- xedoc
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## Calcul de la valeur intrinsèque d'une action

le Dim 22 Mar 2015 - 17:50

Hi guys,

I was wondering if someone knows how to calculate intrinsic value using DCF. some examples would be nice.

Have a nice day.

I was wondering if someone knows how to calculate intrinsic value using DCF. some examples would be nice.

Have a nice day.

**imane**- Nbre méssages : 331

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## Re: Calcul de la valeur intrinsèque d'une action

le Dim 22 Mar 2015 - 21:56

Benjamin Graham a fournit une équation intéressante pour en avoir une idée approximative.

Cette équation de la valeur intrinsèque est :

V= E x (8,5 + 2G) x 4,4/Y

Où:

V= valeur intrinsèque

E= bénéfices par action

G= taux de croissance projeté

Y= taux d’intérêt des obligations corporatives AAA

Cette équation de la valeur intrinsèque est :

V= E x (8,5 + 2G) x 4,4/Y

Où:

V= valeur intrinsèque

E= bénéfices par action

G= taux de croissance projeté

Y= taux d’intérêt des obligations corporatives AAA

- w.sayerh
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## Re: Calcul de la valeur intrinsèque d'une action

le Dim 22 Mar 2015 - 23:19

DCF is a method that estimates the value of a (financial) asset, based on the cash flows it generates.

For example: Let's assume you have a stock of IAM. What are the cash flows you expect from such an asset? The cash flows of a stock are dividends, so you need to estimate the cash flows that the company will give to its shareholders for the following periods (for simplicity, let's assume that IAM gives dividends once a year)

So let's say that these are your estimates:

2015: 12 MAD

2016: 13 MAD

2017: 11 MAD

2018: 10 MAD

2019: 13 MAD

You estimate now that the asset will give you 12 + 13 + 11 + 10 + 13 = 59 MAD. So if I tell you what is the FAIR price of this asset, you will be tempted to say that it is the simple sum of the cash flows, which is 59 MAD. This seems logical, you give 59 MAD today and you get reimbursed progressively until end-2019. This seems fair enough

However, this is far from fair. A fundamental principle of finance states that 1 MAD today worth less than 1 MAD tomorrow. The rationale behind this principal is that you can put 1 MAD today at a saving account in your bank and get a little more that 1 MAD tomorrow. For this reason, 12 MAD that I will receive in one year, worth less than 12 MAD today. Therefore, the entire IAM stock should be estimated at less than 59 MAD.

The value of the IAM stock should not be the sum of the cash flows anymore, but each cash flow should be discounted, separately, according to a specific rate of return that I am willing to invest with (To go even further, any logical investor ties this rate of return to the risk intrinsic to the asset, which is in this example tied to the risk of the company). This is where the terminology (Discounted Cash Flow) comes from.

So let's say that given the risk that I'm bound to by investing in IAM stocks, I am asking for these rates of return:

1-year investment: 10%

2-year investment: 11%

3-year investment: 12%

4-year investment: 13%

5-year investment: 14%

Now I need to get the value of IAM stock by discounting each cash flow by the rate of return I'm asking for each, which gives us:

12/(1+0.10)^(1) + 13 /(1+0.11)^(2) + 11/(1+0.12)^(3) + 10/(1+0.13)^(4) + 13/(1+0.14)^(5) = 42.17 MAD

Maybe if I take a riskier stock, let's say ADI, I will be asking for a higher rate of return because the odds of losing my money is higher. So let's say that for tis level of risk I'm asking for these rates of returns:

1-year investment: 15%

2-year investment: 16%

3-year investment: 17%

4-year investment: 18%

5-year investment: 19%

Let's assume that, for the sake of comparison, the company will generate the same cash flows as IAM.

This will give us a DCF of:

12/(1+0.15)^(1) + 13 /(1+0.16)^(2) + 11/(1+0.127^(3) + 10/(1+0.18)^(4) + 13/(1+0.19)^(5) = 35.13 MAD

You see, we have two companies giving the same cash-flows but one is more valued than the other because it is considered less risky.

This is a good method for valuing financial assets, but the problem with it is that it requires estimating an infinite number of cash flows (dividends in our example). However, the more cash flows are far in the future, the less they will be significant in our result, because the denominators will start becoming smaller and smaller, so we can consider that estimating cash flows for 15 or 20 periods is enough but no less difficult.

Some scholars proposed some formulas to simplify this task for particular cases. For example, the Gordon-Shapiro Dividend Discount Model assumes a constant growth in dividends (dividends follow a geometric suite where the reason is (1+g)). The price of the asset is given by:

Div1/(r-g). Where Div1 is the estimated dividend for the following period, r the required rate of return (here it should be constant across the years), and g which the growth rate.

You can use this method for estimating the value of stocks as we did or any other financial asset such as bonds (cash-flows being interest and principal), mortgage loans (the principal being the monthly payment), etc.

For example: Let's assume you have a stock of IAM. What are the cash flows you expect from such an asset? The cash flows of a stock are dividends, so you need to estimate the cash flows that the company will give to its shareholders for the following periods (for simplicity, let's assume that IAM gives dividends once a year)

So let's say that these are your estimates:

2015: 12 MAD

2016: 13 MAD

2017: 11 MAD

2018: 10 MAD

2019: 13 MAD

You estimate now that the asset will give you 12 + 13 + 11 + 10 + 13 = 59 MAD. So if I tell you what is the FAIR price of this asset, you will be tempted to say that it is the simple sum of the cash flows, which is 59 MAD. This seems logical, you give 59 MAD today and you get reimbursed progressively until end-2019. This seems fair enough

However, this is far from fair. A fundamental principle of finance states that 1 MAD today worth less than 1 MAD tomorrow. The rationale behind this principal is that you can put 1 MAD today at a saving account in your bank and get a little more that 1 MAD tomorrow. For this reason, 12 MAD that I will receive in one year, worth less than 12 MAD today. Therefore, the entire IAM stock should be estimated at less than 59 MAD.

The value of the IAM stock should not be the sum of the cash flows anymore, but each cash flow should be discounted, separately, according to a specific rate of return that I am willing to invest with (To go even further, any logical investor ties this rate of return to the risk intrinsic to the asset, which is in this example tied to the risk of the company). This is where the terminology (Discounted Cash Flow) comes from.

So let's say that given the risk that I'm bound to by investing in IAM stocks, I am asking for these rates of return:

1-year investment: 10%

2-year investment: 11%

3-year investment: 12%

4-year investment: 13%

5-year investment: 14%

Now I need to get the value of IAM stock by discounting each cash flow by the rate of return I'm asking for each, which gives us:

12/(1+0.10)^(1) + 13 /(1+0.11)^(2) + 11/(1+0.12)^(3) + 10/(1+0.13)^(4) + 13/(1+0.14)^(5) = 42.17 MAD

Maybe if I take a riskier stock, let's say ADI, I will be asking for a higher rate of return because the odds of losing my money is higher. So let's say that for tis level of risk I'm asking for these rates of returns:

1-year investment: 15%

2-year investment: 16%

3-year investment: 17%

4-year investment: 18%

5-year investment: 19%

Let's assume that, for the sake of comparison, the company will generate the same cash flows as IAM.

This will give us a DCF of:

12/(1+0.15)^(1) + 13 /(1+0.16)^(2) + 11/(1+0.127^(3) + 10/(1+0.18)^(4) + 13/(1+0.19)^(5) = 35.13 MAD

You see, we have two companies giving the same cash-flows but one is more valued than the other because it is considered less risky.

This is a good method for valuing financial assets, but the problem with it is that it requires estimating an infinite number of cash flows (dividends in our example). However, the more cash flows are far in the future, the less they will be significant in our result, because the denominators will start becoming smaller and smaller, so we can consider that estimating cash flows for 15 or 20 periods is enough but no less difficult.

Some scholars proposed some formulas to simplify this task for particular cases. For example, the Gordon-Shapiro Dividend Discount Model assumes a constant growth in dividends (dividends follow a geometric suite where the reason is (1+g)). The price of the asset is given by:

Div1/(r-g). Where Div1 is the estimated dividend for the following period, r the required rate of return (here it should be constant across the years), and g which the growth rate.

You can use this method for estimating the value of stocks as we did or any other financial asset such as bonds (cash-flows being interest and principal), mortgage loans (the principal being the monthly payment), etc.

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