Advanced Corporate Finance Exercises Session 1 « Pre-requisites: a reminder »

Advanced Corporate FinanceExercises Session 1

« Pre-requisites: a reminder»

Professor Kim OosterlinckE-mail: [email protected]

mailto:[email protected]

« Time value of Money, annuities »

« Bond & Equity Valuation »

« CAPM & Beta »

Q1

• Buy a new house by borrowing• Able to repay 1500€ a month for a mortgage. • The monthly rate is 0.3% per month for a 30 years horizon. • In this case how much would you be able to borrow?

Q2

• The rate the bank is ready to give you: 0.3% per month. • He has seen an ad for a yearly rate of 3.6% and advises you to change. • Should you do so?

– Yearly equivalent rate of 0.3% per month? – What is then the PV of the borrowing (and the difference with the

previous rate)?

Q2 Compounding Interval

Up to now, interest paid annuallyIf n payments per year, compounded value after 1 year :

Example: Monthly payment :r = 12%, n = 12Compounded value after 1 year : (1 + 0.12/12)12= 1.1268Effective Annual Interest Rate : 12.68%

Continuous compounding:[1+(r/n)]n→ern (e= 2.7183)Example : r = 12% e12 = 1.1275Effective Annual Interest Rate : 12.75%

Q2

Should you do so?

Q2

• What is then the PV of the borrowing at 3,6%? (annual) • Difference with the previous rate?

Q3

• What is the quarterly equivalent of a continuous rate of 3%?

• Continuous rate

• Yearly equivalent (ra)

• Quarterly (rq)



« CAPM & Beta »

Q4 - Bonds

• 2 bonds outstanding: – a perpetuity, with a 5% coupon rate, and a 5 000 000$ face value.

Traded at 95% of par, the next coupon is due in exactly a year. – a level bond, issued exactly three years ago and should be reimbursed

in five years. Face value of 1 000 000$, pays a coupon of 4% and trades at par.

=> Issue a five year bond with a face value of 3 000 000$. • At which rate it could be issued (the rating agencies have told the company

that this issue would not change the rating of the company). • Would get a different interest rate if it considered issuing a perpetuity? • What are the yields to maturity for the perpetuity and for the five year

bond?

Q4

• YTM (Yield To Maturity) of the bonds?

– YTM = coupon/Price

– Perpetuity : 5% / 95% = 5,26%

– Level bond : 4% / 100% = 4%

Q4

• Issued the five year bond at 4% • One year after the issue, the interest rates have moved and the company

may now borrow at 3.5%. • New bond price?

Q5 – Equity Valuation

• Your mother is mainly invested in Total • No DCF theories - quick answer:

– Use a DDM framework: fast, easy (only cash is the dividend)

Core figures 2011 2012 2013

EPS 4,64 5,17 5,34

DPS 2,310 2,300 2,360

Ev/Ebitda 3,91 3,3 3,24

Adj P/E 8,35 7,49 7,25

Divi yield 5,96 5,94 6,09

Period Share price2007 58

2010 & 2011 46July 2011 32Jan 2012 42

Q5

• 5.1 What was the DDM value in 2007? – The next expected dividend was 2,1 (year 2008)– ROE was 16%– Payout 50%– Expected return was 9% for levered Total shares

– g = 16%*50% = 8%– P = 2,1 /(9% – 8%)– P = 217,5

• 5.2 Is this DDM value realistic?

Q5

– Historical dividend growth rate of 4%– Expected returns were more likely to be worth 8%

• 5.3 What is your DDM value now for 2007? How does this compare to the actual price of 2007?– g = 4%– P = 2,1 /(8% – 4%)– P = 52,5

• 5.4 For the recent period (2011-2013), can the dividend be paid out of earnings?



« CAPM & Beta »

Q6: analyze the stock exchange

• a) one of these companies should never be chosen. Which one? Why?

• Vinawine is inefficient => lower expected return than vinacoff but higher standard deviation!

Vinamelk Vinawine Vinacoff VinaTExpected return (re) 8% 12% 13% 14%

σe 20% 27% 26% 35%


• b) Diversify his portfolio. Investing part of his assets in a risk free state bond which yields 6% per year. What stock should he consider? Why?

• We use the Sharpe Ratio

• The higher, the better

Vinamelk Vinawine Vinacoff VinaTre 8% 12% 13% 14%sigma e 20% 27% 26% 35%Sharpe ratio 0,10 0,22 0,27 0,23


• c) The investor has decided to follow your advice and invest 50% in the risk free asset and 50% in the other stock. What is the expected return of his portfolio?

• What would the proportion invested in each asset be if he wants to have a 14% expected return?

– Ratio to invest in the stock: (14% - 6%) / (13% - 6%) = 114%– Borrow 14%!


• d) Investing in a diversified portfolio, the market portfolio. Why would he want to do so? The market portfolio has the following features: – expected return: rm 15% – σm = 30%.

Show that it is possible to obtain the same expected returns as above but for a lower risk.

– Ratio to invest in the market portfolio: (14% - 6%) / (15% - 6%) = 89%


• e) Beta. What does it represent? – What is the Beta of the market portfolio? – What are the Betas of the different companies? – What is the beta of the portfolio previously made?

• Beta: relative Volatility of an individual security compared to the Market

• B = (ri – rf) / (rm – rf)• <1• 1• >1

Advanced Corporate Finance Exercises Session 1 « Pre-requisites: a reminder »

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