Your firm has a project with Free Cash Flows (FCF) listed in the table below. Th

Question

Your firm has a project with Free Cash Flows (FCF) listed in the table below. The year 5 FCF consists of $25 million for year 5 and $75 million that represents the present value in year 5 of FCFs in years 6 through 10. After year 10, competition will drive incremental FCF to 0. Your discount rate is 10%.
Time 0 1 2 3 4 5
FCF ($MM) -50 5 10 15 20 100

What constant annual rate of change in FCF in years 6 through 10 is consistent with the $75 million value for the FCF at year 5?

a. -8.22% b. -4.22% c. 0.22% d. 4.22%

Explanation / Answer

Present value of all cash flows given need to be calculated wirh r=0.1

PV= 5/1.1 + 10/1.1^2 + 15/1.1^3   + 20/1.1^4 + 100/1.1^5   - 50

   =49.93 million = 50 million

so we have here

100=A{(1+r)^5-1/[(1+r)^5 *r]

75 =A{(1+r')^5-1/[(1+r')^5 *r']

so solving r'-r =0.00422

hence d)4.22%

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