Högskolan i Borås Institutionen för Handels och IT-högskolan (HIT) Written Exam: CORPORATE FINANCE Day and Time: 013-11-30 09.30-14.30 Number of pages: 8 Check that You have got them all! The exam is on 10 questions. For Pass 50% is required and for Pass with Distinction 75% is required. Complete and correct solutions is required to get full score. Hand in earliest after 60 minutes. Pleae write your name and personal number on EACH paper. NOTE! Please write only on one side of the paper and only one answer on each paper. Name: Personal number: Score: Grade: Mark the questions You have answered! Question 1 3 4 5 6 7 8 8 10 Totalt Answered Question Maxïmum score 4 3 4 4 3 5 6 5 3 3 40 Score
1 Question 1. (4 points) a/ Spume Company is in the same risk class as Froth & Company. Spume has an expected dividend yield over the next year of 10 %, while Froth pays no dividends. The required return on Froth & Company is 0 %. Capital gains is not taxed, but dividends are taxed at 40 %. What is the required pre-tax return on Spume? b/ Now suppose that Spume`s dividend next year will be $10, and after paying dividend the stock will sell for $100. Froth`s current stock price is $50 per share, and shareholders expect next years price will be $60. Assume that dividends are taxed 40 %, and capital gains are taxed at 0 %. What is Spume`s current stock price? Question. (3 points) The XYZ Company has a perpetual EBIT of $ 60 million per year. The after-tax, all equity discount rate r U is 8 percent. The company`s tax rate is 30 percent. The cost of debt capital is 5 percent, and ABC has $450 million of debt in its capital structure. a/ What is ABC`s value? b/ What is ABC`s cost of equity (r E )? c/ What is ABC`s weighted average cost of capital (r WACC )? Question 3. (4 points) NYNEX, the phone utility for the New York area, has approached you for advice on its capital structure. In 004, NYNEX had debt outstanding of $1,14 billion and equity outstanding of $0,55 billion. The firm had earnings before interest and taxes of $1,7 billion, and faced a corporate tax rate of 36%. The beta for the stock is 0,84, and the bonds are rated A- (with a market interest rate of 7,5%). The probability of default for A- rated bonds is 1,41% and the bankruptcy cost is estimated to be 30% of firm value. a/ Estimate the unlevered value of the firm. b/ What Value the firm if it increases its leverage to 50% (D/A). At that debtratio, its bond rating would be BBB, and the probability of default would be,30%.
Question 4. (4 points) Calculate the expected return and the standarddeviation (=risk) for the stockportflio given below. Stock Portfolio share Expected return Standard- deviation Correlation Stock 1 between Stock the stocks Stock 3 Stock 1 40 % 15 % 0 % 1,0 0,3 0,4 Stock 30 % 0 % 30 % 0,3 1,0 0, Stock 3 30 % 5 % 40 % 0,4 0, 1,0 Question 5. (3 points) Over the coming years ragwort s stock price will halve to $50 from its current level of $100 or it will rise to $00. The one-year interest rate is 10 percent. a/ What is the delta of a one-year call option on Ragwort stock with an exercise price of $100? b/ In a risk-neutral world what is the probability that Ragwort stock will rise in price? c/ Use the risk-neutral method to check your valuation of the Ragwort option. Question 6. (5 points) Prosac Inc. issued a 9,5 percent convertible bond wich matures 10 years from now. The conversion price is $ 40 per share and the bonds are callable at 115%. The market price of the stock is $50 per share and the face value of the convertible bond is $10 000. a/ What is the conversion ratio of the bonds? b/ At the current market price for common shares, what is the minimum price at which you would expect the bond to sell? c/ If all other bonds comparable with those of Prosac were selling to a return of 8 percent and interest is payable annually, at what price would you expect the bond to be selling if it did not have the conversion feature? d/ Based on your answer in d/, what part of the bond`s total value depends on the conversion feature? e/ Should the financial manager of Prosac Inc, call the bonds? Why or why not? Question 7. (6 points)
3 The Cumulo & Nimbus Railroad is evaluating whether to lease or purchase a new locomotive, The locomotive, if purchased, will cost $1 00 000 and could be depreciated on a straight line basis over four years. If purchased, a local bank will provide a $1 00 000 loan at 10% to be paid back in four $300 000 principal payments plus interest on the outstanding balance. Principal and interest payments are paid at the end of each year. If leased, annual lease payments are $360 000 paid at the end of the year. Cumulo & Nimbus is in the 30% tax bracket. Assume that the locomotive will be worthless at the end of four years. a/ Calculate the NPV of the lease versus the purchase decision. Should Cumulo & Nimbus buy or lease the locomotive? b/ Calculate the reservation payment = break-even lease payment for Cumulo & Nimbus, the lessee (leasetagare). c/ Cumulo & Nimbus will lease the locomotive from a lessor (leasegivare) in the 40% tax bracket with a cost of debt equal to 10%. Calculate the reservation payment = break-even lease payment for this lessor (leasegivare). Question 8. (5 points) If stock X has a beta of 0,5 and an expected return of 7,5 %, and stock Y has a beta of 1,8 and an expected return of 0,5 %, What is than a/ The risk-free rate of return b/ The expected return of the market You are interested to know the capital cost of your company. You find out that the average beta-value for the stocks of a group of company in your business is equal to 1,9 and that their average debt to equity ratio is,0. Your company has a debt to equity ratio of,5. If the risk-free interest rate is 6 % and the riskpremium of the market portfolio is equal to 8 %: (Assume that the debt is risk-free) c/ What is the expected return for the assets of your company? d/ What is the expected return of the equity of your company?
4 Question 9. (3 points) True or false? The efficient-market hypothesis assumes that: a/ There are no taxes. b/ There is perfect foresight. c/ Successive price changes are independent. d/ Investors are irrational.. e/ There are no transaction costs. f/ Forecast are unbiased. Question 10. (3 points) True or false? a/ Convertible bonds are usually senior claims on the firm. b/ The higher the conversion ratio, the more valuable is the convertible. c/ The higher the conversion price, the more valuable is the convertible. d/ If a company splits its stock, the conversion price is increased. e/ Other things equal, if dividend payments rise, the convertible bondholders are more likely to convert before maturity. f/ Convertible bonds do not share fully in a rise in the price of the common stock, but they provide some protection against a decline.
5 FORMULAS Expected return of a stock portfolio - E[r p ]: (3 stocks) E[r p ] = X 1 E(r 1 ) + X E(r ) + X 3 E(r 3 ) Portfolio variance (σ P ) : (3 stocks) (σ P ) = X 1 σ 1 + X 1 X σ 1 + X 1 X 3 σ 13 + + X X 1 σ 1 + X σ + X X 3 σ 3 + + X 3 X 1 σ 31 + X 3 X σ 3 + X 3 σ 3 X 1, X och X 3 is respective stocks amount of the total of the portfolio. σ 1, σ and σ 3 is respective stocks variance σ 1 = σ 1 is the covariance between stock 1 and stock σ 13 = σ 31 is the covariance between stock 1 and stock 3 σ 3 = σ 3 is the covariance between stock and stock 3 value CAPM: E(r j ) = r f + β j [E(r m ) -r f ] E(rj) is the expected return of stock j E(rm) is the expected return of the market portfolio rf is the risk- free interest rate βj is the beta- value of stock j β j = Cov (rj,rm)/var(rm) = ρjm σ j σ m Stock j:s contribution to the risk of the portfolio β j =
6 MODIGLIANI & MILLER M&M Prop I. Without corporate taxes: V L = V U M&M Prop II. Without corporate taxes: r S = r U + (r U - r B ) M&M Prop I. With corporate taxes: V L = V U + T C B M&M Prop II. With corporate taxes: r S = r U + (r U - r B ) (1-T C ) r WACC = r B (1-T C ) + r S V L = V U = Value of the all equity financed firm (Unlevered firm) V L = Value of the Levered firm B = Value of the debt (bond value) S = Value of the equity (Stock value) T C = Corporate tax rate) r U = Required rate of return of an unlevered firm r S = Required rate of return of the Stocks r B = The cost of Bonds r WACC = Weighted Average Cost of Capital EBIT = Earnings before interest and tax
7 Beta and Leverage Without corporate tax βasset = βequity Equity/(Equity+Debt) + βdebt Debt/(Equity+Debt) if βdebt = 0 βequity = (Equity+Debt)/Equity βasset With corporate tax if βdebt = 0 βequity = [1 + (1- TC) Debt/Equity] βunlevered firm ADJUSTED PRESENT VALUE (=APV) APV = NPV + NPVF NPV = The value of the project to an unlevered firm NPVF = Net present value of the financing side effects FLOW TO_EQUITY APPROACH
The Black-Scholes option pricing model 8 1. S = Current stock price. E = Exercise price of call 3. r = Continuous risk-free rate of return (annualized) 4. σ = Variance (per year) of the continuous return on stock 5. t = Time (in years) to expiration date In addition, there is the statistical concept: N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d Put Call Parity Value of put = Value of call +Present value of exercise price-value of stock) P(E) = C(E) + E/(1+r) t S Annuityfactor (n years, r %) = Nusummefaktorn (n år, r %): [1 (1+r) -n ]/r