by Anshil Bhansali

Imagine you are a **professional, savvy investor** who comes across many investment deals on a regular basis and have to make choices as to which ones to pursue. It's a fresh start to the week, you're feeling really bullish, and ready to invest some money, and **you receive details about 2 investment deals: Project A and Project B.**

Both projects have the same initial investment **$3m**, and last for the same amount of time, **5 years**. The only difference is the cash flows; in Project A you are expected to receive $2m in year 1, $4m in year 2, $4m in year 3, $2m in year 4, and finally nothing in year 5. In Project B, you are only expected to receive a lump sum $14m in year 5.

**Which one do you pick?**

**Discount Cash Flow** gives you the answer. DCF is essentially an investment analysis technique that can be used to value a company, investment projects and in bond pricing. To get a good understanding of DCF, we need to get a good understanding of the **‘Time Value of Money’.**

**Time value of money** is a concept where an amount of money, say $100 is worth more today than $100 in the future. This is because rational investors will always ensure that their money is growing, whether they keep it safe in savings accounts or try to make riskier investments in the stock market. At the very least, money should grow at the “risk free rate of return”, which is basically the US Treasury Bills returns.

This means that $100 in the future is worth less than $100 today. $100 today in 2019 might not be considered a lot, but back in the 1970s, it was considered a large enough amount with significant buying power.

Let’s apply this concept while understanding how DCF analysis will tell us which project to invest in. The essential difference between the 2 projects is WHEN you get your money back. Would you prefer to get $14m after 5 years, or $12m in parts over the 5 years. Think about the time value of money when you answer this question.

To mathematically prove which cash flow is better, it depends on what discount rate we use to discount these future cash flows. We are “discounting” these future dollar values to today’s value at a certain rate. The ‘discount rate’ term can be interchanged with ‘interest rate’ because it is the rate at which we expect our initial investment to grow.

Assume we have other investments growing at a rate of 9% or more, and we want to invest in deals that grow at a minimum of 9%, that is our discount rate. Thus we can discount a future cash flow, for example year 2 for project A with the formula: $4m/(1+r)^n; where r is the discount rate i.e. 0.09 and n is the number of years i.e. 2. The value from that formula, $3.36m, will tell us the present value of $4m 2 years in the future at a rate of 9%, or in simple terms, $3.36m today will grow to $4m if it grew at 9% annually.

**What DCF computes is simply the sum of all future cash flows discounted to today. **

Now back to the example, if we were to compute all the discounted future cash flows of each project, it would look something like this:

**For Project A: **

**For Project B:**

Summing all the DCFs we get $9.7m for Project A and $9.0m for Project B. These are the values of the projects today, assuming these future cash flows are accurate. We subtract our initial investment of $3m from both to get the ‘Net Present Value’ of each project, $6.7m for A and $6m for B. From a pure financial standpoint, we can conclude that Project A is a better choice, and the reasoning is because we receive enough money early on (which can be put towards other investments) back from the project as compared to receiving a lump sum at the end in the other project.

Other applications of DCF can be to valuing companies and pricing of bonds. On a high level, we can estimate a company’s future cash flows based on its financial history, economic cycle, and other macro and micro variables. Based on those future cash flows and an appropriate discount rate, we can assign a value to the company. In the world of bond pricing, the price to be set on a newly issued bond is the value we get from the DCF formula, where the future cash flows are the coupon payments and the discount rate is the interest rate at the time. Once the bond is issued, market demand and supply fluctuates the bond’s price, and because of these fluctuations, the discount rate, or the ‘yield’ on the bond fluctuates in response.

One important thing to touch upon is the elasticity effects of these variables; discount rate, number of years, and future cash flows itself. Think about if these variables changed, which ones have relatively large effects on the DCF. Now that you are armed with this knowledge, try to apply these concepts to real world examples. Happy analysis!

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