University of CaliforniaWalter A. Haas School of BusinessUGBA 103Introduction to FinanceProf. Dmitry Livdan 17 December 2015Solutions to the FINAL(35 points total) Deiter Yolen (D&Y) is an all-equity perpetual company with 10 million sharesoutstanding trading at the current P/E ratio of 5. Its assets have just produced EBIT per shareof $20 and it pays all of its earnings as dividends. Its effective tax rate is equal to 40%. D&Y hasonly assets-in-place and, thus, does not grow.(1) (2 points) What is D&Y’s cost of capital (i.e. rA) and what is its price per share P0?We can calculate rAfrom the P/E ratioP0=E0rA⇒ rA=1P/E=15= 20%.The price per share can be calculated asP0=E0rA=(1 − tc)EBITrA=0.6 ∗ $200.2= $60.(2) D&Y is considering issuing $100 million in perpetual debt at a cost of rD= 5% to buy backsome equity. If D&Y decides to do the buy-back:(i) (1 point) What is the value of the levered firm?We can find the value of the levered firm fromVL= VU+ tcD = $60 ∗ 10M + 0.4 ∗ $100M = $640M.(ii) (1 point) What is the value of equity after the recapitalization?$100M in equity get bought back and the remaining $500M gets the interest tax shieldE0= $500M + 0.4 ∗ $100M = $540M.(iii) (2 points) What is the price at which equity is repurchased?The value added by the tax shield per share is $4 (total tax shield of $40M is divided between10M shares). Thus the new equity price isP00= $64.UGBA 103 FINAL – Solutions 2(iv) (2 points) How many shares have to be repurchased?D&Y buys back $100M worth of equity at $64 per share. Thereforen =$100M$64= 1.56M.(v) (2 points) What is the equity return of the recapitalized (levered) company?We find r0EfromE0=(1 − tc) [EBIT − rDD]r0E⇒ r0E=(1 − tc) [EBIT − rDD]E0=0.6 ∗ ($200M − 0.05 ∗ 100M)$540M= 21.67%.(vi) (1 point) What is D&Y’s WACC?We can find WACC fromVL=(1 − tc)EBITW ACC⇒ W ACC =(1 − tc)EBITVL=0.6 ∗ $200M$640M= 18.75%.(3) D&Y has decided not to go with the recapitalization (i.e. it is still all-equity firm). Instead,D&Y has a new investment opportunity: reinvest $12 per share during first 2 years and then $10per share during last 3 years out of its earnings into developing a new drug. After 5 years the drugwill be developed. The return (before taxes) on the project is 60% (r∗= 60%) for the first 2 years,i.e., in years when you invest $12, and 40% (also before taxes) for the last 3 years, i.e., in yearswhen you invest $10, and each $1 of investment pays forever starting one year after the investmenthas been made. The first investment will be made 1 year from now and the last one will be madein year 5.(a) (8 points) What is the D&Y’s price per share with the project?First, lets find current earnings E0= (1 − tc)EBIT = 0.6 ∗ $20 = $12. Next, we calculateafter-tax returns as 0.6 ∗ 60% = 36% and 0.6 ∗ 40% = 24%. Finally, we find the dividends and thendiscount them.Year EtItDt0 $12 0 $121 $12 $12 $02 $12+0.36*$12=$16.32 $12 $4.323 $12+0.36*$24=$20.64 $10 $10.644 $12+0.24*$34=$20.16 $10 $10.165 $12+0.24*$44=$22.56 $10 $12.566 $12+0.24*$54=$24.96 $0 $24.967 $24.96 $0 $24.96We can now calculate the priceP00=$01.2+$4.321.22+$10.641.23+$10.161.24+$12.561.25+11.25$24.960.2= $69.26.UGBA 103 FINAL – Solutions 3(b) (2 points) What is D&Y’s PVGO per share with this project?We can useP00=(1 − tc)EBITrA| {z }$60+ P V GO ⇒ P V GO = $9.26.(c) After some deliberation, D&Y decides to finance its new project with debt rather thanearnings. Specifically, it will borrow today the PV(All Investment) at 3%, use it to finance all fiveinvestments, and will repay it as a perpetual bond.(i) (7 points) Calculate the new price per share with project and debt financing. (HINT: Nowcompany is levered!)We need to calculate the total debt per shareD =$120.03(1 −11.032) +11.032$100.03(1 −11.033) = $49.62.Then since the debt is perpetual we need to calculate the interest tax shield per sharetcD = 0.4 ∗ $49.624 = $19.8496,and we obtain the new price per shareP00= $69.26 + $19.8496 = $89.11.(ii) (3 points) What is D&Y’s WACC with this financing?We calculate the value of the levered firm asVL= D + E0= $49.624 ∗ 10M + $89.11 ∗ 10M = $138.734 ∗ 10M.We can now use it to calculate WACCW ACC = rA∗ (1 − tcDVL) = 20% ∗ (1 − 0.4 ∗49.62138.734) = 17.14%.(iii) (2 points) Show that you can get the answer in part (a) by discounting D&Y’s dividendswith WACC.P00=$4.321.17142+$10.641.17143+$10.161.17144+$12.561.17145+11.17145$24.960.1714=