How to solve General Cash Flows — NPV and dollar-weighted (money-weighted) return questions on Exam FM?

Question

An investor undertakes a project with the following cash flows (times in years): the investor pays $10000$ at time $t=0$; receives $2000$ at time $t=2$; receives $6000$ at time $t=5$. At an effective annual interest rate of $i = 0.0518$, calculate the net present value of the project.

Accepted Answer

Formula
$NPV(i)=\sum_{t=0}^n CF_t(1+i)^{-t}$; an internal rate of return satisfies $NPV(i)=0$. For the stated one-year simple-interest dollar-weighted approximation, $i\approx(B-A-\sum C_t)/(A+\sum C_t(1-t))$.

Why this formula applies
Discount all signed cash flows to the valuation date. NPV uses a supplied rate; IRR or dollar-weighted return is the rate that makes the same discounted sum equal to zero.

Substitution and calculation
$\text{NPV} = \sum CF_k (1+i)^{-t_k} = -10000(1+0.0518)^{-0} + 2000(1+0.0518)^{-2} + 6000(1+0.0518)^{-5} = -3531.0769$.

Answer
The answer is -3531.0769, option (A).

How to Solve General Cash Flows — NPV and dollar-weighted (money-weighted) return Questions on Exam FM

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