Answer ALL questions in this section. (Questions 1 to 5)

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FIACIAL MAAGEMET ISTRUCTIOS TO CAIATES. CAIATE I o:. EXAM PAPER IS TO BE HAE I ITACT ISIE YOUR ASWER SCRIPT BOOKS AT COCLUSIO OF EXAM. 2. REAIG TIME IS OF 0 MIUTES URATIO 3.

1 FIACIAL MAAGEMET ISTRUCTIOS TO CAIATES. CAIATE I o:. EXAM PAPER IS TO BE HAE I ITACT ISIE YOUR ASWER SCRIPT BOOKS AT COCLUSIO OF EXAM. 2. REAIG TIME IS OF 0 MIUTES URATIO 3. EXAMIATIO IS OF 3 HOURS URATIO 4. This paper cosists of 7 questios. PLEASE CHECK BEFORE COMMECIG. 5. This is a FIAL paper. 6. THIS IS A OPE BOOK EXAM. All material icludig Electroic had held calculators is permitted exceptig for laptop computers, ad mobile phoes. 7.Please read istructios at the top of each sectio carefully before aswerig. A set of Formulae is icluded at the ed of the exam paper for referece. Please also use the Mathematical Tables eeded for computatio from those provided i stadard textbooks if required. 7. Aswer all questios i Part A (questios to 5) ad three questios i Part B (questios 6 to 0). Aswers for Questios should be writte o the space provided, ad the questio paper must be attached to the script book alog with the rest of the exam paper. 8. EXAM PAPER IS TO BE HAE I ITACT AT COCLUSIO OF EXAM. Questio (5 Marks) PART A (40 Marks) Aswer ALL questios i this sectio. (Questios to 5) Select the oe most appropriate correct respose by placig a cross (X) i the cell i the table below for questios. to.5. Each questio carries oe mark. You may do the workig o the questio paper. Questio a b c d e Page of 8

2 . Assume you are evaluatig capital budgetig projects for your compay. Which of the followig is ot a relevat cosideratio for decidig o which project you may wat to choose? a. The chage i the firm s fixed assets b. The chage i the firm s variable costs c. The chage i the firm s depreciatio expese d. The chage i the firm s overhead expese e. oe of the above..2 The expected log-ru retur i a share market is 6% i Hog Kog, where the market risk premium is 8.5%. Usig the market risk premium, what is the risk-free rate of retur for Hog Kog? a. 4.5% b. 7.5% c. 0.0% d. 0.5% e. 2.5%..3 The Securities Market Lie i the CAPM is about: a. Expected retur of a security to the stadard deviatio of a security b. Expected retur of securities to expected retur of portfolios c. Efficiet set of portfolios to the risk-free rate of retur d. Expected retur to the beta ad the market risk premium e. Stadard deviatio to the systematic risk..4 The compay s capital structure refers to: a. The way a compay ivests its assets b. The amout of equity or capital i the compay c. The amout of divideds a compay pays d. The way i which a compay s assets are fiaced e. How much cash the firm holds..5 A compay s debt-to-equity ratio is.00. If it had o debt, its cost of equity would have bee 4%. However, the compay has debt, ad its cost of debt is 0%. What is its cost of equity if there are o taxes or other imperfectios? a. 8% b. 6% c. 4% d. 2% e. oe of the above..6 Whe a firm issues more debt, the tax shield o debt, the agecy costs o debt (i.e. the cost of fiacial distress), ad the agecy cost of equity. a. Icreases; icreases; icreases b. ecreases; decreases; decreases c. Icreases; icreases; decreases d. ecreases; decreases; icrease e. Icreases; decreases; decreases..7 S-mail Pty Ltd has capital value (debt ad equity of $000 millio. The debt is valued at $400 millio. The cost of debt ad equity respectively are 2% ad 5%. Which of the followig is closest to the required rate of retur applicable to the S-mail? (Assume there is o tax shield.) a. 3.2% b. 3.5% c. 3.8% d. 27.0% e. oe of the above. Page 2 of 8

3 .8. The Lucky Compay s corporate tax rate is 36%. It has riskless debt i its capital structure, which makes up 40% of the total capital structure ad equity is the other 60% of the total capital structure. The beta of the assets for this busiess is 0.8. Which of the followig is closest to the value of equity beta of this compay? a b c d..4 e If the ivestor i the commo stock of a compay pays persoal icome tax at the rate of 33% ad the compay aouced a divided amoutig to $3.00: What is your expectatio cocerig the price of the stock? a. The price of the stock should decrease by $2.00 o the date of record (book closig) b. The price of the stock should decrease by $2.00 o the ex-divided date c. The price of the stock should decrease by 4.48 o the date of record d. The price of the stock should decrease by $4.48 o the ex-divided date e. Both b ad c..0 A ew issue of commo stock by a already listed public firm is called a/a: a. Iitial public offer b. Seasoed equity issue c. Useasoed equity issue d. Private placemet e. A sydicated issue.. Which of the followig would ot geerally be icluded i a typical bod issue? a. The basic terms of the bod issue b. etail of the protective coveats to esure o defaults c. Sikig fud arragemets d. Call provisios e. All of the above would geerally be icluded..2 A firm has 00 commo stocks ad 40 warrats outstadig: each warrat gives a right to buy 2 shares at $5 per share. The warrats issued five years ago are about to expire ad the warrat holders have decided to exercise the warrats. Which of the followig is earest to the price per share of the commo stock? a. $5.00 b. $7.78 c. $. d. $20.00 e. oe of the above..3 Suppose that Coles Myer ad Woolworths (Two large departmet stores i Australia) are goig to merge. Igorig potetial implicatios for competitio, the merger will be classified as a: a. iversifyig merger b. Horizotal merger c. Coglomerate merger d. Vertical merger e. oe of the above. Page 3 of 8

4 .4 Workcover Australia (a Isurace scheme for workplace accidets) awarded a ijured worker four paymets of $50,000 to be paid at the ed of each of the ext 4 years. The persoal opportuity cost to this worker is 4%. Which of the followig amouts is closest to the preset value of these paymets? a. $78,495 b. $84,095 c. $8,495 d. $73,255 e. $200, The mea ad variace of two potetial capital budgetig projects are: Project A (mea = 4.4% & variace = 0.584) ad Project B (mea = 4.6% & variace = ). The total ivestmet i the two projects is $00 millio, of which project A is $50 millio. Compute the expected retur ad stadard deviatio of these two projects udertake. Which of the followig are closest to the values you have computed: a %; 37.2% b. 4.50% ; 5.48% c. 8.00% ; 8.20% d. 5.00% ; 0% e. 4.50% ; 0%. Questio 2 (0 marks) Roha Khamis was give a fiacig problem to solve by the Cotroller of Weiss Egieerig. Weiss Egieerig is plaig to raise moey usig a public ote issue. This is what Roha has oticed i the market for otes of similar risk class: oe-year ote yields 5%; 2-year otes yield 5.4%; 3-year otes yield 5.70; 4-year otes yield 5.90; ad 5-year otes yield 6%. If the compay raises moey usig otes issues of differet years, Roha eeds to compute the market price to estimate how may bods eed to be issued to raise a give udisclosed sum of moey to be raised. (i) Explai what a ote issue is. (2 marks) (ii) Compute the likely prices of a 2-year ad a 5-year ote issue. (iii) If the sum of moey to be raised is $20 millio, how may 2-year otes have to be issued? Assume that there is o fee to be icurred to raise this moey. Questio 3 (5 marks) Jim s Gardeig ca purchase a piece of equipmet for $3,600. There is o salvage value for this equipmet after its two-year life. The equipmet has two years life, ad will yield profits of $600 i year oe ad $4200 i year two. Jim s Gardeig applies 5% as the average cost of capital for all its projects. (i) Compute the project s omial payback ad discouted payback i years. (2 marks) (ii) Compute the project s et preset value ad profitability idex. (3 marks) Page 4 of 8

5 Questio 4 (0 marks) You are a aalyst employed by Merryweather Trust. You are give the followig iformatio o the Australia market: With the Reserve Bak s actios recetly, the Treasury yield is as low as 4%. The market yield has bee dowgraded to 2%. Your traiig idicates that this problem requires the applicatio of the CAPM. (i) Estimate the market s risk premium suggested by this sceario. (2 marks) (ii) If the Trust is plaig to ivest i a compay with a beta of.5, what is the expected retur for this ivestmet? (iii) Aother firm you chose to ivest i has a expected retur of.2%. What would you expect its beta to be? Questio 5 (20 Marks) PART B (60 Marks) Aswer ay three questios i this sectio. (Questios 5 to 8) You are the fiacial cotroller of a bak. You assig Mr Robert Jarvis (a staff) a capital structure problem to evaluate. Here is the work carried out by Robert o two importat cliet firms of the bak: Cliets Mea retur Std deviatio R-squared beta Stadard error of beta Firm A s commo stock 6% 6% Firm B s commo stock 4% 2% The above risk estimates show i the table were computed usig historical iformatio over a busiess cycle. The bak is iterested i moitorig the two cliets risk profiles sice both cliets have large borrowigs from the bak. (i) What is the relative risk-adjusted performace of the two cliet firms? Explai your aswer usig the risk ad retur framework.. (ii) Which of the cliets stock prices were most closely related to the stock market? Estimate the proportio of stock s retur accouted for by the market, ad explai givig oe reaso why the differece may exist. (iii) Usig the theory o total risk, what are the firm-specific risk values of the two cliets? Explai oe source for this firm-specific risk (3 marks) (iv) What are the theoretical expected returs usig the CAPM with 5% R f. (6 marks) (v) Suppose the retur i the market ext year is equal to zero. What returs would you expect your cliet firms stocks to yield? Explai why this is a possibility ex post. (3 marks) Questio 6 (20 Marks) Bob Price is the fiacial cotroller of a Melboure-based compay. He recruited a ew CMA, Mr Shakar, for the capital maagemet divisio of the compay. Just prior to the recruitmet of Shakar, Bob has already got the board s i-priciple approval to go ahead with a ivestmet that will cost a udisclosed sum of moey. Bob is woderig whether to issue a cosol or a straight coupo-payig bod to raise the sum of moey for the project. Here are the details: Page 5 of 8

6 If it is a cosol, the coupo offered per year will be $50. A similar class of coupo-payig cosols are sellig at a average price of $500 per cosol. The iterest rate is expected to remai the same over the ext 6 moths eeded to arrage the issue. The alterative is to issue a 5-year term bod with a coupo of $00 per year to fetch a price equal to the face value of $,000. Bob is aware that the iterest rates are likely to go up i the ext 6 moths, as the expected ecoomic growth rate of 4.4% will put pressure o the iterbak market. (i) (ii) (iii) Compute the cost of capital to the compay for the two fiacig alteratives? If the iterest rate remais the same over the ext 6 moths, what would Shakar recommed to Bob about the two forms of fiacig? Explai. (7 marks) Assume the Reserve Bak is likely to icrease the iterest rate by 2 percetage poits i six moths time. I that evet, what would Shakar s recommedatio be? Explai. (9 marks) Questio 7 (20 Marks) Roy Toratio has bee assiged to a merger aalysis group for the evaluatio of a curret proposal. The two firms ivolved i the merger proposal, Compay A ad Compay B, are curretly valued as separate compaies at $500 ad $00 respectively. Both firms are i steel productio i SW, ad a substatial syergistic gai is expected from a ew proprietory smeltig techique developed by Compay B. The gai expected is from the lower cost of smeltig at $20 per to usig this process compared with the Compay A s $60 per to. Give this gai, the combiatio of the two compaies will be worth $700. Roy was iformed that the Board of Compay B wats $50 i cash (assume cash is a alterative i this merger). Compay A has sufficiet retaied earigs to fiace the project. There are 25 shares i Compay A. (i) What is the syergy value of this merger? (3 marks) (ii) What is the premium for the merger ad the et gai from merger? (3 marks) (iii) What is the per share value of A before merger? (3 marks) (iv) If there are 0 shares outstadig i Compay B, ad the exchage is 7.5 shares of A-shares for oe share of B, what is the share value of the merged firm? ( marks) I all of the above computatios, show your workigs, ad explai the relevat theory. Questio 8 (20 Marks) Irvi Levy has just set up a compay i a coutry, which has exempted the compay from payig corporate tax, but iterest costs are still deductible as expeses. Assume the compay is about to commece operatios ow, ad will close dow at the ed of oe year. Thereafter the firm will be take over by local ivestors at o cost (this is the icetive for givig tax exemptio). Irwi estimates that the sale of goods brought ito the coutry will yield a immediate profit of $0,000 ow. At the ed of oe year, the profits will be aother $0,000. Irvi has to decide o how much divideds to pay to himself ad to the other parters of this firm. There are presetly 0,000 shares outstadig with o debt at all i the compay s capital structure. (i) (ii) (iii) What is the per share value of this compay before ay decisio is made to pay divideds? (6 marks) If Irvi had declared a divided of $0,000, what is the value per share of this compay if the firm paid $0,000 as divideds? Assume that the govermet i the host coutry chaged its policy o the tax exemptio. The tax liability is ow 50% of profits. Compute the after-tax profits eared by the compay, the price per share before divided paymet, ad price per share price after the divided paymets. Explai why the share price reacts differetly with ad without divided taxes. (0 marks) Page 6 of 8

7 Sigle sum: Sigle sum: Auity: FV = PV = CF o ( PV [ o ( + ) k FV = ( ) CF FORMULAE Basic time value mathematics + k ]; FV=Future Value; PV=Preset Value ) = CF [ ]; CF = Cash Flow auity = A i text ( + k) + k ; [FVIFA k, ] from Tables k ( + k) = CF k k k + k ; [PVIFA k, ] from Tables ( ) ( ) Auity: PV =CF o Returs (r for ivestors; k = cost for corporatio i text book) Share Retur: R = [ P t + t ] t = ivideds at time t; P = Price Pt It + ( Pt Pt )/ Bod Retur: R = I = iterest; P = Prices; = umber of years 05.( P + P ) t t Geometric Retur: + R = [( + 0 R )( + R 2 )...( + R )] G is geometric G Logarithmic Retur: R L = l [ P t + t ] l is logarithmic P t Average Retur of 2 or more: R = Expected Retur: R = Portfolio Retur: R p = j= W i i= j = R j =umber of returs j=, 2,, P j R j = E(R j ) P j = probability; E(R j ) is writte as μ R i = A i i= E( Ri ) W = wealth proportio = A i i textbook Real Retur: ( + r K ) = ( + K ) (+π) K = omial K; K r = real K; π = iflatio Effective iterest: i eff = [( + i/2) 2 ] i = aual iterest rate 2 Variace: σ = j= P j [R j - R] 2 ; Variace, covariace, correlatios R = average retur; j =, 2,.., ; P j =probability Stadard eviatio: σ = 2 ( Rt R ) for a populatio; σ = risk t= Portfolio Variace: σ = p w σ + w2 σ + 2w 2 w 2 P 2 σ σ 2 ; P 2 = corr. coefficiet Correlatio Coefficiet: P i, j = Cov i, j σ i σ j Cov i,j = Covariace of i ad j = σ ij Page 7 of 8

8 Expected Theoretical Relatios Bod Price: PV 0 = I + ( ( k) ) FV + k ( + k) ; PV 0 = P Bod : k = i = yield to maturity Share Price: P = 0 K ad P = = 0 K g K [ ROE( POR)] = K [ ROE( b)] Security Market Lie: R i = R f + [R m - R f ] β i = K E = E(R i ) = R f +[ E( Rm) - R f ] β i Capital Market Lie: R p = R f + [( R σ p σ p m - R f )] σ = E(R i ) = [ E( Rm)- R f ] m σ m K E = Required Retur = r = Equity cost; idicates expectatio; p = portfolio σ 2 Beta of Security: β i = cov im, m Beta of Portfolio: β p = X i β i i= i = security; m = market p = portfolio; i = idividual security Market Model: R it = α i + β i (R mt ) + e it R= 60 mothly returs; m= market; e=residual Total Risk: σ 2 = β 2 σ m 2 + σ e 2 Arbitrage Theory: Ε( ) R = μ i i + β ( ) j F j e = residual F = R i = a i + b i (F ) + b i2 (F 2 )+ β ( ) Corporate Fiace Maagemet ecisio Rules CF t et Preset Value: PV = 0 = K t t = ( + ) - CF 0 Break-eve: BEP = Cost / Margi = [(FC + EP) ( - τ c )] / [(REV VC) ( - τ c )] τ c =tax rate Equivalet Aual Value: EAV = PV / [PVIFA k, ] Weighted Average Cost: K WACC = A K ( - τ c)+ E A K E A ; A = ratios; K = ebt cost Cost of equity of Levered Firm: usig levered beta Cost of Equity of Levered Firm: Hamada s Theorem: β = E, L EU, K = E, L R + F K = E, L K, EU β + ( ) Adjusted Preset Value: APV = Base PV + Fiacig Effect Adjustig Cost of Capital: E * K = K( T * L) [ ] β E ( ) E, L R R M F + ( EU E K -, K ) ( τ c ) τ c usig Ulevered beta L=Leverage; T*=Tax rate i future Levered Firm Value: V L = V U + τ c BT L= Levered; U=Ulevered Levered Firm: V L =V U +[- ( τ )( ) c τ EQ ] BT τ=tax; c=corporate; B =debt; EQ = equity ( τ B ) Imputatio K-Cost: K = Y + R E, L F (-T I )+ β [K m d m T R F (-T I )]; Y= iv yield E, L Imputatio Credit: I C = (τ c IV) /( - τ c ) I C is imputatio credit Merger: V aft AB = V bef A + V bef ΔCF t B + Sy; Sy = ; PV K t AB = Sy Premium paid t = ( + ) ivided Chage ecisio: IV t = a + c r (EPS t ) + c (IV t- ) + v t : r=payout; c=speed of adjustmet; a=itercept; v=residual of this regressio Page 8 of 8

FINANCIAL MATHEMATICS

CHAPTER 7 FINANCIAL MATHEMATICS Page Cotets 7.1 Compoud Value 116 7.2 Compoud Value of a Auity 117 7.3 Sikig Fuds 118 7.4 Preset Value 121 7.5 Preset Value of a Auity 121 7.6 Term Loas ad Amortizatio 122