The discount rate when used in share valuation models

[TheMotorcycleBoy]

What Mel and I have struggled with over our entrance into equity purchases is share valuation. It's not really an exact science, but I'd like to learn a few ideas.

So far we are aware of a broad categorisation of share valuation methodologies:

1. Using multiples (e.g. PE, EV/EBITDA etc.)
2. Using projected cash flow/cash profit/dividend yields over the next 10 years, and applying a "discount rate" to bring each future cash flow back to present value.

(3. I'm also aware of another valuation method where the discontinued annual div. payouts are combined with discounted value of the estimate future net asset value).

So whilst I'm quite aware of the reason for a discount rate, i.e. the appreciation of the time value of money, what I'm less clear on, is how this rate is actually selected. In several texts I've seen, values such as 7%, 10% seem to be often picked. These seem pretty high.

Does the current rate of inflation, the 10 year gilt rate or the BoE base rate have any effect on the selection of this value?

Is it appropriate to merely think in terms of current inflation rate + one's required rate of return above that?

e.g. say if the current inflation is 2.5% and I desire 4% rate of return on my share investment, should I then use 6.5% as the discount rate in my sums?

M&M

[Alaric]

In several texts I've seen, values such as 7%, 10% seem to be often picked. These seem pretty high.

If you are discounting future dividend payments and asset prices, the uncertainty factor on what's going to be paid is pretty high. Using a high discount rate is a long established short cut way of reflecting this.

Investment trusts might be suitable for such an approach, given their approach of stable dividends and the floor value implied by the underlying asset holdings.

Older texts may have been written in an era when gilt rates were much higher.

Discount rates and internal rates of return can be two sides of the same coin. If by holding a share you eventually get an internal rate of return of 10%, you were right to value its future payments at 10%, the day before you bought it.

[TheMotorcycleBoy]

I guess that I'm still feeling a little bit green about the whole concept of "discount rate".

I thought the idea was to reflect the time value of money. IOW, you may well be *sure* of collecting, for example, £10 cash flows annually from an investment, but how much are all those future tenners actually going to be worth today?

I believed that the discount rate is the rate in which you use to bring future cash back to present value.

I picture this in a couple of ways:

1. Using purchasing power of goods/commodities e.g. it currently it costs £8.60 a head at the nearby Buffet restaurant, but in 5 years time it will probably cost £10 for the same deal. I arrived at that by assuming approx. 3% inflation. In other words the "present value" of a tenner 5 years in the future would be £8.60.

2. Another way of understanding discount rates and present values, in my mind, is to visualise what alternative options we could pursue with any of today's tenners or the future cash flows. Maybe we could invest in a high return / high risk investment, promising an annual return of 11.11%. Then if I invest £9 this year, next year I have £10. So in this scenario, the "present value" of next year's tenner is £9.

So in the above two scenarios discount rates of either 3% or 11.11% could be assumed.

But given as these figures will yield wildly differing results when entered into an valuation model how is a "sensible" value or range of values arrived at in the present day when doing a valuation?

I believe I've read previously from Buffet/Graham type writings that this rate should be established by taking the "risk free rate of return" i.e. the current yield on a 10 year gilt which is about 1.5% now and then adding a suitable value which somehow measures ones desired additional return given that this share has more risk associated with it than the gilt.

[scrumpyjack]

I take the view that most companies engage in real economic activity, and so should as a starting point in the long term maintain their value in inflation adjusted terms, whereas gilts and bonds won't (except for indexed linked gilts)

It could therefore be argued that the real terms risk free rate of return at present is negative and even indexed linked gilts are priced at present to lose value in real terms.

Where this leaves the 'correct' discount rate for equity valuation is difficult to see!

The real answer is that a share, like any other asset, is 'worth' what someone else will pay for it. The future 'values' and 'risk level' are pure guesses. If you think you know better than the market good luck to you.

[Alaric]

I believe I've read previously from Buffet/Graham type writings that this rate should be established by taking the "risk free rate of return" i.e. the current yield on a 10 year gilt which is about 1.5% now and then adding a suitable value which somehow measures ones desired additional return given that this share has more risk associated with it than the gilt.

When discounting future dividends depending on uncertain future profits and uncertain future director decisions, a risk addition of 8.5% may well be appropriate, thus giving 10%. If the payment to the investor is fixed and limited over time, as in a corporate bond, the risk addition may well be much lower, that's why corporate bonds might have a yield of 4% to 5% being the 1.5% gilt rate and 2.5% to 3.5% for risk. That's not just default as being unable to sell at an expected price because of a lack of demand comes in as well under "liquidity risk".

There's a limit to what you can do with dividend pricing models. Two companies of similar size operating in similar markets making much the same profits should have much the same share price. If they differ in their dividend policy, a method which only discounts dividends is going to give a false value signal by missing out the eventual disposal proceeds. It might be expected that the Company with the lower dividend policy would have a higher future selling price because of the retained earnings increasing its worth. That's highly speculative of course and the HYP method promoted elsewhere on TLF prefers companies that distribute to companies that retain.

[tjh290633]

My simplistic understanding is that you take the anticipated flow of dividends to infinity, find the net present value at your preferred discount rate, and that gives you your share value, which may be higher or lower than the market price. If it is higher, then you might decide to buy, or sell if it is lower than the market price.

TJH

[TheMotorcycleBoy]

I've had a bit more of a think about this topic, and I believe I now have a reasonable understanding of what exactly is meant by, the discount rate when used in share valuation models. And I believe that it is completely subjective. It was after re-reading this:

https://www.investopedia.com/terms/g/go ... hmodel.asp
then this https://www.investopedia.com/terms/r/rateofreturn.asp

in particular, that the discount rate as mentioned in the first link, is nothing more (?) than what the current/prospective investor considers to be their desired rate of return.

The wiki page also helped to throw the penny on the floor, since half way down the page it allowed me to tie together this somewhat esoteric concept into the cost of capital to the company, and the opportunity cost to the investor, as two sides of the same coin:

Some properties of the model
....
b) This equation is also used to estimate the cost of capital...

In other words it (the rate!) is a measure of how much risk the investor is prepared to bear in holding part of the firm. So the firm will need to make themselves seem attractive by making profit and thus making their perceived value rise (share price) and/or pay out divs. If the firm doesn't seem valuable, i.e. too high risk to investors, the shares sell for less and less, and the firm could be taken over, thus for this situation not to occur the firm will have to essentially raise it's div payouts, or do something wonderful to make the market re-value it.

(I believe Alaric probably hinted at something like this earlier.)

So yeah, it really is a subjective value, which common sense suggests will be higher than the risk free rate of a gilt. In other words one investor may be prepared to accept say a 4% return on a share, and that may result in them valuing the asset at £5, whereas another might require 8% which could result in a £3.50 estimation.

Apologies, to a lot of you veterans out there.... I imagine that some have grappled with this concept many moons ago - but for us the penny is just starting to really drop!

M&M

[Alaric]

In other words it (the rate!) is a measure of how much risk the investor is prepared to bear in holding part of the firm. So the firm will need to make themselves seem attractive by making profit and thus making their perceived value rise (share price) and/or pay out divs.

Another way of looking at it would be to observe that a Company needs to raise capital in order to trade. How it does this doesn't affect how much it raises and what it uses it for. So you could compare the relative costs of borrowing from a bank, using a fixed interest loan or by equity with dividends.

[Gengulphus]

... And I believe that it is completely subjective. It was after re-reading this:

https://www.investopedia.com/terms/g/go ... hmodel.asp
then this https://www.investopedia.com/terms/r/rateofreturn.asp

in particular, that the discount rate as mentioned in the first link, is nothing more (?) than what the current/prospective investor considers to be their desired rate of return.
...
Apologies, to a lot of you veterans out there.... I imagine that some have grappled with this concept many moons ago - but for us the penny is just starting to really drop!

For what it's worth, I saw this thread yesterday. Not having thought about the question of what discount rates should be much before despite probably being a "veteran" in your terms (mainly because I decided long ago, in the turn-of-the-century tech bubble, that discounted dividend / cash flow / etc models were pretty useless in practice, as I've said in more detail on your thread about them), I didn't have an answer then. But one has slowly crystallised overnight, just from mulling it over - no looking at Investopedia and other internet sources.

And now that I've come back to the thread, I find that you've basically already found my answer elsewhere! Though I might add a word: it's the investor's realistically desired rate of return. If you set it at an unrealistically high level, you're either not going to find anything to invest in that you don't consider overvalued, or worse, you're going to end up indulging in wishful rose-tinted ideas about companies' future prospects to get apparently undervalued shares. That's a particular trap during stockmarket bubbles, because they're characterised by lots of people indulging in such ideas and so give a misleading 'safety in numbers' feeling of confidence that one is right...

Gengulphus

[TheMotorcycleBoy]

And now that I've come back to the thread, I find that you've basically already found my answer elsewhere! Though I might add a word: it's the investor's realistically desired rate of return. If you set it at an unrealistically high level, you're either not going to find anything to invest in that you don't consider overvalued, or worse, you're going to end up indulging in wishful rose-tinted ideas about companies' future prospects to get apparently undervalued shares.

Exactly. The setting of the discount rate, and the idealised estimation of an asset price, seems reflective of either the investor's optimism, pessimism, foolishness, wisdom and so on.

M&M

[Hariseldon58]

Some years ago I was a mathematician at one of the dreaming spires colleges and from that perspective, using a discount rate to value shares, making assumptions years into the future is pretty well useless !

Very small changes in your assumptions give wildly different results. From a mathematical perspective it’s deeply unsatisfactory as a model.

There are numerous circumstances where discounted cash flow is useful and that’s often within a more proscribed set of circumstances, leases etc spring to mind, but as the length of the lease gets longer and interest rates lower then again you can get perverse calculations. Eg the value given to freeholds of leasehold flats using the ground rents as the income source.

The assumptions made on long contracts that interest rates remain at the same level for decades....again if you throw in different assumptions, then the valuations dramatically change.

We assume that the future will look like today and there are many investors on these forums and this thread who have long memories and are well aware that the past was unlike today and the tendency to extrapolate the present was prevalent in the past too !

One only has to look at the Investment Trust Sector to see trusts that borrowed for 25 years or more at interest rates of 12%+ to gear their portfolios, without any form of break clause, because they felt certain that investment returns would exceed those rates for the next 25 years !

My crystal ball is very cloudy but I am confident that the next 10 years will be different to the last 10 years, unfortunately I have no idea of the details !

[TheMotorcycleBoy]

Some years ago I was a mathematician at one of the dreaming spires colleges and from that perspective, using a discount rate to value shares, making assumptions years into the future is pretty well useless !

Very small changes in your assumptions give wildly different results. From a mathematical perspective it’s deeply unsatisfactory as a model.!

I think many, if not all, here would be inclined to agree with you.

So out of interest, and assuming that you do purchase individual shares, and further that you do take an interest at purchasing at a reasonable price, then what methodology do you prefer for assuring yourself that your purchasing decisions are within your risk/return principles?

M&M

[Alaric]

then what methodology do you prefer for assuring yourself that your purchasing decisions are within your risk/return principles?

The discount method can be used over short periods. If you expect an 8% dividend in a year's time, but the share price has dropped 8% or more, your return over the year is negative and your wealth would be greater if you just didn't bother to invest. You could push it out to 5 years. Will the Company maintain or even increase its dividend over that period and what is its possible share price at the end of the period? That could enable a direct comparison to a shortish Corporate Bond.

Another way to look at it is also derived from a discount approach. If you have a 2% dividend yield, but the dividend increases by 6% a year, then in a year's time, the share price is going to be 6% higher if "the market" still requires a 2% yield. Your total return is 8% and you have done rather better than the investor who opted for the 8% yield only to see the share price drop.

[TheMotorcycleBoy]

Thanks Alaric, indeed as you point out the discount rate method may have value in some areas.

The reason behind my last post was to see if this poster

Some years ago I was a mathematician at one of the dreaming spires colleges and from that perspective, using a discount rate to value shares, making assumptions years into the future is pretty well useless !

Very small changes in your assumptions give wildly different results. From a mathematical perspective it’s deeply unsatisfactory as a model.

was willing to elaborate on any alternatives which they know of.

[Hariseldon58]

@Mel
My experience of valuing individual shares simply confirmed that mathematicial methods often tend to delude by apparent precision !

You can probably start with an assumption that the market values the shares correctly, consistent with the generally accepted market knowledge. My personal belief is that you need to take a view on these assumptions and if you disagree then you might consider the effects of these differences.

[TheMotorcycleBoy]

@Mel
My experience of valuing individual shares simply confirmed that mathematicial methods often tend to delude by apparent precision !

You can probably start with an assumption that the market values the shares correctly, consistent with the generally accepted market knowledge. My personal belief is that you need to take a view on these assumptions and if you disagree then you might consider the effects of these differences.

Yeah, that's sound reasoning. We are just feeling our way to be honest. This summer I read a couple of books along the Buffett/Graham talking about buying a stock at less than it's "intrinsic value", so I thought some methods were worth a look.

But of course, the stock can make a fool out of anyone.

M&M

[Hariseldon58]

@mel
You might consider looking at Investment Trusts and discounts..

Ben Graham refers to the US equivalent, closed end investment companies in the Intelligent Investor

Some of the investment trusts trading at a discount specialise in Value investing, a double whammy perhaps ?

[TheMotorcycleBoy]

Thanks Hari,

I've not got as far as reading "The intelligent investor" - it's still on the shelf! But in the summer I read:

https://www.amazon.co.uk/Warren-Buffett ... 0982967624

which was very good, I thought. In the book there's a discounted div valuation method. But there's a twist to it - it terminates after 10 years then adds a discounted estimate of the firms NAV after 10 years.

I may write a thread on it sometime.

thanks again for your input!
Matt

[Gengulphus]

... In the book there's a discounted div valuation method. But there's a twist to it - it terminates after 10 years then adds a discounted estimate of the firms NAV after 10 years.

That's a very reasonable approach in my view - but note that it does suffer from the usual problem of NAV-based valuation methods, namely that some types of business operation are much more capital-intensive than others and that there can be issues about whether the company's assets (especially goodwill) are actually worth their book values. And the approach is typically very significantly NAV-based: I think the discounted 10-year NAV is likely to be half or more of the final total.

But it does cut down on what is the biggest source of uncertainties in a pure discounted-dividend valuation, namely the use of very long-term dividend 'forecasts'. Cut down, not eliminate: 5-10 year dividend 'forecasts' are IMHO pretty pure wishful thinking, but it's arguable that their total effect is no worse than other uncertainties in company valuation methods. (Note by the way that that is about dividend forecasts for companies, not total-dividend forecasts for the industries they're in. For instance, I would have felt pretty confident in forecasting long-term rises in total dividends from the IT industry at any time in the last few decades, and still do. But which companies will be the winners and which the losers within that industry is another question entirely, and I wouldn't feel confident about forecasting any IT company's dividends even five years ahead...)

Gengulphus

[TheMotorcycleBoy]

... In the book there's a discounted div valuation method. But there's a twist to it - it terminates after 10 years then adds a discounted estimate of the firms NAV after 10 years.

That's a very reasonable approach in my view - but note that it does suffer from the usual problem of NAV-based valuation methods, namely that some types of business operation are much more capital-intensive than others and that there can be issues about whether the company's assets (especially goodwill) are actually worth their book values. And the approach is typically very significantly NAV-based: I think the discounted 10-year NAV is likely to be half or more of the final total.

Sorry to be slow as usual....so are saying, for example that if you calculate an evaluation based:

1. the next 10 years of forecast dividends discounted back = y
2. the projected equity value 10 years on, discounted back = z

are you implying that if X is the value you estimate for your "present day market value" estimate:

where:

X = y + z

then z >= y more times than not?