# 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.

# A new challenge has entered the ring!

My first social life in the first 6 months of year 2012 has been compromised by a new challenge I decided to take on this year, the Chartered Financial Analyst (CFA) curriculum.

The CFA program is divided in 3 exams denoted Level I, II and III. The candidate gets the CFA designation upon completing the 3 levels which can be taken every year. I am hence taking the Level I in June.

The reason why I decided to take on this challenge is because I believe it contains interesting general finance topic and covers some of the basic concepts of quantitative finance. Let’s face it, it’s also good value to my CV if I can manage to pull it off.

I will try from time to time to put some summaries of what  I have encountered, in order to help me remember the formulas and to share with the community the key concepts.

I must add that I will use the resources provided by Kaplan Schweser which are from what I have seen so far a must-have in order to complete this curriculum successfully, especially if you do have a full position at the same time.

I’ll try to soon add my summary of the quantitative finance part.