How to solve Time Value of Money — equation of value (NPV / accumulated value) for dated flows questions on Exam FM?

Question

An investor has the following cash flows (times in years): pay $2000$ at time $t=0$; receive $1500$ at time $t=2$; receive $300$ at time $t=4$. Using an effective annual interest rate of $i = 0.0415$, calculate the net present value of these flows.

Accepted Answer

Formula
At focal date $T$, the signed value is $V_T=\sum_t C_t(1+i)^{T-t}$. Equivalent cash-flow streams have equal values at that date; their signed difference is zero.

Why this formula applies
Choose one comparison date and move every cash flow to that date using the applicable accumulation factors. The equation is valid only when all values are expressed at the same time.

Substitution and calculation
$\text{NPV} = \sum CF_k (1+i)^{-t_k} = -2000(1+0.0415)^{-0} + 1500(1+0.0415)^{-2} + 300(1+0.0415)^{-4} = -362.1904$.

Answer
The answer is -362.1904, option (A).

How to Solve Time Value of Money — equation of value (NPV / accumulated value) for dated flows Questions on Exam FM

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