CFA Level 1 Review: Quantitative Finance, Time Value of Money.

In this post, I will present a summary of the quantitative finance part of the CFA Level 1 exam.

The time value of money is a trivial concept in Finance, which can be summarized as “one dollar today is better than one dollar tomorrow“, because of the risk-free interest rate \(r\). The following formulas allow to compute the present value \(PV\) of a future cash flow \(FV\) (in case of a single cash flow) or \(CF_i\) (in case of several future cash flows).
$$PV=FV (1+r)^{-t}=\frac{FV}{(1+r)^t} \quad (1)$$

$$PV=\sum_{i=1}^N \frac{CF_i}{(1+r)^i} \quad (2)$$

That’s all trivial.

If there are infinite cash flows of constant value c, the product is called a perpetuity and its values is computed as follows:

$$PV_a=\frac{c}{r}$$

The only tricky part comes when you have multiple cash flows coming at the beginning \(PV_b\) or at the end of the period \(PV_e\). To compute the value of the investment, you just have to know that \(PV_b = (1+r) PV_e\) as the two computation are basically shifted one period from one to the other.

When trying to compute the value of a project, the idea is to compute the NPV (net present  value) of the project which is the present value of the project cash flows which can be computed easily using (2). Any project with \(NPV < 0\) should be rejected.

That was pretty easy anyway.

I’ll be back with more.

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