# 17. Weighted average cost of capital and Terminal Growth

## 17.1 – Recap

As far as the theoretical concept of valuation is concerned, we are now almost at the end of it. In this chapter, we will discuss two critical points, and then in the next chapter, we will start implementing the Discounted cash flow valuation model in our primary model.

A quick recap of the last few chapters before we proceed –

• There are three valuation techniques – relative valuation (also called the method of comparable), option-based valuation technique (valuation contingent upon an event), or the absolute valuation technique employing the discounted cash flow analysis
• We are discussing the discounted cash flow analysis or the DCF model. The DCF valuation is on a stock basis and not year on year basis
• When we re-order the balance sheet equation, we get Fixed assets = Net Debt + Equity
• From the above equation, you can choose to value the assets of the company, which is essentially valuing the entire firm, also called ‘Enterprise valuation,’ or you can choose to value just the equity portion of the company
• Valuation is driven by the cashflow, the growth rate of the cashflow, and the timing of the cash flow
• To calculate the free cash flow, you start with PAT and add back non-cash expenses, interest charges, and factor in changes in working capital
• If you are valuing based on the entire company, then the return expectation is a blended rate called WACC (we will discuss more in this chapter). If you value basis just the equity, then the cost of capital is the return expectation
• Return expectation of equity holders is always higher than the debt holders, and this can be estimated using the CAPM model
• Lastly, when you add back interest to PAT in the FCF calculation, we need to ensure the tax shield is considered.

We have discussed all the above over the last three chapters. If you cannot follow, I suggest you revisit the previous three chapters, read them, and post your queries to seek clarification. In this chapter, we will wind up the conceptual discussion around the discounted cash flow model.

## 17.2 – Effective cost of debt

By now, we are very clear about the discount rates we need to use when calculating the free cash flow to the firm (FCF) and the free cash flow to equity (FCFE). To reiterate –

• If we are valuing the company basis the free cash flow to the equity holders (FCFE), then we use the CAPM model to figure the equity holder’s return expectation i.e., Re = Rf + β *( Rf – Rm). Please refer to the previous chapter for more details on this equation.
• If we value the company basis the entire firm (firm = equity holders + debt holder), then we have to discount the cashflow basis the blended rate called the weighted average cost of capital (WACC)

We briefly discussed the concept of WACC in chapter 15 under section 15.3, but now that we learned about the tax shield in the previous chapter, let’s revisit the idea of WACC.

Perhaps the best way to understand WACC is by taking an example. Assume a company has Rs.300Crs in debt and Rs.200 Crs in Equity. Equity folks expect a 12% return, while debt holders expect 8%.

Given the capital structure, what is the blended rate or the weighted average cost of capital?

We know that WACC is  = Weight of debt * return expectation of debt holders + weight of equity * return expectation of equity holders.

The total capital = Debt + Equity

= 300 + 200

= 500 Crs

Weight of debt = 300 / 500

= 60%

Weight of equity = (1-weight of debt)

= 1- 60%

= 40%

Hence, the blended rate or WACC is =

= 60% * 8% + 40%*12%

= 9.6%

But, here is the twist. The company also enjoys a tax shield on the interest that the company pays. Think about it; assume the following –

EBIT of a company = 100 Crs

Interest expense = 20 Crs

Profit Before tax = 80Crs

Tax = 30% or 24 Crs

PAT =  56 Cr

Now, for a moment, think there is no interest obligation. In this case, PBT is 100 Crs, and the tax payout at 30% will be 30Cr. The presence of interest expense reduces my tax outflow, which is called the ‘tax shield’; we discussed this in the previous chapter. Hence, whenever we consider the cost of debt, we also need to consider the tax shield benefit and factor in the tax shield benefit. The cost of debt after considering the tax shield is referred to as the ‘Effective cost of Debt.’

The formula for the effective cost of debt is : Cost of Debt *(1-Tax rate). In this example –

= 8% *(1-30%)

= 5.6%

Notice how the rate reduces once you incorporate the impact of tax on the. We can plug the effective cost of debt back into the WACC example and check the new rate –

= 60% * 5.6% + 40% * 12%

= 8.16%

We will incorporate the effective cost of debt equation in the main model as well

### 17.3 – Terminal value

Think about a company; we invest in the company with an expectation to create wealth. Wealth creation does not happen overnight but rather over multiple years. The implicit assumption is that the company will continue to exist and function efficiently for all those years and beyond. In essence, the company is a going concern. As much as I’m personally uncomfortable with the assumption, the discounted cash flow model assumes that the company will continue to exist to infinity.

Let us live with that assumption for now.

Now, think about it: on the one hand, we are projecting the future cash flow up to the next five years; on the other hand, we expect the company to exist forever, which implies it will continue to generate a cash flow as long as it exists. If you were to imagine a timeline of sorts, it would look like this –

We assume a specific growth rate when we project the cash generated for the next five years. We need to do something similar to the cash generated from the 5th year onwards to infinity, which means we need a growth rate for cash from the 5th year ahead to infinity.

The growth rate is called ‘The terminal value growth rate,’ and the terminal value growth rate is usually equal to the long-term inflation. I hope you have noticed the following so far –

• For the first five years of our model, we make a detailed analysis of the cash flow
• From the fifth year onwards to infinity, we stop making a detailed analysis, and we assume growth in cashflow (terminal value)
• The implicit assumption is that the cash flow from the 5th year onwards will be stable and also a positive cash flow. Discounted cash flow analysis will not work if the cashflows are negative.

Once we have the terminal value growth rate, which is usually equal to the long-term inflation of the country, we can calculate the present value of each future cash flow by applying a discount rate. The discount rate is either the return expectation of equity investors or the return expectation of the firm (WACC). But practically speaking, we cannot apply the standard present value formula to identify the current value of the future cash flows because this cash flow goes up to infinity. Hence, for calculating the present value of the terminal value, we use a unique formula –

Present value of Terminal Value = C (1+ g)/(r-g)

Where –

C = cash as of today

g = growth rate i.e. inflation rate

r = discount rate (either for equity investors or the firm as such)

The formula’s derivation is fairly easy, but I’ll skip getting into the details for now. However, please think through what we are trying to do here. Assume, from the 5th year onwards, i.e., for the 6th year and onwards towards infinity, we start computing the cashflow –

6th Year – FCF is 50Cr

7th Year – FCF is 53 Cr

8th Year – FCF is 55 Cr

So on and so forth till infinity. When you compute the present value of the terminal value, you essentially calculate the lump sum amount you are willing to pay today for this stream of cash flow in the future.

I hope you’ve got a gist of what we are trying to discuss here. Do go through this chapter again if you found it confusing. In the next chapter, we will implement everything we have discussed over the last few chapters and complete our valuation model.

The DCF model is super sensitive to the company’s terminal value because the terminal value is a huge number, so any slight change in our assumption will significantly impact our final valuation, which will become apparent to you in the next chapter.

### Key takeaways from this chapter

• While calculating WACC, the debt holder’s return expectation should factor in the tax shield, which is called the effective cost of debt.
• The company is a growing concern, expected to generate cash at a steady rate.
• The detailed analysis stops at the 5th year.
• We expect the cash to grow at the inflation rate.
• We apply the principle of present value to get the terminal value
• The discounted cash flow model is sensitive to the terminal value

1. JAY KOTECHA says:

sir please provide pdf of this module and upload test related to this module and previous module in app so we can check how much we can check for our mistakes as well as gain certificates

• Karthik Rangappa says:

PDF will be done once the module is complete. It will after another chapter or so. The test is after the module comes on the app.

2. Mohammed Intekhab Khan says:

I don’t comment often and this is the first time I’m speaking out as I couldn’t resist my inner desire to Thank You for such a great effort. I’m very highly grateful to you sir for this module. You’ve done an amazing job. I’ll request you to please also provide advance level modules on Financial Modelling once this module is completed. And your writing skills are great sir because I found it very helpful in understanding and easy to comprehend far better than a video.
Thank You so much sir.
Sir, I’d like to know how many chapters are left and when those chapters will be available?

• Karthik Rangappa says:

Thanks for letting me know, Mohammed, it means a lot 🙂

Based on how people respond to this module, I’ll figure out if another module on the advanced topics is required. As far as the number of chapters are concerned, I think maybe 1 or 2 more in this module. We just have to implement the DCF model on our primary model, and we are done.

3. kanhaiya kumar says:

can you send in pdf form

• Karthik Rangappa says:

PDF is not updated yet, we will do that after completing this module.

4. Vishnu says:

Sir thank you for the yeoman service in teaching us Finance.Is this the last of the modules we will see in Varsity or will there be more courses?

Grateful

• Karthik Rangappa says:

There is another chapter or so in this module, Vishnu. After this, I’ll probably update all the modules. Not sure..but there will be more 🙂

5. Faraz Rahman says:

Sir when will the course be added in the varsity app?

• Karthik Rangappa says:

In a month or so, Faraz.

6. Chandramouli Sridhar says:

Karthik Sir,

I have just finished going through all your modules. I must confess that your presentation skill is amzing. I have read several books and material on various topics such as options and futures etc. but your manner of presentation beats them all. I am eagerly looking forward to more material in Zerodha

• Karthik Rangappa says:

Thanks for the kind words and happy learning 🙂

7. Abhi says:

I think this formula is incorrect in section 17.2
“Re = Rf + β *( Rf – Rm)” as stated in this page.
As per Earlier page the formula should be “Re = Rf + β*(Rf – Rm)” , I think this is correct.Also got bit confused while seeing difference.
Risk premium = B*(Rm – Rf), where
Rf = Risk-free rate
Β = Beta of the stock
Rm = Market rate

Amazing content,Coding it out.

• Karthik Rangappa says:

Hey Abhi, its Rm – Rf, given Rm > Rf.

8. Sathish says:

1. Sir, how to figure out market return expectations in the cost of equity formula? Is it the return expected for the next year or the CAGR for the next 10 years in general?

2. If I were to expect a market return for a declining sector like say chemicals, what return expectations should I keep? Should it be negative or a low positive number?

Thanks.

• Karthik Rangappa says:

1) You can consider the oportunity cost as a proxy for cost of equity. Basically the risk free rate available in the market.
2) It should certainly not be -ve, as in why would you want to invest in equity or any asset if the returns are -ve. You can consider a single digit +ve number.

9. Sathish says:

1. I do understand that sir. I do calculate cost of equity everytime to calculate WACC and discount the cash flows with that. In that calculation(Rf+beta*(Rm-Rf) for inputing Rm – expected rate of the stock, I didn’t understand whether the expected return rate(I mean the premium above risk free rate) should be based on next year’s return expectation of that stock or expection in general for the next 10 years.

2. I do understand the expected returns cannot be negative. But this is my confusion. I want to value chemical stocks, and it is expected that the chemical sector is going to give poor returns atleast in FY24. In that case what returns should I input for expected Rm despite knowing that it is going to give negative returns next year? Should I keep the Rm expected after the sector recovers in that case since it is a long term investment?

• Karthik Rangappa says:

1) Not 10 years, maybe this can be evaluated on every 3 year basis.
2) Rm is market return right? You will have to consider the actual market return 🙂

10. Sathish says:

1. Actual market as in NIFTY returns? I thought market return of that particular stock under consideration.

2. I Use to keep it at 15%. Do you think it is fine or should I redo the calculation with a more reasonable lower number like 10 to 12%?

I’m really grateful to you for having a lot of patience to help slow learners like me. Its just that these things are new to me.

• Karthik Rangappa says:

1) You can consider market returns as its more broad based
2) Maybe you can redo, given the economic conditions may have changed.

Happy learning!

11. Anshu Gupta says:

Hy Karthik Sir, I hope you are doing great.
I have a doubt regarding how the terminal growth rate is linked to long term inflation number. Infact, I think it should be linked to long term nominal gdp growth rate because only inflation number will assume that our business is not growing in real terms like increase in sales quantity. And taking Nominal GDP Growth rate number will incorporate both the things i.e. real growth as well as inflation. Kindly resolve it sir.

• Karthik Rangappa says:

Its linked to long term average inflaction, more like 3-5%. Which I think is a fair assumption given that we are factoring it for perpetuity.

12. Anshu Gupta says:

Ok sir, thank you for it. Alternatively I guess we can also take risk free rate of currency in which cash flows are, As it will also include inflation also. Right sir?

• Karthik Rangappa says:

You can, I guess. I’ve never tried that 🙂

13. Anshu Gupta says:

Ok, Thank you sir. Indeed you are doing great work.

• Karthik Rangappa says:

Happy learning 🙂

14. Rithin says:

Hi sir could you please make the downloadable pdfs available for all the remaining modules after technical analysis. Also the course is so structured and detailed ,Thanks to the entire varsity team for the effort!

• Karthik Rangappa says:

Will do, thanks Rithin.

15. Ashay says:

which valuation method is used for negative cashflow companies
As DCF can only used for positive cashflow

• Karthik Rangappa says:

You can use relative valuations, Ashay.

16. Brahma says:

how much tax should i consider in wacc calculation, is 30% is industry standard ?

• Karthik Rangappa says:

You can check the MD&A in annual report to see what the company has to say about their tax outflow. That will give you a realistic view on taxes.