed (inferred from the table
data upper). Is the JBM title overvalued or undervalued? You are building a
portfolio in which you place 50% of your funds in the title JBM, 20% in
Treasury bills and 30% in a title named KLM which presents the same
characteristics in terms of risk and expected return than the market
5) What is the expected return of this portfolio?
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