Key to Final Exam

# Key to Final Exam - BA 103 SUMMER 2007 FINAL EXAMINATION 1...

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BA 103 S UMMER 2007 F INAL E XAMINATION J UNE 29, 2007 1. Amazing Technologies Corporation (ATC) just paid an annual dividend of \$1.80. The dividends are expected to grow at the rate of 16% per year for the next 4 years. From t =4 onwards, the dividends are expected to grow at 4.5% in perpetuity. The market capitalization rate for the stock is 16%. Work out the current price of the stock. [8 points] The Dividend at t=1 is \$1.8*1.16, and its present value is \$1.8. Therefore the present value of the first four dividends is \$1.80*4 = \$7.20. D5 = \$1.80*1.16 4 *1.045 = \$3.41. Therefore P4 = D5/(r-gL) = \$3.41/(.16 – 0.045) = 29.62. PV(P4) = \$16.36. P0 = 16.36 + 7.20 = \$23.56 2. Ms. Heike Alvarez owns and manages an all-equity firm. The firm is currently valued at \$1.5 million. However, an additional investment of \$6 million is needed for expansion, which can be raised either as debt at 13.5%, or as equity. The annual cash flows that the expanded firm will generate depend, among other things, on how hard Ms. Heike Alvarez works. If she works an average of 6 hours a day, the annual cash flows that the firm generates are expected to be \$900,000. On the other hand, if she works 10.5 hours a day, the annual cash flows are expected to be higher by a factor of 1.35. Assuming that there are 250 working days in a year, work out the Ms. Heike Alvarez’s average hourly compensation in all four cases: (a) expansion is financed by debt and Ms. Heike Alvarez works 6 hours a day, (b) expansion is financed by debt and Ms. Heike Alvarez works 10.5 hours a day, (c) expansion is financed by equity and Ms. Heike Alvarez works 6 hours a day, and (d) expansion is financed by equity and Ms. Heike Alvarez works 10.5 hours a day. Also work out the hourly compensation that Ms. Heike Alvarez receives on the additional 1125 hours a year (if she works 10.5 hours a day, she puts in an additional 4.5 hours a day for 250 days) (i) if the expansion is financed by equity and (ii) if the expansion is financed by debt. Briefly comment on the incentives that Ms. Heike Alvarez will have to work longer hours in the two cases. [8 points] The Annual cash flow with 10.5 hr days is \$1.35*\$900,000 = \$1,215,000. If \$6millon is raised as debt, the interest on it is \$6m*.135 = \$810,000. With debt financing the hourly compensation is as follows: 6-H OUR D AYS 10.5-H OUR D AYS A NNUAL C ASH F LOW \$900,000 \$1,215,000 I NTEREST \$810,000 \$810,000 C ASH F LOW TO O WNER -M ANAGER \$90,000 \$405,000 #(H OURS )/ YEAR 1500 2625 H OURLY C OMPENSATION \$60 \$154.29 With equity financing, other owners own \$6m of the expanded \$7.5m firm. Thus others’ stake is 80% 6-H OUR D AYS 10.5-H OUR D AYS A NNUAL C ASH F LOW \$900,000 \$1,215,000 P AYMENT TO O THERS (80% OF CF) \$720,000 \$972,000 C ASH F LOW TO O WNER -M ANAGER \$80,000 \$243,000

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H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT B ERKELEY BA 103 S UMMER 2007 A VINASH V ERMA N AME : #(H OURS )/ YEAR 1500 2625 H OURLY C OMPENSATION \$120 \$92.57 With debt financing, she makes \$315K for additional 1125 hours, and her hourly compensation is \$280 per hour. With equity financing, she makes \$63K for additional 1125 hours, and her hourly compensation is \$56 per hour. She will have greater incentive to work hard if the expansion is financed by debt.
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