Högskolan i Borås Institutionen för Handels och IT-högskolan (HIT) Written Exam: CORPORATE FINANCE Day and Time: 2013-11-30 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 2 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 20 %. 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 20 %. What is Spume`s current stock price ? Question 2. (3 points) The XYZ Company has a perpetual EBIT of $ 60 million per year. The after-tax, all equity discount rate rU 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 (rE)? • c/ What is ABC`s weighted average cost of capital (rWACC) ? Question 3. (4 points) NYNEX, the phone utility for the New York area, has approached you for advice on its capital structure. In 2004, NYNEX had debt outstanding of $12,14 billion and equity outstanding of $20,55 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 debt-

ratio, its bond rating would be BBB, and the probability of default would be 2,30%.

2

Question 4. (4 points)  Calculate   the   expected   return   and   the   standarddeviation   (=risk)   for   the  stockportflio  given  below.      

 Stock  

Portfolioshare  

Expected  return  

Standard-­‐deviation  

Correlation  Stock  1  

 between  Stock  2  

the  stocks  Stock  3  

Stock  1   40  %   15  %   20  %   1,0   0,3   0,4  Stock  2   30  %   20  %   30  %   0,3   1,0   0,2  Stock  3   30  %   25  %   40  %   0,4   0,2   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 $200. 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 $1 200 000 and could be depreciated on a straight line basis over four years. If purchased, a local bank will provide a $1 200 000 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 20,5 %, 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 2,0. Your company has a debt to equity ratio of 2,5. 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[rp]: (3 stocks) E[rp] = X1 ∗ E(r1) + X2 ∗ E(r2) + X3 ∗ E(r3) Portfolio variance (σP)2 : (3 stocks) (σP)2 = X1

2 ∗ σ12 + X1∗ X2∗σ12 + X1∗ X3∗σ13 +

+ X2∗ X1∗σ21 + X22 ∗ σ2

2 + X2∗ X3∗σ23 + + X3∗ X1∗σ31 + X3∗ X2∗σ32 + X3

2 ∗ σ32

where:

X1 , X2 och X3 is respective stocks amount of the total value of the portfolio. σ1

2 , σ22 and σ3

2 is respective stocks variance σ12 = σ21 is the covariance between stock 1 and stock 2 σ13 = σ31 is the covariance between stock 1 and stock 3 σ23 = σ32 is the covariance between stock 2 and stock 3 CAPM: E(rj) = rf + βj ∗ [E(rm) -rf] where:   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    

βj  =  Cov  (rj,rm)/var(rm)  =  ρjm  ∗  mσσ j  

 Stock  j:s  contribution  to  the  risk  of  the  portfolio    

  βj    =    

6

MODIGLIANI & MILLER M&M Prop I. Without corporate taxes: VL = VU M&M Prop II. Without corporate taxes:

rS = rU + (rU - rB) ∗

M&M Prop I. With corporate taxes: VL = VU + TC ∗B M&M Prop II. With corporate taxes:

rS = rU + (rU - rB) ∗ ∗(1-TC)

rWACC = rB ∗(1-TC) + ∗ rS

VL =

where: VU = Value of the all equity financed firm (Unlevered firm) VL = Value of the Levered firm B = Value of the debt (bond value) S = Value of the equity (Stock value) TC = Corporate tax rate) rU = Required rate of return of an unlevered firm rS = Required rate of return of the Stocks rB = The cost of Bonds rWACC = 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    where:  NPV      =  The  value  of  the  project  to  an  unlevered  firm  NPVF  =  Net  present  value  of  the  financing  side  effects    FLOW  TO_EQUITY  APPROACH    

 

 

8

The Black-Scholes option pricing model

where:

1. S = Current stock price 2. E = Exercise price of call 3. r = Continuous risk-free rate of return (annualized) 4. σ2 = 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