## Lesson 9 – Discounted cash flow analysis

In this lesson, I will discuss discounted cash flow analysis, a technique to find the value of a stock. In the last lesson we had looked at ways to get an understanding of value based on P/E and P/B ratios.

Let us understand discounted cash flow analysis (DCF) step by step.

## Free cash flow to firm

You would recall that every company records a profit after tax (PAT). It also has a cash flow from operations. In DCF cash is important, not PAT. Cash is what matters to shareholders.

The principle behind DCF is that the cash flows of the company from today to infinity yield the value of the company.

But we don’t use cash flow from operations directly. We use free cash flow.

A company spends money on capital expenditure. This might be for setting up new plants or capacity for example. This has to be deducted from the cash flow from operations to get free cash flow.

Free cash flow to firm = Cash flow from operations + Interest * (1-tax rate) – Capital Expenditure

We look at how free cash flow to firm has grown in the past few years and get a fair idea of the past growth rate. We then forecast future cash flows based on this number and the growth prospects for the company respectively.

## Discounted cash flows

Suppose I have to pay you Rs. 1,000. I give you two choices.

1. I will pay you Rs. 1,000 today

2. I will pay you Rs. 600 today and Rs. 400 in a year from today.

You will surely select the first option.

Why?

Because you get to use the cash in whatever way you want. You might have an option of investing the cash at 10%.

In the first option you have Rs. 400 extra cash to invest at start of year as compared to the second option.

What do you have in hand one year down?

1. Rs. 1000 + Rs. 100 interest for 1 year = Rs. 1,100.

2. Rs. 600 + Rs. 60 interest for 1 year + Rs. 400 at end of year = Rs. 1,060.

You are better off in the first option by Rs. 40.

This brings us to the concept of time value of money. **Money is worth more today than tomorrow.**

You might be linking this up already to the free cash flow concept. If intrinsic value of the company is derived from free cash flows, this helps us.

Suppose we have a free cash flow forecast for next 5 years.

FCFF1, FCFF2, FCFF3, FCFF4 and FCFF5.

With the time value concept you know that we need to “reduce” the cash from later years to “bring” it to today.

Present value of future cash flows is calculated as follows,

PV = FCFF1/(1+k) + FCFF2/(1+k)^{2} + FCFF3/(1+k)^{3} + FCFF4/(1+k)^{4} + FCFF5/(1+k)^{5}

k is the discount rate.

Assume that k is 10%. For the first term, the divisor would be 1.10. For the second term, the divisor would be 1.21. The divisor keeps increasing as we go into the future.

Discounting increases for future cash flows. Impact of future cash flows in total value is progressively decreased.

## General present value formula

In the earlier case we calculated present value for only 5 years. A company in real-life is not expected to run for only 5 years. It is assumed to run forever (practically not possible, but some things have to be simplified in formulae).

Does that mean that you would have to forecast cash flows till infinity?

FCFF6, FCFF7,…FCFF2033,…FCFF54,736…..

That’s going to be a problem since one cannot forecast till infinity.

The general formula for present value is derived with a mathematical simplification. Without getting into details of how we did it, this is what it looks like,

PV = FCFF1/(1+k) + FCFF2/(1+k)^{2} + FCFF3/(1+k)^{3} + FCFF4/(1+k)^{4} + ……..+ FCFFn/(1+k)^{n} +TFCFF/(1+k)^{n}

where n is the Terminal Year.

TFCF is the terminal cash flow. It is calculated as follows,

TFCFF= FCFFn*(1+g)/(k-g)

where,

g = Terminal growth rate of cash flows

k = Discount rate.

Conservatively, g may be taken at 2-3% for the Indian economy. Well, below the country’s GDP growth rate of 5-9%.

## Discount rate calculation

There is one term that is left to explain – the discount rate k.

In a company’s balance sheet, there is net worth (covered in previous lessons). There may be debt which is raised from banks and financial institutions.

Weighted average cost of capital (WACC) is calculated as follows,

WACC = Kd * Rd * (1-tax rate) + Ke * Re

Kd = Proportion of debt

Ke = Proportion of equity

If a balance sheet has

Net worth = Rs. 200

Total debt = Rs. 120

Ke = 200/(200+120) = 200/320 = 0.625 = 62.5%

Kd = 120/(200+120) = 120/320 = 0.375 = 37.5%

Rd or cost of debt can be taken as the interest rate on loans. You can get a rough idea of interest rate by dividing the interest paid in the year (from P&L statement) by the outstanding debt amount (from balance sheet). It usually would be a figure higher than prevailing home loan interest rates by any 2-5%. This is a thumb rule and not the norm.

Re is cost of equity.

Re = Rf + Beta * (Rm – Rf)

Rf is Risk free rate on 10 year government bond. As of the day of writing this it is approximately 8%. (Bloombeg Link for 10 year rates)

Beta is a measure of the volatility of a stock as compared to the index (say the Nifty or the BSE). If Beta is 1.5 it means that the stock moves are 1.5 times the move in the Nifty, in either direction.

Rm is Market return expected from an equity investment. Past data shows that the main indices like Sensex have yielded around 13-14% returns.

Say, you keep it at 15%.

Thus, for a stock with beta of 1.1, Rf=8% and Rm=15%, you will get Re = 15.7%.

## Equity value

The result of present value calculations if done in this fashion is value of the firm.

Value of firm = Market value of equity + Market value of debt – Cash on books

Market value of equity = Value of firm – Market value of debt + Cash on books

You will subtract the outstanding debt (found in the balance sheet) from the Value of firm that you calculate and the cash on books to get the equity value.

## DCF Analysis Example

I recommend that you download the DCF Analysis example.

## Conclusion

This lesson will have been the most challenging in terms of numbers. You might want to revise it once again since these might be new concepts for you. Also, unless you try this out for a stock that you are studying it will remain at an academic level. A DCF model is not an exact science. It is as good as the assumptions of cost of equity (ke), terminal growth rate (g) and no. of years of forecast for cash flows (n).

You will notice that the DCF calculation is quite sensitive to the terminal growth rate. It is dependent on the cash flow forecast till the terminal year. If you are too optimistic in projections you can get present value figures which will suggest that the stock is a screaming buy but you might end up making an investment mistake based on your analysis.

Do use this in conjunction with methods of P/E and P/B that you learned in the previous lesson. Stock analysis through multiple methods is prudent. It helps you avoid gross mistakes by any one method.

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