University of California Walter A Haas School of Business UGBA 103 Introduction to Finance Prof Dmitry Livdan 11 December 2017 Solutions to the FINAL 35 points total Pegoretti Inc pays 40 in corporate taxes and is financed entirely by common stock with a 1 000 shares outstanding trading at 60 per share Pegoretti has only assets in place and thus does not grow 1 5 points total Pegoretti s CFO wants to use CAPM to calculate Pegoretti s equity beta E However she does not know several key variables like the market risk premium market s standard deviation and the risk free rate She does know that the stock market s Sharpe s ratio is equal to 0 4 She also knows that since CAPM applies to every security she can find some of these values using data from Pegoretti s two competitors Merxx and Pinarello both of which have no debt i 2 points If Merxx s and Pinarello s assets have a cost of capital equal to 13 and 21 respectively and their asset betas are equal to 0 8 and 1 6 respectively what are the risk free rate and the stock market risk premium rM rf CAPM for Merxx MX rE rf M X rM rf 0 13 rf 0 8 rM rf while CAPM for Pinarello P rE rf P rM rf 0 21 rf 1 6 rM rf Subtracting the first equation from the second yields 0 08 0 8 rM rf thus yielding rM rf 10 Substituting it back into the second equation yields rf 5 ii 2 points What is Pegoretti s cost of equity capital if its market risk is equal to 0 375 From market risk we have 0 375 C M and we can find M from the market s Sharpe s ratio 0 4 0 1 M 0 25 M Therefore C 0 375 0 25 1 5 From the CAPM we have rE 5 1 5 10 20 UGBA 103 FINAL Solutions 2 iii 1 point What is Pegoretti s EBIT per share Using Pegoretti s share price we obtain 60 1 t EBIT 0 6 EBIT EBIT 20 rE 0 20 2 10 points total Pegoretti considers embarking on a 5 year growth plan presented in the table below Year PBR ROE POR 1 2 3 4 5 0 4 0 4 0 4 0 4 0 6 50 50 50 50 55 0 6 0 6 0 6 0 6 0 4 First investment is made in the year 1 year 1 ROE is the return on the year 1 investment and so on Each investment pays forever Investment is paid out of the earnings After finishing this investment plan Pegoretti once again becomes a no growth company i 1 point What is the Pegoretti s EPS investment and dividend in year 1 Start by calculating EP S0 1 t EBIT 0 6 20 12 then it follows that EP S1 EP S0 I1 0 4 12 4 80 and D1 12 4 80 7 20 ii 1 point What is the Pegoretti s EPS investment and dividend in year 2 EP S2 12 0 5 0 4 12 1 2 12 14 40 I2 0 4 14 40 5 76 and D2 14 40 5 76 8 64 iii 1 point What is the Pegoretti s EPS investment and dividend in year 3 EP S3 EP S2 1 2 1 2 14 40 17 28 I3 0 4 17 28 6 91 and D3 17 28 6 91 10 37 iv 1 point What is the Pegoretti s EPS investment and dividend in year 4 EP S4 1 2 EP S3 1 2 17 28 20 74 I4 0 4 20 74 8 30 and D4 1 2 D3 1 2 10 37 12 44 v 1 point What is the Pegoretti s EPS investment and dividend in year 5 EP S5 1 2 EP S4 1 2 20 74 24 89 UGBA 103 FINAL Solutions 3 I5 0 6 24 89 14 93 and D5 24 89 14 93 9 96 vi 4 points What is Pegoretti s price P 0 with this reinvestment policy Lets calculate EP S6 first EP S6 12 0 55 4 80 5 76 6 91 8 30 14 93 34 39 all of which are now paid as dividends since the investment opportunity is over We can now calculate the price using the discount rate of 20 from the first part P0 9 96 1 34 39 7 20 7 20 1 20 7 20 1 202 7 20 1 203 97 10 1 20 1 202 1 203 1 204 1 205 1 205 0 20 vii 1 point What is PVGO from such investment policy P V GO P 0 95 97 10 60 37 10 3 20 points total Pegoretti is considering an alternative 5 year project Since this project is very different from Pegoretti s current assets the adjusted present value will be used to value the project The project requires an initial investment of 75 000 in new assets which will be depreciated straight line to 0 over the project s 5 year life These assets will be worthless in five years i e they will not be resold Each year for five years the project is expected to generate pre tax revenues of 60 000 and to require pre tax costs of 24 000 The entire project will be financed through a 5 year bank loan with an annual rate of 10 it is also the discount rate The principal on the loan will be repaid in equal installments of 15 000 each i e each year the company pays 15 000 in principal and pays the interest on the outstanding loan It is estimated that the pre tax costs payable at time zero of negotiating the loan will be 4 of the amount borrowed and these costs cannot be amortized The project s risk is very similar to the risk of Rebus Dodd RD Inc s assets This firm is currently financed by 100 000 shares worth 12 50 each and 750 000 worth of debt and has the same tax rate as the Pegoretti s The beta of RD s stock is 1 5 and the company borrows at a rate of 11 The values for the risk free rate and the market risk premium are the same as in the first part of this exam i 4 points What is the appropriate discount rate for the project Round to two digits e g 0 33 instead of 0 3266 RD for the DR Lets first calculate rE RD rE 5 1 5 10 20 The project s discount rate can be calculated by unlevering RD s weighted average cost of capital WACC RD W ACCL 1 t rD D RD E rE 1 0 4 0 11 0 375 0 20 0 625 0 15 V V UGBA 103 FINAL Solutions 4 Since W ACCL W ACCU 1 t D V we have rA W ACCU 0 15 W ACCL 0 18 D 1 0 4 0 375 …