b. 2. Graph (a) the relationships between capital costs and leverage as measured by D/V, and (b) the relationship between value and D. Answer: Figure 1 plots capital costs against leverage as measured by the debt/value ratio. Note that, under the MM no-tax assumption, rd is a constant 8 percent, but rs increases with leverage. Further, the increase in rs is exactly sufficient to keep the WACC constant--the more debt the firm adds to its capital structure, the riskier the equity and thus the higher its cost. Figure 2 plots the value against leverage firm’s (debt). With zero taxes, MM argue that value is unaffected by leverage, and thus the plot is a horizontal line. (Note that we should not really extend the graphs to D/V = 100% or D = $2.5 million, because at this amount of leverage the debtholders become the owners, and thus a discontinuity exists.) firm’s Figure 1 c. Using the data given in part B, but now assuming that firms L and U are both subject to a 40 percent corporate tax rate, repeat the analysis called for in B(1) and B(2) under the MM with-tax model. Answer: With corporate taxes added, the MM propositions become: Proposition I: VL = VU + TD. Proposition II: rsL = rsU + (rsU rd)(1 - T)(D/S). – There are two very important differences between these propositions and the zero-tax propositions: (1) when corporate taxes are added, VL does not equal VU; rather, VL increases as debt is added to the capital structure, and the greater the debt usage, the higher the value of the firm. (2) rsL increases less rapidly when corporate taxes are considered. This is seen by noting that the Proposition II slope coefficient changes from (rsU rd) to (rsU rd)(1 t), so at any positive T, the slope coefficient is – – – smaller. Note also that with corporate taxes considered, VU changes to VU = = = $2,142,857 versus $3,571,429.
b. 2. Graph (a) the relationships between capital costs and leverage as measured by D/V, and (b) the relationship between value and D. Answer: Figure 1 plots capital costs against leverage as measured by the debt/value ratio. Note that, under the MM no-tax assumption, rd is a constant 8 percent, but rs increases with leverage. Further, the increase in rs is exactly sufficient to keep the WACC constant--the more debt the firm adds to its capital structure, the riskier the equity and thus the higher its cost. Figure 2 plots the firm’s value against leverage (debt). With zero taxes, MM argue that value is unaffected by leverage, and thus the plot is a horizontal line. (Note that we should not really extend the graphs to D/V = 100% or D = $2.5 million, because at this amount of leverage the debtholders become the firm’s owners, and thus a discontinuity exists.) Figure 1 c. Using the data given in part B, but now assuming that firms L and U are both subject to a 40 percent corporate tax rate, repeat the analysis called for in B(1) and B(2) under the MM with-tax model. Answer: With corporate taxes added, the MM propositions become: Proposition I: VL = VU + TD. Proposition II: rsL = rsU + (rsU – rd)(1 - T)(D/S). There are two very important differences between these propositions and the zero-tax propositions: (1) when corporate taxes are added, VL does not equal VU; rather, VL increases as debt is added to the capital structure, and the greater the debt usage, the higher the value of the firm. (2) rsL increases less rapidly when corporate taxes are considered. This is seen by noting that the Proposition II slope coefficient changes from (rsU – rd) to (rsU – rd)(1 – t), so at any positive T, the slope coefficient is smaller. Note also that with corporate taxes considered, VU changes to VU = = = $2,142,857 versus $3,571,429.
FM14e_SM_Ch21.docx