Question

11.a)   Find the PV of the following stream of cash flows, if the discount rate is 7%:

   Years       Cash Flow
   1-15       $ 12,000
   16-35       $ 18,000
   36-40       $ 20,000

b)   Following up on the above stream, what would the PV be if the 39th cash flow was missing?
c)   What would the FV of part (a) be? At the same 7% rate.

d)    what would the FV be if the last cash flow was missing?

Answer 1

11. a) Discount Rate = 7%
PV of cash flow(using annuity formula) = PV of 1-15 years cash flow + PV of 16-35 years cash flow + PV of 36-40 years cash flow = 12000*(1-(1+7%)^-15)/7% + 18000*(1-(1+7%)^-20)/(7%*(1+7%)¹⁵) + 20,000*((1-(1+7%)^-5)/(7%*(1+7%)³⁵) =
109,294.9681 + 69,115.6493 +  7680.7308 = 186,091.35

b) If 39th cash flow was missing then PV = 186,091.35 - 20,000/(1+7%)³⁹ = 184,662.25

c) FV of cash flow using (FV of annuity formula) =  PV of Annuity *(1+7%)⁴⁰ = 2,786,617.05

d) FV if 39 th class class flow was missing = 2,786,617.05 - 20,000*(1+7%) = 2,765,217.05

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