Question

Q1. A project's base case or most likely NPV is $44,000, and assume its probability of occurrence is 50%. Assume the best case scenario NPV is 85% higher than the base case and assume the worst scenario NPV is 35% lower than the base case. Both the best case scenario and the worst case scenario have a 25% probability of occurrence. Find the project's coefficient of variation.

Q2. Rick Kish has a $140,000 stock portfolio. $50,000 is invested in a stock with a beta of 1.25 and the remainder is invested in a stock with a beta of 2.45. These are the only two investments in his portfolio. What is his portfolio’s beta?

Q3. ABC Company's stock has a beta of 1.95, the risk-free rate is 2.25%, and the market risk premium is 7.75%. What is ABC's required rate of return using CAPM?

Answer 1

1). E(NPV) = [Pi x NPV_i]

= [0.5 x $44,000] + [0.25 x {$44,000 x (1 + 0.85)}] + [0.25 x {$44,000 x (1 - 0.35)}]

= $22,000 + $20,350 + $7,150 = $49,500

(NPV) = [{Pi x (E(NPV) - NPV_i)²}]^1/2

= [{0.5 x ($49,500 - $44,000)²} + {0.25 x ($49,500 - $81,400)²} + {0.5 x ($49,500 - $28,600)²} ]^1/2

= [$15,125,000 + $254,402,500 + $109,202,500]^1/2 = [$378,730,000]^1/2 = $19,460.99

CV = [(NPV) / E(NPV)] x 100%

= [$19,460.99 / $49,500] x 100% = 0.3932 x 100 = 39.32%

2). _P = [Wi x _i] = [(50/140) x 1.25] + [(90/140) x 2.45] = 0.45 + 1.58 = 2.02

3). Required Return = rF + beta[Market Risk Premium]

= 2.25% + [1.95 x 7.75%] = 2.25% + 15.11% = 17.36%