Consider a series of $110 end-of-period CFs spanning 2051-2056 and a $126 CF at the beginning of 2023. The interest rate is 2.1%. What is the equivalent value of these CFs at the end of 2042?
Present value of CF's spanning 2051-2056 at the end of 2051 =
We will solve it using the formula of present value of annuity i.e.
Present value = $110 × [{1-(1+0.21)-6}/0.021] = $614.08
Now, present value of CF's spanning 2051-2056 at the end of 2023 =
Present value (A) = $614.08/(1+0.021)8 = $520.02
Now,
future value of CF of 2023 at the end of 2042 (B) = $126 × (1+0.021)20 = $190.94
Equivalent value of CF = A + B = $520.02 + $190.94 = $710.96 or $711
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