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Berkeley UGBA 103 - FINAL – Solutions

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University of CaliforniaWalter A. Haas School of BusinessUGBA 103Introduction to FinanceProf. Dmitry Livdan 10 December 2018Solutions to the FINAL(35 points total) Sirap Co. pays 40% in corporate taxes and is financed entirely by commonstock with a 1,000 shares outstanding trading at $75 per share. Sirap has only assets-in-place and,thus, does not grow. The risk-free debt yields 5% and the market risk premium is equal to 8%. LetEPS stand for earnings per share, E for equity, and D for debt.(1) The CAPM beta of Sirap’s equity, βE, is twice the portfolio weight on the risk-free asset ofthe efficient portfolio with a return equal to 6.6%. Calculate:(i) (3 points) Sirap’s beta, βE;The return of the efficient portfolio is equal to:6.6% = 5% + w ∗ 8% ⇒ w = 0.2,from where we can find that the portfolio weight on the risk-free asset is equal to 1 − 0.2 = 0.8which implies βE= 2 ∗ 0.8 = 1.6.(ii) (1 point) the required return on the Sirap’s stock; Using CAPM we obtain:rE= 5% + 1.6 × 8% = 17.8% = rA.(iii) (1 point) Sirap’s (P/EPS) ratio (keep 3 digits after the decimal point);We have:(P/EP S) =1rE=10.178= 5.618.(iv) (1 point) Sirap’s EPS (keep 2 digits after the decimal point);We have:$75EP S= 5.618 =⇒ EP S = $13.35.(2) (For this part of the solution, all the “primed” variables, like E0, denote “after-refinancing”variables.) Sirap now decides to switch toDE0= 2 by using debt to repurchase common stock. Ifthe debt is risk-free, calculate:(i) (3 points) The amount of debt issued (keep 2 digits after the decimal point);UGBA 103 FINAL – Solutions 2After debt is issued we have that:VL= D + E0= 1.5D = VU+ τD = 1, 000 × 75 + τ D,which we can solve for D = $75, 000/1.1 = $68, 181.82.(ii) (1 point) The new price per share (keep 2 digits after the decimal point);The new price is the old price plus the interest tax shield per share:P0= $75 + 0.4 × $68.18 = $102.27.(iii) (2 points) The number of repurchased shares (please round the number to make it integer);We can calculate the number of repurchased shares by dividing the debt by the share price$68, 181.82/$102.27 to get 667 or 2/3 of all shares.(iv) (2 points) The new earnings per share (EPS0) (keep 2 digits after the decimal point);After the refinancing, we need to pay after tax interest to the debtholders leading to the followingvalue of the total earnings, ERN’:ERN0= $13, 350 − (1 − τ )rDD = $13, 350 − 0.6 × 0.05 × $68, 181.82 = $11, 310.Since we have only 1/3 of the shares remaining EP S0= $11, 310/333 = $33.95.(v) (1 point) The new price/earnings ratio (keep 2 digits after the decimal point); We have thenew price and new EPS’(P/EP S)0=$102.27$33.95= 3.01.(vi) (3 points) Beta of the common stock after the refinancing; After the refinancing, we haveusing MMTII (with taxes) andDE0= 1:rE0= rA+ (1 − τ)DE0(rA− rD) = 17.8% + 0.6 × 2 × (17.8% − 5%) = 33.16%,which implies from the CAPM:βE0=33.16% − 5%8%= 3.52.It is also correct to use:rE0=$33.95$102.27× 100% = 33.2%,to find rE0.UGBA 103 FINAL – Solutions 3(3) Sirap has decided not to go with the recapitalization (i.e. it is still all-equity firm). Instead,Sirap considers the following 5-year growth plan: it will reinvest $10 out of its earnings per sharefor 5 years starting from year 1. It will stop the reinvestment in year 6 and will continue on theno-growth path paying all EPS as dividends. The after-tax return on equity (ROE) is 30% in year1, 25% in year 2, and 20% forever starting from year 3. Each investment pays forever. Keep 2digits after the decimal point for your answers throughout this question.(i) (1 point) What is the Sirap’s EPS and dividend in year 2?EP S2= $13.35 + 0.30 ∗ $10 = $16.35;I2= $10 and D2= $6.35.(ii) (1 point) What is the Sirap’s EPS and dividend in year 3?EP S3= $13.35 + 0.25 ∗ ($10 + $10) = $18.35;I3= $10 and D3= $8.35.(iii) (1 point) What is the Sirap’s EPS and dividend in year 4?EP S4= $13.35 + 0.2 ∗ ($10 + $10 + $10) = $19.35;I4= $10 and D3= $9.35.(iv) (1 point) What is the Sirap’s EPS and dividend in year 5?EP S5= $13.35 + 0.2 ∗ ($10 + $10 + $10 + $10) = $21.35;I5= 10 and D5= $11.35.(v) (3 points) What is Sirap’s EPS in year 6 and price, P0, with this reinvestment policy?EP S6= $13.35 + 0.2 ∗ ($10 + $10 + $10 + $10 + $10) = $23.35;We can now calculate the price using the discount rate of 16% from the first part:P0=$3.351.178+$6.351.1782+$8.351.1783+$9.351.1784+$11.351.1785+11.1785$23.350.178= $80.22.(vi) (1 point) What is PVGO from such investment policy?P V GO = P0− $75 = $80.22 − $75 = $5.22.UGBA 103 FINAL – Solutions 4(4) Sirap decides to use debt instead of earnings to finance the investments from part (3).Specifically, it will get a 5-year risk-free loan with a face value per share equal to the PV(AllInvestments) and then will repay it in five equal installments of $10 per share. Each installmentconsists of the principal and interest payments. Keep 2 digits after the decimal point for youranswers throughout this question.(i) (1 point) What is the face value of the loan (total, not per share)?D =10, 0000.05[1 −11.055] = 43, 294.77.You need to figure out the interest payment on the debt each year. Table below will navigateyou through this task. The top raw of the Table shows the amount of principal that needs to berepaid and on which the interest is charged, i.e. Interest Paid(t) = rD∗ Principal Outstanding(t).The total annual repayment of 10, 000 consists of the Interest Paid(t) and Principal Paid(t). Fillin the table by answering questions below.End of Year1 2 3 4 5Principal outstanding 43,294.77 35,459.51 27,232.49 18,594.11 9,523.82Payments on the debt 10,000.00 10,000.00 10,000.00 10,000.00 10,000.00Interest paid 2,164.74 1,772.98 1,361.62 929.71 477.18Principal paid 7,835.26 8,227.02 8,638.38 9,070.29 9,523.82Interest tax shield 865.90 709.19 544.65 371.88 190.87(ii) (1 point) What are the InterestPaid(t), PrincipalPaid(t), and interest tax shield in year 1?Interest Paid(1) = 2,164.74, Principal Paid(1) = 7,835.26, and interest tax shield = 865.90.(iii) (1 point) What are the InterestPaid(t), PrincipalPaid(t), and interest tax shield in year 2?Interest Paid(2) = 1,772.98, Principal Paid(2) = 8,227.02, and interest tax shield = 709.19.(iv) (1 point) What are the InterestPaid(t), PrincipalPaid(t), and interest tax shield in year 3?Interest Paid(3) = 1,361.62, Principal Paid(3) = 8,638.38, and interest tax shield = 544.65.(v) (1 point) What are the InterestPaid(t),


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