Solving for missing cash flows

Your friends, Lee and Kuan, are struggling to solve for the missing cash flows of the following cash flow stream:

Year 0 - $0

Year 1, Year 2 - $505

Year 3 - $853

Year 7 - 2.5x

In fact, they're convinced that "x" must be $115.16. Note that the present value of the above cash stream with annual payments is $5,095.00, and the discount rate is 8.9411% compounded 365 time(s) per year. This cash flow stream pays a growing annuity starting the end of year 3 for which the growth rate is 4.00%. Also, it pays a perpetuity starting the end of year 7. What is the value of the missing cash flows? And, are Lee and Kuan correct?

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Solving for missing bond coupons