Equity

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CHAPTER 17 Does Debt Policy Matter? Answers to Practice Questions 1. a. The two firms have equal value; let V represent the total value of the firm. Rosencrantz could buy one percent of Company B’s equity and borrow an amount equal to: 0.01 × (DA - DB) = 0.002V This investment requires a net cash outlay of (0.007V) and provides a net cash return of: (0.01 × Profits) – (0.003 × rf × V) where rf is the risk-free rate of interest on debt. Thus, the two investments are identical. b. Guildenstern could buy two percent of Company A’s equity and lend an amount equal to: 0.02 × (DA - DB) = 0.004V This investment requires a net cash outlay of (0.018V) and provides a net cash return of: (0.02 × Profits) – (0.002 × rf × V)…show more content…
Total income is positive: $113,049 – $108,536 = $4,513 4. a. Before refinancing: r r ⎛ A A ⎞ ⎛ E ⎞ ⎛ 40 ⎞ ⎞ ⎛ 300 × r ⎟ +⎜ ⎟ ⎜ D + E × rE ⎟ = ⎜ 40 + 300 × 0.05 ⎟ + ⎜ 40 + 300 × 0.10 ⎟ ⎟ ⎝ D D+E ⎠ ⎠ ⎝ ⎝ ⎠ ⎝ ⎠ =⎜ ⎜ D = 0.0941 After refinancing: r =r E b. A + (r A ⎛ D⎞ ⎛ 80 ⎞ − r )⎜ ⎟ = 0.0941 + (0.0941 − 0.05)⎜ ⎟ = 0.1077 = 10.77% D ⎜ E⎟ ⎝ 260 ⎠ ⎝ ⎠ Jacques owns a portfolio with €60,000 of his own money and €40,000 borrowed at the risk-free rate. The weights for this portfolio are 1.67 invested in Rastignac stock and –0.67 invested in the risk-free asset. The expected return for the portfolio is: (1.67 × 0.10) + (–0.67 × 0.05) = 0.1335 = 13.35% 138 Let βE-B and βE-A represent the equity beta for Rastignac before and after the refinancing, respectively. The beta for Jacques’ portfolio before the refinancing is: (1.67 × βE-B). Use the following equation to determine the relationship between βE-B and βE-A: ⎛ D ⎞ ⎛ E ⎞ βA = ⎜ ⎜ D + E × β D ⎟ + ⎜ D + E × β E-B ⎟ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎞ ⎞ ⎛ 300 ⎛ 40 βA = ⎜ × β E-B ⎟ × 0⎟ + ⎜ 340 340 ⎠ ⎠ ⎝ ⎝ 340 × βA β E-B = 300 Also: ⎞ ⎞ ⎛ E ⎛ D βA = ⎜ ⎟ ⎟ ⎜ ⎜ D + E × β D ⎟ + ⎜ D + E × β E- A ⎟ ⎠ ⎠ ⎝ ⎝ ⎞ ⎞ ⎛ 260 ⎛ 80 βA = ⎜ × β E-B ⎟ × 0⎟ + ⎜ ⎠

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