With rF

= 4% and E(˜rM) = 12%, the cost of capital for a project with a beta of −3 is E(˜r) = rF

+ [E(˜rM) −

rF] . βi

= 4% + (12% − 4%) . (−3) = −20%. Yes, it does make sense that a project can offer a negative expected rate of return. Such projects are such great investments that you would be willing to expect losses on them, just because of the great insurance that they are offering.