ME2064 181026 Final Exam with answers PDF

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1

EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

KTH Industrial Engineering and Management

FINAL EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018, 8.00 - 12.00 A reminder!  Start the answer of a question on top of a new piece of paper!  Write your name and person number on top of all pages!  Try to answer all questions and explain your reasoning!  When you answer problems you need to: 1. show the equations that you use with correct symbol for variables (define variables only as needed) 2. show calculations 3. clearly show your answer.  All calculations should be handed in. No points for just an answer if calculations are needed. Deductions will be made if you don't state the equation.  Unreadable text will not be graded. Grading There are 10 questions with a total of 100 points For grade A 90 % out of 100 % is needed For grade B 80 % out of 100 % is needed For grade C 70 % out of 100 % is needed For grade D 60 % out of 100 % is needed For grade E 51 % out of 100 % is needed For grade Fx 48 % out of 100 % is needed, Fx can be upgraded to E by doing a supplementary exam. 47 % and below is F (fail).

CALCULATOR AND THE FORMULA SHEET HANDED OUT AT EXAM ALLOWED NO BOOKS, NO DICTIONARIES, NO NOTES

Most of all – stay focused, be systematic.

Best of Luck!

EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

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Problem 1a (Max 5 points) •

Banacob Inc. has a beta of 0,92. Assume the economy has a 75% chance of the market return will be 22% next year and a 25% chance the market return will be -13% next year. Assume the risk-free rate is 7%. – What is Banacob’s expected return next year?

•

Solution –

E[RMkt] = Sum (Probability of outcome x Expected return)

–

E[RMkt] = (75% × 22%) + (25% × (-13%=)) = 13,3%

–

E[R] = rf + β ×(E[RMkt] − rf )

–

E[R] = 7% + 0,92 × (13,3% − 7%) = 12,8%

Problem 1b (Max 5 points)

•

Answer the following questions related to the diagram for bonds below : – a. What are these types of curves called? – b. What is the profile of the 2006 curve called (downward slope)? – c. What is the profile of the 2008 curve called (upward slope)?

– d. What are Nominal interest rates?

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EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

– e. What are Real interest rates?

Solution: •

a. Yield Curves

•

b. Inverted Yield Curve

•

c. Increasing Yield Curve

Problem 2 (Max 10 points) •

Pacman and Tetris stocks have the historical annual returns shown in the table. – a) What are the expected returns and volatility for each of the two stocks? (6p) – b) What is the correlation between the two stocks? (4p)

•

Year

Pacman Return

Tetris Return

2009

-7%

-4%

2010

12%

-2%

2011

18%

22%

Solution –

Expected Return •

E[R] = (1/T) x Sum of observations(R)

EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

–

–

–

Ep (Pacman) = (1/3) x (-0,07 + 0,12 +0,18) = 0,085 = 7,7%

•

Et (Tetris) = (1/3) x (-0,04 - 0,02 + 0,22) = 0,085 = 5,3%

Variance •

–

•

4

VAR(R) = (1/(T-1) x Sum of observations ((R – E(R))^2 •

VARp= (1/(3-1)) x ((-0,07 – 0,077)^2 + (0,12-0,077)^2 + (0,18-0,077)^2) = 0,0170

•

VARt= (1/(3-1)) x ((-0,04 – 0,053)^2 + (-0,02-0,053)^2 + (0,22-0,053)^2) = 0,0209

Volatility = Standard Deviation •

SD (R) = (VAR(R))^0,5

•

SDp= 0,0063 ^0,5 = 0,131 = 13,1%

•

SDt= 0,0209 ^0,5 = 0,145 = 14,5%

Covariance •

COV(p,t) = (1/(T-1) x Sum of observations (((Rp - Ep(R))*(Rt- Et(R)))

•

COV(p,t) = (1/(3-1)) x ((-0,07 – 0,077)*(-0,04 – 0,053) + (0,12-0,077)*(-0,020,053) + (0,18-0,077)*(0,22-0,053)) = 0,0139

Correlation •

Corr (p,t) = COV(p,t)/(SDp*SDt) = 0,0139/(0,131*0,145) = 0,732

Problem 3a (Max 7 points) •

You are considering getting a race boat. The boat is expected to last for 10 years. There are two alternative. 1) You can buy the boat for $4000 up front and $6000 in 5 years; or 2) You are offered to pay $110 per month for 10 years. The interest rate for both alternatives is 10% APR with semi-annual (2 times/year) compounding. – Show which alternative is better

•

Solution – 1 + EAR = (1 + APR/k)^k = (1 + 0,1/2)^2 = 1,1025

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EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

– Annual rate EAR = 1,1025 -1 = 0,1025 = 10,25% – Monthly rate EMR = (1+EAR)^(1/12) -1 = 0,00817 •

Alt 1: – PV= C0 + C5/(1+EAR)^N1 = 4000+6000/(1+0,1025)^5= $7683

•

Alt 2: – PV=C x (1/EMR) x (1 – (1 / (1+EMR))^N2) = 110 * (1/0,00817) x (1 – (1 / (1+0,00817))^120) – PV = $8393

•

You should take Alternative 1.

Problem 3b (Max 3 points) •

•

Name the financial models that use the following equations

Div1 Div2   1  rE (1  rE ) 2

–

a)

P0 

–

b)

PV0 

–

c)

P0 



PV (Future Total Dividends and Repurchases) Shares Outstanding 0 V0  Cash0  Debt 0 Shares Outstanding0

Solution –

a) Dividend Discount Model

–

b) Total Payout Model

–

c) Discounted Free Cash Flow Model

Problem 4 (Max 10 points) •

DivN PN  N (1  rE ) (1  rE ) N

Answer with correct names for letters a to j below.

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EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

– Give the proper names for a to g in the graphs below (c, d, and e are labels on respective axis) ( b, c and g are the same in both charts).

a c

b

c

b

f

g

g

d

e

– Capital Asset Pricing Model CAPM has three main assumptions. State for h to j what words have been left out.

•

•

Investors can buy and sell all securities at ____h_______ market prices (without taxes or transactions costs) and can borrow and lend at the risk-free interest rate

•

Investors hold only ___i___ portfolios of traded securities—portfolios that yield the maximum expected return for a given level of volatility

•

Investors have ____j____ expectations regarding the volatilities, correlations, and expected returns of securities

Solution –

a) Capital Market Line

–

b) Market, Efficient or Tangent Portfolio

–

c) Expected Return

–

d) Volatility or Standard Deviation

–

e) Beta

EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

–

f) Security Market Line

–

g) Risk free investment

–

h) competitive

–

i) efficient

–

j) homogeneous

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Problem 5a (Max 7 points) •

You have the following bonds: a) A no default risk, 2-year, zero coupon bond with a risk free rate of 6% and face value of $2000. - What are the price and the yield to maturity of the bond? (show calculations) b) A risk of default, 2-year, zero coupon bond with face value of $2000. Risk free rate is 6%. Probability of default is 40%; if default it pays $1200, otherwise full face value. - What are the price and the yield to maturity of the bond? c) A certain default, 2-year, zero coupon bond with face value of $2000. Risk free rate is 6%. The bond issuer will pay 90% of the obligation. - What are the price and the yield to maturity of the bond?

•

Solution – a) P= FV / (1+YTM)^N = $2000 / (1+0,06)^(1/2) = $1780 •

YTM = (FV/P)^(1/N) – 1 = (2000 / 1780)^(1/2) -1 = 6% (same as risk free rate)

– b) P1 = $2000 x 0,60 + $1200 x 0,40 = $1680 •

P = P1 / (1+YTM1)^N = 1680 / (1+0,06)^2 = $1495

•

YTM = (FV/P)^(1/N) – 1 = (2000 / 1495)^(1/2) -1 = 15,7%

– c) P = P1 / (1+YTM1)^N = ($2000 x 0,90) / (1+0,06)^(1/2) = $1602 •

YTM = (FV/P)^(1/N) – 1 = (2000 / 1602)^(1/2) -1 = 11,7%

EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

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Problem 5b (Max 5 points) •

Breman SA has an enterprise value to EBITDA multiple of 7,8. The company has $190 million in debt, $3120 million in cash, EBITDA of $2460 million, and 300 million shares outstanding. – Estimate the value for a share of Breman stock.

•

Solution –

Using the enterprise value to EBITDA multiple, Breman’s enterprise value is •

V = EBITDA x EBITDA multiple = $2460 million x 7,8 = $19188 million.

•

V = E + D - Cash so E = V – D + Cash = 19188 -190 + 3120 = $22118 million

•

P = E / Number of shares = $22118 million / 300 million = $73,73

Problem 6a (Max 7 points) •

Andrea has a portfolio consists of two stocks; a short position of $19000 in Cools and a long position of $22000 in Birken. Correlation between the two stocks is 0,57. Birken has an expected return of 9% and volatility of 14%, while Cools has an expected return of 7% and volatility of 13% – Calculate the expected return and the volatility (standard deviation) for the portfolio.

•

Solution –

Total investment is $22000 – 19000 = $3000

–

Portfolio weights, xj = 22000/3000 = 7,33 xw = –19000/3000 = –6,33

–

E(Rp) = xb x E(Rb) + xc x E(Rc) = 7,33 x 0,09 + (-6,33) x 0,07 = 0,217 = 21,7%

–

SD(Rp) = [( xb^2 SD(Rb)^2) + ( xc^2 SD(Rc)^2) +( 2xbxcCorr(xb,xc) SD(Rb) SD(Rc)) ]^.5

–

SD(Rp) = [( 7,33^2 x 0,14^2) + ( (-6,33)^2 x 0,13^2) +( 2 x 7,33 x (-6,33) x 0,57 x 0,14 x 0,13) ]^.5

–

SD(Rp) = 87,6%

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EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

Problem 6b (Max 5 points) •

•

You want to buy a one-year call option and a one-year put option on Bell. The strike price for each is $17. The current price per share of Bell is $16,54. The risk-free rate is 6%. The price of each call is $3,43 –

Using put-call parity, what should be the price of each put?

–

Draw a diagram showing the resulting position of holding the two options at maturity. Show key data / crossing points.

–

For which stock prices is trade not profitable?

Solution –

Put-Call Parity states:

–

S + P = PV(K) + C

–

16,54 + P = 17/(1+0,06) + 3,43

: Price of Put P= $2,93

$17

$0 $-6,36 =(-2,93-3,43) 17-6,36=$10,64 17+6,36=$23,36



Trade is not profitable between $10,64 and $23,36.

 Problem 7 (Max 8 points) 

Fletch-B PLC expects to have free cash flow in the coming year of $X million, and its free cash flow is expected to grow at a rate of 4 % per year thereafter. The value of its

EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

interest tax shield is $18 Million. Fletch-B has an equity cost of capital of 16 % and a debt cost of capital of 6%. It maintains a debt-equity ratio of 0.5, and the corporate tax rate is 40%. o What is the free cash flow in the coming year ($X million) for Fletch-B?



Solution o

Pretax WACCu = [(E/(E+D)) x re] + [(D/(E+D)) x rd] 

o

= [(1/(1+0.5)) x 0,16] + [(0.5/(1+0.5)) x 0,06] = 0,1267 = 12,67%.

Aftertax WACCl = [(E/(E+D)) x re] + [[(D/(E+D)) x rd] x (1 – tauc)] 

WACCl = [(1/(1+0.5)) x 0,16] +[[(0.5/(1+0.5)) x 0,06] x (1 – 0,4)] = 0,1187= 11,87%

o

Vu = FCF/(WACCu – g) = $X Million / (0,1267 - 0,04) = $X/0,0867 Million

o

Vl = FCF/(WACCl – g) = $X Million / (0,1187 - 0,04) = $X/0,0787 Million

o

PV (Interest tax shield) = Vl – Vu = $18 Million

o

$18 Million = $X/0,0787 Million - $X/0,0867 Million

o

Free cash Flow X= $ 15,35 million

Problem 8a (Max 7 points) Provide the terminology that matches the definitions a to j below: a) A contract that gives its owner the right (but not the obligation) to purchase an asset at a fixed price as some future date b) A contract that gives its owner the right (but not the obligation) to sell an asset at a fixed price as some future date c) Options that allow their holders to exercise the option on any date up to, and including, the expiration date d) Options that allow their holders to exercise the option only on the expiration date e) Price at which an option holder buys or sells a share of stock at expiration f) State of firm that has difficulty meeting its debt obligations (but has not failed)

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EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

11

g) State of firm that fails to make the required interest or principal payments on its debt, or violates a debt covenant (condition). Debt holders are given rights to assets of firm. •

Solution a) Call Option b) Put Option c) American Option d) European Option e) Strike Price or Exercise Price f)

Financial Distress

g) Default

Problem 8b (Max 3 points) Regarding Bond prices and Bond trading. Fill in the blanks in a) and b), and answer c):  

a) When the bond price is greater than face value: We say the bond trades ****. b) When the bond price is equal to face value: We say the bond trades ****.



c) When the bond price is less than face value: Indicate how the Coupon rate relates to Yield to maturity?

Solution a) above par or at a premium b) at par c) less than

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EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

Problem 9 (Max 10 points)



Fixerb is considering launching a new product which they expect to sell during a 3 year period. Sales will be $50 million each year. Cost of Goods Sold will be 68% of sales. Additional selling costs will be $5 million per year (years 1 to 3).



Fixerb has to spend $6 million to buy equipment immediately (before they can start sales). The equipment has a three year life and straight line depreciation is used. After one year the company has to buy additional equipment for $2 million depreciated in straight line over two years. Tax rate is 30 %.



Receivables will be 20 % of current year’s sales and payables 15 % of current year’s cost of goods sold. Inventory of 5% of the following year’s sales are needed. - Calculate change in Net Working Capital for years 0-4. - Calculate incremental Free Cash Flows for years 0-4. - Calculate NPV of the new product (Fixerb’s cost of capital is 15%). - (Note: Show calculations in table. Show formulas used in table with variables.)

Year Sales

•

0

Solution

1 50

2 50

3 50

4 0

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EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

Year Sales Cost of goods sold Gross profit Selling Costs Depreciation EBIT Tax Net income + Depreciation Capital exp. Change NWC FCF

0

2 50 -34 16 -5 -3 8 2.4 5.6 3

3 50 -34 16 -5 -3 8 2.4 5.6 3

4 0 0 0 0 0 0 0 0 0

-6 -2.5 -8.5

1 50 -34 16 -5 -2 9 2.7 6.3 2 -2 -4.9 1.4

0 8.6

2.5 11.1

4.9 4.9

NWC (Berk/DeM) Receivables Payables Inventory Sum Change

0 0 2.5 2.5 -2.5

10 -5.1 2.5 7.4 -4.9

10 -5.1 2.5 7.4 0

10 -5.1 0 4.9 2.5

0 0 0 0 4.9

20% 15% 5%

PV of FCF NPV

-8.5 9.32

1.22

6.50

7.30

2.80

15%

0

0

68%

30%

Problem 10 (Max 8 points) •

Speziale SpA plans a recapitalization. The company plans to borrow $ 150m on a permanent basis and use the borrowed funds to repurchase outstanding shares. The tax rate is 40%. Other values are as given in table. – Fill the empty spaces in the table with correct values. Show calculations as appropriate below.

Market Value

Initial

Step1:

Step 2:

Step3:

Recap Announced

Debt Issuance

Share Repurchase

Balance Sheet ($ Million) Assets: Cash Original Assets Interest Tax Shield

0 500m 0

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EXAM COURSE ME2064 FRIDAY, OCTOBER 26, 2018

Total assets

500m

Liabilities: Debt

0

Equity

500m

Shares Outstanding

25m

Price per Share

$20

Calculations:

•

Solution

Market Value Balance Sheet ($ Million) Assets: Cash Original Assets Interest Tax Shield Total assets Liabilities: Debt Equity Shares Outstanding Price per Share

Initial

Step1:

Step 2:

Step3:

Recap Announced

Debt Issuance

Share Repurchase

0

0

150

0

500m

500

500

500

0

60

60

60

500m

560

710

560

0

0

150

150

500m

560

710

410

25m

25m

25m

18,3m

$20

$22,40

$22,40

$22,40

Tax shield (permanent debt) = Debt * Tax rate = 150m * 0,40 = 60m Number of shares purchased = Repurchase amount / Share price = 150m / 22,4 = 6,70 m Remaining outstanding shares = Initial number of shares - number of shares repurchased= 25 m - 6.70 m = 18,3 m New share price = Equity after repurchase / Remaining outstanding shares = 410 m / 18,3 m = $22,40...