Question

Healthy Food Inc (HFI) is currently all-equity financed with a total value of $90 million and a cost of capital of 18%. If HFI’s capital structure is changed to include $30 million of debt at 6%, and we assume a world without taxes where the risk-free rate is 4% and the expected market return is 14%. Determine the below values, then explain whether a risk averse investor would prefer to invest in the unlevered HFI or the levered HFI.

a. RE

b. ßU

c. ßD

d. ßE

e. ßWeighted Average

Answer 1

Levered ß = Unlevered ß * (1 + D/E)............... Equation 1

Unlevered ß, expected market return = Rm =14%, risk-free rate = Rf = 4%

a. cost of equity= RE = 18% as given for  all-equity financed case

d. cost of equity= RE = Rm + ßE *(Rm-Rf) = 18%

or, 14 %+ ßE * (14% -4%) = 18%, so  ßE = 0.4

c. ßD = 0 (always)

b. ßU = Unlevered ß = ßE = 0.4 (as no debt so D/E is zero in all-equity financed case)

e. D = 30, E = 60 as total value = 90 = D+E

so, Wd = 30/90 = 0.33 and We = 1-0.33 = 0.67

ßWeighted Average = ßE We * + ßD*We = 0.67*0.4 + 0 = 0.1675

As Levered ß = Unlevered ß * (1 + D/E)............... Equation 1

and D/E = 30/60 = 0.5

Levered ß = 0.4 * (1+0.5) = 0.6 which is greater than Unlevered ß

as risk averse investor prefer lower beta, they will invest in unlevered HFI.