For Company X: equity beta = 1.6, D/(D+E) = 50% ⇒ D = E, tax = 30%.

Ungear to get asset beta:

βa=βeEE+D(1−T)=1.6×11+1×0.7=1.6×11.7≈0.94\beta_a = \beta_e \frac{E}{E + D(1-T)} = 1.6 \times \frac{1}{1 + 1×0.7} = 1.6 \times \frac{1}{1.7} \approx 0.94βa​=βe​E+D(1−T)E​=1.6×1+1×0.71​=1.6×1.71​≈0.94

Re-gear for Company Y with 60% equity, 40% debt (D/V=0.4, E/V=0.6):

βe′=βaE+D(1−T)E=0.94×0.6+0.4×0.70.6=0.94×0.880.6≈1.38\beta_e' = \beta_a \frac{E + D(1-T)}{E} = 0.94 \times \frac{0.6 + 0.4×0.7}{0.6} = 0.94 \times \frac{0.88}{0.6} \approx 1.38βe′​=βa​EE+D(1−T)​=0.94×0.60.6+0.4×0.7​=0.94×0.60.88​≈1.38

CAPM ( rf=5%r_f = 5\%rf​=5%, rm=10%r_m = 10\%rm​=10% ):

Ke′=5%+1.38×(10%−5%)=5%+1.38×5%≈5%+6.9%=11.9%K_e' = 5\% + 1.38 × (10\%-5\%) = 5\% + 1.38×5\% \approx 5\% + 6.9\% = 11.9\%Ke′​=5%+1.38×(10%−5%)=5%+1.38×5%≈5%+6.9%=11.9%