Question

HCA Healthcare is considering an acquisition of Mission Health. Mission Health is a publicly traded company, and its current beta is 1.30. Mission Health has been barely profitable and had paid an average of only 20 percent in taxes during the last several years. In addition, it uses little debt, having a debt ratio of just 25 percent. If the acquisition were made, HCA would operate Mission Health as a separate, wholly owned subsidiary. Mission Health would pay taxes on a consolidated basis, and the tax rate would therefore increase to 35 percent. HCA also would increase the debt capitalization in the Mission Health subsidiary to 40 percent of assets, which would increase its beta to 1.50. HCA estimates that Mission Health if acquired, would produce the following net cash flows to HCA's shareholders (in millions of dollars): Year Free Cash Flows to Equityholders 1 $1.30 2 $1.50 3 $1.75 4 $2.00 5 and beyond Constant growth at 6% These cash flows include all acquisition effects. HCA's cost of equity is 14 percent, its beta is 1.0, and its cost of debt is 10 percent. The risk-free rate is 8 percent.

a. What discount rate should be used to discount the estimated cash flow? (Hint: Use HCA's cost of equity to determine the market risk premium.) Note: format for question 'a' is xx.x%

b. What is the dollar value of Mission Health to HCA's shareholders?

Answer 1

a)

14% = 8% + 1*Market risk premium

Market risk premium = 6%

Required return = Risk free rate + (Beta * (Market risk premium))

Required return = 8% + (1.5 * 6%)

Required return = 8% + 9%

r = 17%

b)

terminal year cashflow = D5*(1+g)/(r-g) = 2*(1+6%) / (17% - 6%) = 2.12 / 11% = 19.27

PV of CF1 = 1.30/1.17 = 1.11

PV of CF2 = 1.50/1.17^2 = 1.10

PV of CF3 = 1.75/1.17^3 = 1.09

PV of CF4  = (2.00 + 19.27)/1.17^4 = 11.35

shareholders value in $m = 1.11+1.10+1.09+11.35 = 14.65