Important! Do not forget to write the ExamCode on each paper you hand in.

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1 Corporate Finance 7.5 ECTS Ladokcode: 1FT1C The exam is given to: ExamCode: Date of exam: Time: Means of assistance: Calculator Total amount of point on exam: 40 points Requirements for grading: To get respective grade the the following points is required: < 0 points = FX = U 0 points = E = G points = D 6 points = C 30 points = B = VG 34 points = A Next re-exam date: Exact date not decided yet The marking period is, for the most part, 15 working days, otherwise it s the following date: Important! Do not forget to write the ExamCode on each paper you hand in. Good Luck! Examiner: Urban Österlund Phone number:

2 1 Question 1. (6 points) Use the following information for stock C and for the market portfolio to solve the following questions. State of the economy Rapid growth Moderate growth Normal growth Recession Probability of state 0,10 0,0 0,50 0,0 Return on C 0,5 0,10 0,15-0,1 Return on market 0,18 0,0 0,04 0,00 a/ What is the expected return for stock C and for the market portfolio? 1p b/ What is the standard deviation for stock C and the market portfolio? p c/ What is the covariance and the correlation between stock C and the market portfolio? p d/ Calculate the beta-value for stock C. 1p Question. (5 points) The Sabine Corporation has 1,6 million shares outstanding with a current price of $5 per share. The firm also has $0 million face value long term debt and $6 million face value short term debt outstanding. The long term debt matures in 19 years, has a 10% coupon, and is presently priced at $1 089,50 per bond. The yield to maturity of the long term debt is 9% and each bond has a face value of $ The short term debt matures in three years, has an 8% coupon, and each bond is priced att $1 054,46. The yield to maturity of the short term debt is 6% and each bond has a face value of $ When the debt matures, new similar maturity debt will be issued in such amounts to maintain the same proportions of debt-to-value. The firm pays a $5,00 dividend per share, and this is not expected to change in the foreseeable future. The tax rate is 34%. a/ Calculate Sabine Corporations weighted average cost of capital (r WACC ). b/ Calculate Sabine Corporations unlevered cost of equity (r U ).

3 Question 3. (4 points) A stock has a beta of 1,4 and an expected return of 14 percent. A risk-free asset currently earns 4 percent. a/ What is the expected return on a portfolio that is equally invested in the two assets? b/ If a portfolio of the two assets has a beta of 0,84, what are the portfolio weights? c/ If a portfolio of the two assets has an expected return of 8 percent, what is beta? Question 4. (3 points) The NOGROWTH 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 NOGROWTH has $450 million of debt in its capital structure. a/ What is NOGROWTH`s value? b/ What is NOGROWTH`s cost of equity (r E )? c/ What is NOGROWTH`s weighted average cost of capital (r WACC )? Question 5. (6 points) The Cumulo & Nimbus Railroad is evaluating whether to lease or purchase a new locomotive, The locomotive, if purchased, will cost $ and could be depreciated on a straight line basis over four years. If purchased, a local bank will provide a $ loan at 10% to be paid back in four $ 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 $ 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.

4 3 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 6. (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 7. (4 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.

5 4 Question 8. (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 $ 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 9. (3 points) Fill in the missing words!!! (0,5 points per question) a/ An option that can only be exercised on the day it matures is a option. b/ An option that can be exercised anytime up to the day it matures is an option. c/ Professional money managers, as a group, cannot outperform market indexes. This fact is consistent with the form of the efficient market hypothesis. d/ The is the efficient set for all assets. e/ An examination of the behavior of security returns following an announcement of new information is called an. f/ For the market model, the line that relates expected returns to betas for the single factor is called the.

6 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 X X 1 σ 1 + X σ + X X 3 σ X 3 X 1 σ 31 + X 3 X σ 3 + X 3 σ 3 where: 3 3 X 1, X och X 3 is respective stocks amount of the total value 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 σ 3 = σ 3 is the covariance between stock and stock CAPM: E(r j ) = r f + β j [E(r m ) -r f ] where: E(r j ) is the expected return of stock j E(r m ) is the expected return of the market portfolio r f is the risk-free interest rate β j is the beta-value of stock j β j = Cov (r j,r m )/var(r m ) = ρ jm σ j σ m Stock j:s contribution to the risk of the portfolio σjp β j = X σ j p

7 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 ) B S 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 ) B S (1-T C) r WACC = B (B + S) r B (1-T C ) + S (B + S) r S EBI T (1 - T ) C V L = R WACC where: 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

8 7 Beta and Leverage Without corporate tax β asset = β equity Equity/(Equity+Debt) + β debt Debt/(Equity+Debt) if β debt = 0 β equity = (Equity+Debt)/Equity β asset With corporate tax if β debt = 0 β equity = [1 + (1-T C ) Debt/Equity] β Unlevered firm ADJUSTED PRESENT VALUE (=APV) APV = NPV + NPVF where: NPV = The value of the project to an unlevered firm NPVF = Net present value of the financing side effects FLOW TO_EQUITY APPROACH Cash flow from project to equityholders of the levered firm r S

9 The Black-Scholes option pricing model -rt C = S N(d ) - E e N(d ) ln S E r + 1 σ where: d 1 = σ t t d = d - 1 σ t 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

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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