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

Advanced Corporate Finance Exercises Session 1 «  Pre-requisites: a reminder ». Professor Kim Oosterlinck E-mail: koosterl@ulb.ac.be. « Time value of Money, annuities » «  Bond & Equity Valuation » «  CAPM & Beta » . Q1. Buy a new house by borrowing

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

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  1. Advanced Corporate FinanceExercises Session 1 « Pre-requisites: a reminder» Professor Kim Oosterlinck E-mail: koosterl@ulb.ac.be

  2. « Time value of Money, annuities » «  Bond & Equity Valuation » «  CAPM & Beta »

  3. 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?

  4. Q1

  5. Q1

  6. 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)?

  7. Q2 Compounding Interval • Up to now, interest paid annually • If n payments per year, compounded value after 1 year : • Example: Monthly payment : • r = 12%, n = 12 • Compounded value after 1 year : (1 + 0.12/12)12= 1.1268 • Effective Annual Interest Rate : 12.68% • Continuous compounding: • [1+(r/n)]n→ern(e= 2.7183) • Example : r = 12% e12= 1.1275 • Effective Annual Interest Rate : 12.75%

  8. Q2 Should you do so?

  9. Q2 • What is then the PV of the borrowing at 3,6%? (annual) • Difference with the previous rate?

  10. Q3 • What is the quarterly equivalent of a continuous rate of 3%? • Continuous rate • Yearly equivalent (ra) • Quarterly (rq)

  11. « Time value of Money, annuities » «  Bond & Equity Valuation » «  CAPM & Beta »

  12. 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?

  13. Q4 • YTM (Yield To Maturity) of the bonds? • YTM = coupon/Price • Perpetuity : 5% / 95% = 5,26% • Level bond : 4% / 100% = 4%

  14. 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?

  15. 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)

  16. 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?

  17. 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?

  18. « Time value of Money, annuities » «  Bond & Equity Valuation » «  CAPM & Beta »

  19. 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!

  20. Q6: analyze the stock exchange • 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

  21. Q6: analyze the stock exchange • 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%!

  22. Q6: analyze the stock exchange • 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%

  23. Q6: analyze the stock exchange • 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

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