Question

13-1     a.   Project A requires $9 million initial capital outlay at T=0, with WACC = 11%, and cash flows as shown below in millions. There is 50% chance that the Project A will generate $6 million each year for 3 years, and 50% chance to generate $1 million each year for 3 years, what is the expected NPV for the Project A, and will the Project be accepted?

            0                      1             2             3                            

50% Prob.                    |              |              |                            

                                   6             6             6                            

           -9

                                    |              |              |                            

50% Prob.                    1             1             1

b.   If the project is hugely successful, $10 million will be spent at the end of Year 2, and the new venture will be sold for $20 million at the end of Year 3, as shown below, what is the expected NPV for the Project A, and will the Project A be accepted?

            0                      1             2             3                            

50% Prob.                    |              |              |                            

                                   6              6             6                            

                                                -10         +20                            

           -9                                    -4            26

                                    |              |              |                            

50% Prob.                    1             1             1

c.   What is the value of growth option (the difference between NPV with growth option and without option, using 0 if the NPV is negative)?

Answer 1

13-1a). Expected NPV = sum of (probability*NPV for the branch)

NPV for the top branch = -9 + 6/(1+11%) + 6/(1+11%)^2 + 6/(1+11%)^3 = 5.662 million

NPV for the bottom branch = -9 + 1/(1+11%) + 1/(1+11%)^2 + 1/(1+11%)^3 = -6.556 million

Expected NPV = (50%*5.662)+(50%*-6.556) = -0.447 million

b). NPV for the top branch = -9 + 6/1.11 -4/1.11^2 + 26/1.11^3 = 12.170 million

NPV for the bottom branch = -6.556 million (as calculated in part (a))

Expected NPV = (50%*12.170)+(50%*-6.556) = 2.807 million

c). Value of growth option = NPV with growth option - NPV without growth option

= 2.807 - 0 = 2.807 million (Since NPV without growth option is negative, project won't be undertaken without growth option. In that case, NPV without growth option = 0.)