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# Finance Final Prep 70-450

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This 31 page Test Prep (MCAT, SAT...) was uploaded by Ajit Notetaker on Monday January 4, 2016. The Test Prep (MCAT, SAT...) belongs to 70-450 at Carnegie Mellon University taught by Xi lI in Fall 2016. Since its upload, it has received 52 views. For similar materials see Corporate Finance in Finance at Carnegie Mellon University.

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Finance (70-391) Fall 2014 Final Examination ▯ Time allowed = 3 hours ▯ Admissible materials: { Writing instruments. Calculator. Nothing else. { Computers, cell phones, smart-phones, PDAs and any other such electronic devices are not permitted. { Electronic calculators are permitted, including scienti▯c and ▯nancial cal- culators, but these devices must not have communication capabilities. The ▯nance functions of ▯nancial calculators will not deliver any advantage. A \simple" calculator will do just ▯ne. ▯ There is a formula list at the end ▯ Show all work. Partial credit may be given for incorrect and/or incomplete answers. ▯ There are 5 questions. There are 110 possible points on the exam: { 30 points for Question 1, 5 points for each of (a) { (f) { 10 points for Question 2 { 16 points for Question 3 { 21 points for Question 4 { 23 points for Question 5 { A 10% bonus will be applied to the total points if a student has done the Course Evaluation and the Course Evaluation Con▯rmation on Blackboard Budget your time accordingly. Final Examination 2 Question 1 (30 Points, 5 for each) For each of the following statements, indicate whether the statement is true, false or uncertain, and justify your answer. Unjusti▯ed responses will receive a grade of zero. (a) Amazon can buy a new machine called the \aisle widener" for $1.4 million. The machine will increase EBIT by $400 thousand per year, for 5 years, starting next year. Amazon’s tax rate is 30%. There is no risk. The cost must be expensed immediately. The risk-free interest rate is 5%. Statement. Amazon should buy the machine. (b) Between 2008 and 2014 Radio Shack’s revenue declined by about 25%. Their net income declined by much more: about 200%. 1 Question (forget the True/False thing here). Why the big di▯erence? Full points for a good guess with a short explanation. Source: \In need of rewiring," New York Times, August 20, 2014, page B1. Final Examination 3 (c) Financial statement data for Company XYZ are as follows. Most companies in the same industry as Company XYZ have P/E ratios that are close to 10. Statement. Relative to its peers, Company XYZ’s stock price must be re ec- tive of a large number of \growth options" to be undertaken in the future. (d) The optimal portfolio of risky assets has an expected return of 12% and a volatility of 20%. The riskless asset has a return of 4%. An investor wants to hold a portfolio with a volatility that does not exceed 27%. Statement. The highest expected return that can be achieved is 13%. (e) Rice Energy Inc. needs to raise $100 million in debt ▯nancing. They plan on issuing a one-year coupon bond with face value = $100 million. They believe that investors believe that (i) the default probability is 8%, (ii) the recovery rate will be 70% of the bond’s face value, (iii) the bond’s beta will be 0:25. The risk free rate of interest is 2% and the market equity premium is 6%. Statement. If Rice o▯ers investors a coupon rate of 5% then they will be successful in raising the ▯nancing that they require. (f) An unlevered ▯rm has 40 shares outstanding. The ▯rm decides to borrow 400 and pay the borrowed funds out to its shareholders as a one-time dividend. The debt is riskless and perpetual and the interest rate is 5%. The ▯rms faces a corporate tax rate of 20%. Statement. After the transactions are all completed the price-per-share will have decreased by $8. Final Examination 4 Question 2 (10 Points, 5 for each) TTYS Inc. makes high-performance backcountry skis. They o▯er a de▯ned-bene▯t pension plan to each of their employees. For their current set of retirees, the plan will make a payment to each retiree of $6 thousand, next month. In each subsequent month the payment will grow by an annualized rate of 2.0%. The growth is to adjust for in ation. There are currently 75 retirees and TTYS estimates that this number will remain the same, inde▯nitely. TTYS has a pension fund, a pool of capital set aside so that it can pay its pension obligations. The pension fund’s balance sheet looks like this: TTYS Assets Liabilities 2,144.91 Bonds Future pension payments Note: All quantities are in thousands. The value of each bond is $97 (a) The discount rate for riskless payments is 4.0%, annualized. By how much is TTYS’s pension fund underfunded? Give your answer as a percentage of the value of the liabilities. (b) Suppose that TTYS changes its pension fund’s balance sheet to look like this. TTYS Assets Liabilities 832.22 Stocks Future pension payments Note: All quantites are in thousands. The value of each stock is $250.00 The expected return on the stocks is 12% whereas that on the bonds (from Part (a)) is about 3%. By how much is TTYS’s pension fund underfunded? Give your answer as a percentage of the value of the liabilities. Interpret your answer in light of the \pension rate-of-return fallacy." TTYS stands for \Tele ’Till Yer Smelly." Final Examination 5 Question 3 (16 Points, 5 for (a-b), 6 for (c)) You are a corporate loan o▯cer. A potential client seeks to borrow $50.00 over a one-year period and wants a standard loan in which interest is paid after 6 and 12 months and principal is paid back after 12 months. You view this loan as riskless. Market data are as follows Bond Data (semi-annual coupons, face value = $1) Coupon (% p.a.) Price Six-Month Bond 0.00 0.981 Twelve-Month Bond 6.00 0.979 (a) What are the 6 and 12 month discount factors for riskless cash ows? What are the 6 and 12 month discount rates (\spot rates")? (b) What is the lowest possible 6-month annual percentage rate (APR) that you can a▯ord to o▯er? What is the e▯ective annual rate associated with this APR? (c) Banks make pro▯ts (and get compensated for credit risk) by charging higher interest rates on loans than they pay on deposits. Equivalently, banks discount loan repayments at higher rates than the riskless spot rates. With this in mind, re-answer part (b) by adding a 1% spread to each of the spot rates. What is 3 the APR, the e▯ective annual rate and the dollar pro▯t on the resulting loan. By \pro▯t" I mean that the loan has a positive NPV from your perspective as the banker. Final Examination 6 Question 4 (21 Points, 4 for (a-d), 5 for (d)) An entrepreneur has identi▯ed a one-period project. The cost is 25. It will pay either 23.8 or 37.8, with equally-likely probability. The project’s beta is 1.9, the risk-free interest rate is 2.5% and the equity risk premium is 5%. (a) Should the entrepreneur undertake the project (presume that NPV=0 projects should be undertaken)? (b) If the entrepreneur funds the project with 50% debt, what is the entrepreneur’s expected return and volatility of return? (c) Immediately after undertaking the project, the entrepreneur sells the entire equity portion to a group of equity investors. These investors, naturally, are willing to pay the market value for the equity portion of the project. What is the expected return on equity (for these new investors), on debt, and on \owning the entire ▯rm?" What is the equity-beta (i.e., the \levered beta") and the debt-beta? (d) Referring to part (c), there are 20 shares outstanding. One particular investor has wealth of $2 and, in addition to a position in the risk-free asset, she owns 3 shares. What are the investor’s portfolio weights and what is the expected return on her portfolio? (e) Returning to part (b), suppose that the entrepreneur funds the project with 95% debt. The beta of the debt is 0.25. What yield-to-maturity must the ▯rm o▯er to the bondholders in order to raise the requisite ▯nancing? Final Examination 7 Question 5 (23 Points, 10 for (a-b), 3 for (c)) American Multi-Cinema (AMC) owns and operates roughly 5,000 movie theatres in the United States. AMC is considering a radical new business plan that involves ren- ovating some of their theatres by making the seats a lot bigger and more comfortable. The main drawback | aside from the required CAPEX | is that the number of seats in each theatre will be drastically reduced. They are hoping that this is o▯set by a combination of higher ticket prices and higher attendance. AMC has paid a team of consultants $1.5 million to come up with some estimates of exactly how attendance will respond to the changing seat and ticket price landscape. The typical existing theatre that is being considered for renovation currently works (on average) as follows. It has 120 seats and the attendance rate is 30%. The ticket price is $8.00. Gross pro▯t margin is 30% and ▯xed costs are $90 per show. There are 3 shows per day and the theatre is open 365 days per year. AMC’s tax rate is 35%. The theatre will last for 10 years, after which the horizon value is zero. The cost-of-capital (the discount rate) that applies for all future years is 10%. (a) What is the present value of one of these existing theatres? Ignore cash ows in the current year. Assume that AMC as a whole is pro▯table, so that losses in any given theatre generate tax savings on AMC’s consolidated income statement. (b) If AMC renovates a given theatre things will work as follows: ▯ The renovation cost is $350,000, payable now, in the current year, and this CAPEX must be straight-line depreciated over the life of the theatre. 4Question, data and graphic are based on \Now at the Movies: Fully Reclining Seats," Erich Schwartzel, Wall Street Journal, July 6, 2014. The graphic image is just FYI. You do not need to use information from it. Final Examination 8 ▯ The number of seats will be reduced by half. But the good news is that the attendance rate is expected to increase to (roughly) 93% | this means 56 seats sold, per show | and the ticket price will increase from $8.00 to $9.50. ▯ In order to renovate, a theatre must be closed for 30 days next year. Fixed costs, however, remain the same ($270 per day), no matter if the theatre is open or closed. ▯ The required inventory of spare parts for the new seats will increase by $20,000, this year. Show what the incremental cash ows are for a renovated theatre. (c) Should AMC renovate? If so, what will be the NPV per renovated theatre that they will enjoy. Final Examination 9 Formulae Discounting ▯ Compound Interest. Future value of C dollars invested for t years at an APR of r% per-year with compounding m times per-year. ▯ ▯ V = C 1 + r mt t m ▯ Continuous Compounding. Future value of C dollars invested for t years at an APR of r% per-year with continuous compounding rt Vt = Ce = C exp(rt) ▯ E▯ective Annual Interest Rate (EAR). If r is the APR (from above), then the EAR satis▯es ▯ ▯t ▯ r▯tm 1 + EAR = 1 + ▯ ▯ ▯ mr▯ =) 1 + r EAR = 1 + m m ▯ Spot Rates and Discount Factors. The \spot rate" for some date that is t-years in the future it r , the EAR on a zero-coupon bond with a discount factor DF . ▯ ▯t 1 = DF 1 t r t ▯ 1 ▯1=t =) r t = ▯ 1 DF t ▯ Present Value. Present value of a stream of cash ows discounted at rate r: 1 X Ct V0 = t t=0 (1 + r) ▯ Perpetuity. Present value of a perpetual sequence of payments, C: C V0 = r ▯ Growing Perpetuity. Present value of a perpetuity that grows at rate g with the ▯rst payment C, received in one period (i.e.,1C = C, C2= C(1 + g), C 3 C(1 + g) , C t+1= C t1 + g)) C V0 = r ▯ g Final Examination 10 ▯ Annuity. Present value of an annuity. Receive C each period for t periods. C ▯ 1 ▯ V0 = 1 ▯ r (1 + r)t ▯ Delay. A perpetuity or annuity in which the ▯rst payment is delayed by t periods (so that the ▯rst payment is received at period t + 1) has present value V = V 1 ; 0 t(1 + r)t where Vtis the value at date t, arrived at using the appropriate formula that appears above. ▯ Yield-to-Maturity. A bond with price V0and cash ows c 1c 2:::c t has a yield- to-maturity de▯ned by V = c1 + c1 + ::: + ct : 0 (1 + y) (1 + y)2 (1 + y)t Value-Based Management ▯ Accounting Identity: V = D + E ▯ Return on Invested Capital (ROIC) NOPAT NOPAT Sales ROIC = = ▯ Invested Capital Sales Invested Capital NOPAT = \Net Operating Pro▯t After Tax." NOPAT is EBIT (\Earnings Before Interest and Taxes") less estimated taxes. Estimated taxes are the tax rate times EBIT, where we get the tax rate by dividing taxes actually paid by Net Income. \Invested Capital" can be computed as Debt plus Equity less cash, or as Total Assets less Current Liabilities less cash. Present Value of Growth Options and the P/E Ratio ▯ Constant Growth Model: g = PLOW ▯ ROE ▯ ▯ BV E t+1 = BV E 1 1 + g t ▯ ▯ EPS t+1 = EPS 1 1 + g t ▯ ▯ = BV E ▯ 1OE 1 + g t ▯ ▯ DIV t+1 = DIV 1 1 + g t ▯ ▯ = EPS ▯ PAY 1 + g t 1 ▯ ▯ = BV E ▯ ROE ▯ PAY 1 + g t 1 Final Examination 11 ▯ Valuation. Given the dividend-price ratio, we can compute the cost of capital: DIV 1 r = + g P0 Given the cost of capital, we can compute the price-per-share: DIV 1 P 0 = r ▯ g ▯ Present Value of Growth Options (PVGO) and the P=E ratio PV GO = P ▯ EPS 1 0 r P 0 PV GO 1 =) EPS = EPS + r 1 1 Portfolio Theory ▯ De▯nition of Correlation (second equation just de▯nes notation based on the ▯rst) Cov(x; y) Corr(x; y) = ▯x▯ y ▯ ’ = xy xy ▯x▯ y ▯ Portfolio Moments (expected return, standard deviation and Sharpe ratio) ▯p = ▯1+1 ▯2 2 ▯ 2 2 2 2 1=2 ▯p = 1 1 2 +22 1 2)12 ▯ 2 2 2 2 ▯1=2 = 1 1 2 +22 1 2▯12 1 2 Sharpe Ratio = ▯p▯ rf ▯ p CAPM ▯ ▯ ▯ ▯ E ri▯ rf = ▯ Eir M ▯ r f Cov(r i rm) ▯ im ▯i = 2 ▯ 2 ▯m ▯m Corr(r ; r )▯ ▯ ’ ▯ ▯ = i m i m ▯ im i m ▯m ▯m2 Final Examination 12 Statistical De▯nitions, Notation and Discrete Distribution Formulae P ▯ Mean: E(x) = psxs s p p p P P ▯ Standard Deviation: Var(x) = E(x ) ▯ E(x) = spsxs▯ ( spsxs) P P P ▯ Covariance: Cov(x; y) = E(xy) ▯ E(x)E(y) = spss s ▯ s s s s ps s ▯ Correlation: Corr(x; y) = Cov(x; y)x(y ▯ ) p 2 ▯ Notation: ▯x ▯ E(x), ▯x ▯ Stdev(x) = Var(x), ▯x ▯ Var(x), ▯ xy▯ Cov(x; y), ’ ▯ Corr(x; y) = ▯ =(▯ ▯ ). xy xy x y Capital Structure Beta Stu▯: ▯ Firm value, V satis▯es V = (Cash + Assets) and V = (D + E), where Cash, Assets, D and E are the value of cash, assets, debt and equity, respectively. Since the beta of a portfolio is a value-weighted average of the betas of the components of the portfolio, \▯rm betV," ▯ , can be written in two ways: Cash Assets ▯V = ▯Cash+ ▯Assets V V D E ▯V = ▯ D ▯E V V Final Examination 13 Free Cash Flow Template Final Examination 14 Free Cash Flow Template Final Examination 15 Solutions Question 1 (30 Points, 5 for each) For each of the following statements, indicate whether the statement is true, false or uncertain, and justify your answer. Unjusti▯ed responses will receive a grade of zero. Grading Rubric \Yes" is full marks. \Maybe" is part marks. \No" (not shown) is zero marks. Yes Maybe Setup of NPV criteria 2 1 (a) Recognition of annuity 2 0 Number and correct answer 1 0 Total 5 Yes Maybe Recognition of leverage e▯ect 2 1 (b) Quality of explanation 2 1 Mention operating and ▯nancial leverage 1 0 Total 5 Yes Maybe Compute P/E 2 1 (c) Recognize relation between P/E, r and PV GO 2 1 Answer question based on industry logic 1 0 Total 5 Yes Maybe Setup equation/picture for target vol 2 1 (d) Compute answer 2 0 Answer question 1 0 Total 5 Yes Maybe Cognition of PV relationship 2 1 (e) Computation (either solve for coupon or compute PV) 2 1 Answer question/explain 1 0 Total 5 Yes Maybe Tax value e▯ect 2 1 (f) Capital structure must change 2 1 Number and correct answer 1 0 Total 5 Final Examination 16 (a) Amazon can buy a new machine called the \aisle widener" for $1.4 million. The machine will increase EBIT by $400 thousand per year, for 5 years, starting next year. Amazon’s tax rate is 30%. There is no risk. The cost must be expensed immediately. The risk-free interest rate is 5%. Statement. Amazon should buy the machine. FALSE. The present value of the after-tax cash ow is c(1 ▯ ▯)▯ 1 ▯ PV = r 1 ▯ (1 + r)T = 1:212253468 : So the NPV = ▯0:187746532. So Amazon should not buy the dreaded aisle widener.5 At least, they shouldn’t if their objective is to make money (which one sometimes wonders about). (b) Between 2008 and 2014 Radio Shack’s revenue declined by about 25%. Their 6 net income declined by much more: about 200%. Question (forget the True/False thing here). Why the big di▯erence? Full points for a good guess with a short explanation. ANSWER. One word: leverage. Probably both operating and ▯nancial lever- age. Leverage ampli▯es changes in revenue into bigger changes in earnings, especially if we are talking about \after interest and ▯xed cost" measures of earnings (like Net Income). Full points for (i) saying \leverage" (or some suit- able synonym), and (ii) explaining a tiny bit using some verb like \amplify", and (iii) mentioning both ▯nancial AND operating leverage. Take-away 1 points for failing to mention operating leverage, since, as we discuss in class, both forms of leverage play an important role in the mapping between revenue and earn- ings. Parenthetically (not part of the question), a quick look at Radio Shack’s ▯nancials shows that their BOOK Debt/Value ratio is 90%! And, their Sell- ing/Admin expenses (lots of which is a \▯xed cost" for the big drop in 2013) are about 42% of revenue (1.5b out of 3.5b). So our best guess is spot on. 5\Dreaded" by Chris Telmer, who, upon showing up for his ▯rst job at age 14, working for a grocery store called the Red & White, was immediately sent next door, to the hardware store, to buy said aisle widener. The hardware store sta▯ were quite amused, in particular because the previous new6worker had been sent over to purchase a left-handed hammer (a tired old joke). Source: \In need of rewiring," New York Times, August 20, 2014, page B1. Final Examination 17 (c) Most companies in the same industry as Company XYZ have P/E ratios that are close to 10. Statement. Relative to its peers, Company XYZ’s stock price must be re ective of a large number of \growth options" to be undertaken in the future. TRUE. According to the dividend discount model, the price per share is DPS DPS 0:64 PPS = = = = 33:896 ; r ▯ g r ▯ PLOW ▯ ROE 0:12 ▯ 0:695 ▯ 0:145 where ROE equals earnings per share divided by the book value of equity per share, and the plowback ratio, PLOW, equals 1 minus (dividends per share divided by earnings per share) (note that dividends per share, in the numerator, must also (by construction) equal ROE times PAY OUT times BV E per share). So the P/E ratio is P=E = 16:14 : P/E ratios will be \big" if the cost of capital is big, or if the PVGO is big, or from a bit of both. In this question, we are comparing companies in the same industry. So it makes sense to think of their costs of capital being comparable. So, if XYZ has a relatively high P/E, it must be because its PVGO is relatively big, implying that it has a relatively large number of \growth options" | positive NPV investment opportunities | into which it can invest its retained earnings in the future. Indeed, the ROE of XYZ is 14.5%, which exceeds the cost of capital of 12%. This is precisely what it means for XYZ to have NPV >0 investment opportunities in the future. We assume that it will be able to reinvest its earnings, forever!, and earn a return that exceeds the cost of capital. Big assumption! Final Examination 18 To see that high P/Es must be associated with either high PVGO or high cost of capital, rewrite the de▯nition of PVGO as follows: EPS PV GO ▯ PPS ▯ r PPS PV GO 1 =) = + : EPS EPS r (d) The optimal portfolio of risky assets has an expected return of 12% and a volatil- ity of 20%. The riskless asset has a return of 4%. An investor wants to hold a portfolio with a volatility that does not exceed 27%. Statement. The highest expected return that can be achieved is 13%. FALSE. In order to achieve a \target volatility" of 27% (and hold an e▯cient portfolio), an investor should allocate the following fraction of their money to the optimal portfolio of risky assets: 0:27 (1 ▯ ▯f) = = 1:35 ; 0:20 where ▯fis (following notation from class) the fraction in the riskless asset. The expected return is then ▯ p ▯ f 0:04 + (1 ▯ ▯ f ▯ 0:12 = 0:148 : So, the question is false because, if an investor is willing to tolerate as much as 27% volatility, then she can achieve an expected return higher than 13%. She can achieve 14.8%. (e) Rice Energy Inc. needs to raise $100 million in debt ▯nancing. They plan on issuing a one-year coupon bond with face value = $100 million. They believe that investors believe that (i) the default probability is 8%, (ii) the recovery rate will be 70% of the bond’s face value, (iii) the bond’s beta will be 0:25. The risk free rate of interest is 2% and the market equity premium is 6%. Statement. If Rice o▯ers investors a coupon rate of 5% then they will be successful in raising the ▯nancing that they require. FALSE. The present value of the bond is B = pFR + (1 ▯ p)F(1 + c) ; 1 + r Final Examination 19 where p = :08 is the default probability, F = 100 is the face value of the bond, R = 0:70 is the recovery rate, c is the coupon rate, and r is the discount rate that is appropriate for this bond. Since the beta is 0.25, then the discount rate = :02 + 0:25 ▯ 0:06 = 0:035. Solving for the coupon rate: c = (1 + r)B ▯ pFR ▯ (1 ▯ p)F (1 ▯ p)F Set B = 100 and the result is c = 0:06413. Therefore a coupon rate of 5% would be inadequate. At 5% they would only raise $98.74396135 of ▯nancing. Note that, with a coupon rate of 6.4%, the yield would also be 6.4% (since the face value and present value of the bond would be the same). But with a coupon rate of 5%, the yield would be higher than the coupon rate, at 0.063356164%. (f) An unlevered ▯rm has 40 shares outstanding. The ▯rm decides to borrow 400 and pay the borrowed funds out to its shareholders as a one-time dividend. The debt is riskless and perpetual and the interest rate is 5%. The ▯rms faces a corporate tax rate of 20%. Statement. After the transactions are all completed the price-per-share will have decreased by $8. TRUE. By issuing debt the ▯rm value will increase by the present value of the tax shields, which is 0.2 ▯ 400 = 80. So the price-per-share will increase by $2, immediately upon announcement of this policy. Then, when the ▯rm pays $400 to it’s shareholders, the ▯rm value must fall by 400, so the price-per-share must fall by 400/40. Net, therefore, the price-per-share must fall by 400/40 - 2 = 8. This answer assumes that the conditions of the \Miller model" are satis▯ed. This is what we did in class and on problem sets and students should be familiar with this. Final Examination 20 Question 2 (10 Points, 5 for each) Grading Rubric \Yes" is full marks. \Maybe" is part marks. \No" (not shown) is zero marks. Yes Maybe Organization of #s 1 0 PV equation 2 1 (a) Un-annualization of rates 1 0 Correct answer 1 0 Total 5 Yes Maybe Compute asset value 1 0 (b) Answer \fundedness" 1 0 Description of \fallacy" 3 1-2 Total 5 (a) The monthly growth rate in the monthly payment (to adjust for in ation) is g = (1 + 0:020)1=12▯ 1. The monthly discount factor is r = (1 + :04)1=1▯ 1. Note that we often express these things in annual units (an \APR"). To do so we’d multiply them by 12. Then, to do calculations, we’d divide them by twelve. I will skip this here. Be aware that r and g, in this solution, are in monthly units whereas you will often see them in annual units. This is an example of a growing perpetuity. Next month, the total payment is 450 (thousand). The month after it is 450(1 + g). The month after that, 450(1 + g) . And so on. The present value of the perpetuity is 450 Present Value = r ▯ g Percentage underfunded is de▯ned by 100 times: Dollars Underfunded % Underfunded = PV(Liabilities) PV(Assets) ▯ PV(Liabilities) = PV(Liabilities) The main issue of the question | and the entire debate about pension liabilities in the world | is about calculating PV(Liabilities). Calculating PV(Assets) is trivial. You just look at the brokerage statement of the pension fund. This tells you how much you could sell the assets for .... right now. This, then, indicates that we should calculate PV(Liabilities) in the same manner; ask Final Examination 21 how much we could \sell them" for? To do so means getting someone else to assume the liabilities. Since they are (supposed to be) riskless promises then, unambiguously, we should calculate PV(Liabilities) by discounting them at the riskless rate. For some reason, many people seem to think that it is legit to discount the liabilities using the expected return on the assets. This is simply incorrect, as the \how much could you sell them for" argument proves. (b) As the numbers (below) show, the underfunding is identical to that of Part (a). Nothing has changed about the liabilities. Nothing has changed about the value of the assets. In class, we have discussed extensively the \pension rate of return fallacy." This is the argument that I’ve tried to articulate above, in the answer for Part (a). It indicates that the 12% expected return on the assets is irrelevant for the question of pension funding. So a should make good mention of this. Final Examination 22 Question 3 (16 Points, 5 for (a-b), 6 for (c)) Grading Rubric \Yes" is full marks. \Maybe" is part marks. \No" (not shown) is zero marks. Yes Maybe Discount factors, approach 2 1 (a) Discount rates, approach 2 1 Numbers and correct answer 1 0 Total 5 Yes Maybe PV equation 3 1-2 (b) What is APR? 1 0 Number and correct answer 1 0 Total 5 Yes Maybe Adjust spot rates 2 1 (c) New PV equation 2 1 Solution: new APR, EAR and pro▯t 2 1 Total 6 Answer (a) Final Examination 23 (b) (c) Final Examination 24 Question 4 (21 Points, 4 for (a-d), 5 for (d)) Grading Rubric \Yes" is full marks. \Maybe" is part marks. \No" (not shown) is zero marks. Yes Maybe PV = E(payoff)=(1 + E(return)) 2 1 (a) CAPM gives expected return 1 0 Number and correct answer 1 0 Total 4 Yes Maybe Structure of levered cash ows 2 1 (b) Expected return 1 0 Vol 1 0 Total 4 Yes Maybe Understand: cost becomes market value 1 0 (c) Expected returns 1 0 Betas 2 0 Total 4 Yes Maybe Comprehension of \portfolio calculations" 2 1 (d) Weights 1 0 Expected return 1 0 Total 4 Yes Maybe Setup of PV equation 3 1-2 (e) Solve 1 0 What is YTM here? 1 0 Total 5 Final Examination 25 Answer (a) The valuation problem here is \divide expected cash ow by the appropriate expected return." CAPM tells us the latter: ▯ ▯ Project Expected Return = r + ▯ E(r ) ▯ r f M f = 0:025 + 1:9 ▯ 0:05 = 0:12 The project’s market value is given in the following table. The entrepreneur is able to buy the project for less than its market value. The NPV, therefore, is positive. We can say that the project’s \book value" of 25 is less than its \market value" of 27.5. (b) 50% debt means that the entrepreneur must raise half of the project’s cost of 25 with debt. So, the present value of the debt must be 12.5. Since the debt is riskless | owing to the (relatively low) amount of debt | the coupon must be the riskless interest rate. Here is how the cash ows are divided. Final Examination 26 The entrepreneur’s expected return increases (relative to zero debt) and the volatility increases. (c) Now we switch from the entrepreneur to some equity investors that the en- trepreneur sells to. They are di▯erent from the entrepreneur because they don’t have the luxury of paying below-market cost for the project. They have to pay the market cost of 27.5. So, for them, the expected return on the levered ▯rm must be lower: they paid more. Note that all \value calculations" | most importantly the value-weighted averages that give the betas | must be done at market value, not at the entrepreneur’s acquisition cost. Final Examination 27 (d) (e) This is the most challenging part. The point is that, with 95% leverage, there is not enough cash ow to pay the debt holders, for sure. So, in the low-state, they just get the entire project. In the high state, they get what was promised. Since the debt is now risky, the debt holders will not lend 95% of the project value to the ▯rm if they are only promised a coupon-rate equal to the riskless rate. This is exacerbated by the fact that the debt beta is not zero, so the expected cash ow must be discounted at a higher rate that the riskless rate. Here’s how to solve the problem. 95% leverage means that the ▯rm must raise $23.75 of debt. So, the debt cash ows must have value of $23.75. Call this the \face value" and recognize that it must also equal the \market value." This means that 0:5cd+ 0:5(32(1 + c)) 23:75 = 1 + E(r ) (1) d where cdis the project cash ow in the bad state, c is the coupon rate that is \promised" to the debt-holders, and E(r )dis the expected return on the debt. The latter we compute using CAPM: ▯ ▯ E(r d = r + f debtEquity Risk Premium = 0:025 + 0:25 ▯ 0:05 = 0:0375 Solve Equation (1) for c: 2 ▯ 23:75(1 + E(r d) ▯ c d 23:75) c = 23:75 = 0:073 which means a coupon rate of 7.3%. This is also the yield-to-maturity, since we’ve ensured that the market value and the face value of the bond are the Final Examination 28 same. That is, the YTM is de▯ned as y such that 00 Market Value = \Promised Cash Flow 1 + y 23:75 = 23:75(1 + 0:073) 1 + y =) y = 0:073 The yield is the maximum return not the expected return. Final Examination 29 Question 5 (23 Points, 10 for (a-b), 3 for (c)) Grading Rubric \Yes" is full marks. \Maybe" is part marks. \No" (not shown) is zero marks. Yes Maybe Cash ow organization, conceptual 5 3 (a) Taxes contribute FCF 1 0 Add up to FCF 2 1 PV the annuity 2 1 Total 10 Yes Maybe Incremental revenue 2 1 Incremental ▯xed cost (zero) 1 0 (b) Opportunity cost of closure (expensed) 2 1 Capitalize and depreciate CAPEX 2 1 Working capital 1 0 Add up to FCF 2 1 Total 10 Yes Maybe Year zero and Year 1 costs 1 (c) Years 2-10 discounted correctly and NPV rule 2 1 Total 3 Final Examination 30 Comments: First, note that the $1.5 is a sunk cost. It has no bearing on the value of an existing (i.e., non-renovated) theatre, for which the value is simply the PV of the future FCF. The sunk cost also has no bearing on the decision as to whether or not AMC should renovate. It is a sunk cost. (a) The numbers above are, I hope, self explanatory. The PV of the FCF is negative, owing mostly to the size of the ▯xed costs (i.e., rent, labor, etc.) relative to the revenues. This captures the notion in the WSJ article that AMC has a bunch of theatres that are way under-performing. Note that the 10-year nature of the problem means that students must PV a 10-year annuity. Note that the tax impact of losing money | of having negative EBIT | is positive. It increases the FCF of each theatre in question because the losses can be applied to AMC’s Final Examination 31 overall tax bill to reduce their tax liability. The crucial assumption is that they are making money, as a ▯rm. The WSJ article attests to this. Of course, losing money is still losing money, and, in absence of the option to renovate (or something else), AMC would create even more value by simply shutting down. The tax angle here is just that they are losing less than they would be, were the losses not valuable in terms of reducing taxes owed on other pro▯table activities. (b) The question asks for a tabulation of incremental cash ow associated with renovation. The following issues arise { Incremental revenue, per show, equals the number of previously unoccupied seats times the new ticket price plus the number of previously occupied seats times the change in the ticket price. { Incremental ▯xed costs are zero. This is true (it was given), in spite of the fact that for 30 days the theatre is closed for renovation. The idea is that the ▯xed costs are mostly labor and that the workers will be helping with the renovation or something like that. { In Year 1 the incremental EBITDA per year equals the per-show EBITDA times the number of days open (365 minus 30) times 3 shows per day. In Years 2-10, this value is the full 365 days times 3 times the per show EBITDA. { An additional incremental cash ow associated with renovation is the loss in gross pro▯t (per show) from having to close. This equals the gross-pro▯t prior to renovating, times 3 times 30. Think of it this way. If we didn’t renovate, we’d earn 30 more days of gross pro▯t, but at the low ticket price and attendance. If we do renovate, then we lose this, we have zero revenue for the ▯rst 30 days of the year, after which we start operating at higher prices with more people in the seats. The opportunity cost associated with having to close can’t be evaluated at the \new revenue," because we don’t have the \opportunity" to earn that revenue without closing. Note that we could also adjust for the \opportunity cost of foregone revenue" below NOPAT, by subtracting the after-tax opportunity cost of \old gross pro▯t per show" times 3 times 30 times (1 ▯ tax rate). { Incremental FCF, then, adds this up. In Year 0 we have the combined e▯ect of the CAPEX and the increase in inventory (which enters as a negative number because if \eats up" cash). Year 1 incremental FCF is a little lower than Years 2-10 because of the cost of closure. (c) The NPV boils down to adding the CAPEX plus increase in WC to the present value of the Year 1 FCF (ie, Y ear 1 FCF=(1+r)), to the Year-1 PV of a 9-year annuity that starts in Year 2. Renovation is a good idea. The NPV is positive.

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