The Market Outlet has a beta of 1.38 and a cost of equity of 14.945 percent. The risk-free rate of return is 4.25 percent. What discount rate should the firm assign to a new project that has a beta of 1.25?

The discount rate assign to a new project with a Beta of 1.25 is 13.94%

Explanation:

The applicable formula is the Capital Asset Pricing Model formula of Miller and Modgliani  quoted below:

Ke = Rf + (Market risk premium x Beta)

Currently Ke=14.945%

Beta =1.38

Risk free rate of return (Rf) is 4.25%

Market risk premium is the unknown

14.945%=4.25%+(Market Risk Premium)*1.38

14.945%-4.25%=Market Risk Premium*1.38

10.70% =Market Risk Premium*1.38

10.70%/1.38=Market Risk Premium

Market Risk Premium =7.75%

However, the new project cost of equity has to be determined due to having a different Beta factor of 1.25(a different risk appetite)

Using the above formula, we have

Ke=4.25%+(7.75% *1.25)

Ke =13.94%