Dividend Valuation Models

I have the following questions and the answers. Can anyone show me how they got the answers.

Question
9. Company B paid a $1.00 dividend per share last year and is expected to continue to pay out 40% of its earnings as dividends for the foreseeable future. If the firm is expected to generate a 10% return on equity in the future, and if you require a 12% return on the stock, what is the value of the stock?
Answer
d. $17.67

Question
10. A stock is not expected to pay dividends until three years from now. The dividend is then expected to be $2.00 per share, the dividend payout ratio is expected to be 40%, and the return on equity is expected to be 15%. If the required rate of return is 12%, the value of the stock today is closest to;
Answer
c.$53

I will have a look at this for you Aaron when I get some free time over the next few days so before I chastise you for asking others for help I will see whether I can make sense of it myself. But this was the sort of thing I was working on last year.... so hopefully I can do it.

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Originally Posted by belgarion

Aaron, where did the questions come from?

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Fundamentals of Investing by Gitman, Joehnk, Juchau...2nd edition. They are CFA exam questions on page 326. The other questions are easy and the answer to these two questions will be in the previous chapter. I just need to spend a bit more time to find the step(s) I keep missing. I just thought someone might easily show me where I'm going wrong. I wouldn't spend too much time on it. I will post my workings if I get it right.

Under the Gordon Growth Model, the value at T-Zero equals:

D/(k-g)

Where:

D is the dividend at the end of the first period
k is the required Rate of Return
g is the expected growth rate

g is calculated by multiplying the Retention Rate (ie 1- Dividend Payout Ratio) and ROE.

So in Question 1:

g = 0.6 x 0.1
= 0.06

D = 1 x 1.06 = 1.06 (the dividend of 1 dollar just paid will be 1.06 next year)

k = 0.12

P = 1.06/(0.12-0.06)
= $17.67

The second one is a little bit more tricky:

g = 0.6 x 0.15 = 0.09

D = 2

k = 0.12

Dividends start at T+3. Therefore you can apply the same model as at T+2 as above and discount the result back to its present value:

P2 = 2/(0.12-0.09) = 66.67

To discount that value back to T-0, simply divide by (1+required ROR)^T ie 1.12^2, giving you $53.14.

Thanks Lego Man. I had trouble with the growth rate. I guess it makes sense that what is not paid out as dividends will grow depending on the Return on Equity. Seems simple now, thanks.

Just looking at dividend history for Contact Energy on the NZX but the NZX site only has two years unless you want to pay $4,695 per annum.

Dividendyield.co.nz (thanks Birmanboy)and Contacts website both have the cash dividend paid but not the imputation credits attached. Same with the IRG yearbook.

Is there anywhere I can find the gross dividend including imputation credits attached as Contact does not always attach them at 28%.

Would there be a section in the company annual report that would cover this without me having to read all 90 odd pages to find the info?

I want the gross dividend information as using the cash paid would be like getting an interest rate based on net interest paid without know at what rate tax was deducted. Or have I got that wrong?

I do have the history of cash payments so maybe someone has an idea how I could use that, such as assuming fully imputed dividends (but risk over estimating).

I will take it that the lack of replies means there is no historical data easily available that anyone knows about.

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Originally Posted by Aaron

I will take it that the lack of replies means there is no historical data easily available that anyone knows about.

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I couldn't see any available in the eg 2013 annual or interim reports.

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Originally Posted by Aaron

Just looking at dividend history for Contact Energy on the NZX but the NZX site only has two years unless you want to pay $4,695 per annum.

Dividendyield.co.nz (thanks Birmanboy)and Contacts website both have the cash dividend paid but not the imputation credits attached. Same with the IRG yearbook.

Is there anywhere I can find the gross dividend including imputation credits attached as Contact does not always attach them at 28%.

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Aaron, I have done a bit of work myself on Contact dividends in the past. It is no longer quite up to date but you may find some of my historic posts on the CEN thread gives you a start. I have been a Contact Energy shareholder since day 1. So I was able to calculate the rate of imputation from my own dividend statements.

Post 1590 titled 'The overoptimisation of imputation credits' is here.

https://www.sharetrader.co.nz/showth...end#post757386

That post shows the somewhat patchy imputation record since the FY2015 50c 'special dividend'. That special dividend cleared out imputation credits before Origin Energy departed from the share register. IIRC the interim and final dividends were all fully imputed before this.

There is a problem with using historical dividends to value Contact Energy though. In FY2018 Contact changed their dividend policy to pay out 100% of 'Operating Free Cashflow', up from 80% of 'Operating Free Cashflow'. That means that the historical dividend payout is not representative of what would have happened had the FY2018 onward dividend policy been in place. I did the exercise and worked out what the dividend would have been over the previous ten years, had the current dividend policy been in place. This work is from the same page, my post 1579 titled. "FY2018 Dividend Policy: Scenario Analysis (2018 Perspective)".

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Originally Posted by Aaron

Would there be a section in the company annual report that would cover this without me having to read all 90 odd pages to find the info?

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There is a section on the dividend in each annual report. However, I am not sure it lists the detailed imputation credit details that you asked about.

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Originally Posted by Aaron

I want the gross dividend information as using the cash paid would be like getting an interest rate based on net interest paid without know at what rate tax was deducted. Or have I got that wrong?

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No, I think you have it right!

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Originally Posted by Aaron

I do have the history of cash payments so maybe someone has an idea how I could use that, such as assuming fully imputed dividends (but risk over estimating).

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No need to do that. That first post I referenced should give you the imputation credit information that you require, up until EOFY2018 at least! HTH.

SNOOPY

Many Thanks Snoopy. Also 100% dividend policy will make a big difference to my calculations that I was not aware of. I see you used 6% for your Contact valuation back in May. Still 6%?

I really need to put in the hard yards like you do to get a better understanding of things.

I thought if I start with something simple like the dividend discount model as a starting point to get a potential buy price, I can work backwards on the assumptions such as the dividend and likelihood of future dividends. The capitalisation rate is a stab in the dark and adding a growth rate to try and make the share seem affordable is also a stab in the dark. Looking at the cash dividend history back to 2003 I was going to say there was little growth but I suppose there has been but it has been up and down.
Current share price looks fair at around $6 with a discount rate of 7% and using an average of dividends paid over the last four years. The increased payout ratio would have helped.

I put a bid in at $5 when it started heading back up after the crash but was too slow and didn't chase it.

My gut and historical precedent says we are in for another leg down when the economic impact of the world wide lockdown comes through in earnings and other figures but the optimist in me says word of a vaccine and the end of the lockdown with central bank lunacy supporting asset prices it will mean we are back to the races.

As Peat has said I can't wait for the bell at the bottom so I should at least make some effort towards basing decisions on something other than hope and luck and making some purchases now if they make sense.

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Originally Posted by Aaron

Many Thanks Snoopy. Also 100% dividend policy will make a big difference to my calculations that I was not aware of.

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The dividend policy is actually 100% of 'free cashflow', which is actually more than 100% of earnings!

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Originally Posted by Aaron

I see you used 6% for your Contact valuation back in May. Still 6%?

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I think you are reading the 'quoted' bit of that post which was from a year earlier. I said in the post proper:

"If we assume that a business cycle investment 'gross return' of 5.5% is required, ..."

I use a slightly higher figure than some because I know that when interest rates rise, as they inevitably do, that means the fair price of my income earning asset goes down. By using a slightly higher than market gross return as my yardstick, I am effectively building in a rise in interest rates down the track. I think of that as a 'safety margin' to stop me paying too much!

Nevertheless where we are now with the cash rate at just 0.5%, for a year at least, I can see these 'all time low interest rates' going lower. So I am starting to think a gross return of 5% on Contact Energy shares might be my update yardstick!

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Originally Posted by Aaron

I really need to put in the hard yards like you do to get a better understanding of things.

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I have put in the hard yards, but I can't say I am fully on top of things yet. Continually paying out substantially more than your earnings as dividends still does my head in!

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Originally Posted by Aaron

I thought if I start with something simple like the dividend discount model as a starting point to get a potential buy price, I can work backwards on the assumptions such as the dividend and likelihood of future dividends. The capitalisation rate is a stab in the dark

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The capitalisation rate is what you think is an acceptable gross return. Only a stab in the dark if you can't make up your mind! I have chosen my own capitalisation rate that you might not agree with and that is fine. You are entitled to your own opinion, and I am not going to say you are wrong if you choose differently.

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Originally Posted by Aaron

and adding a growth rate to try and make the share seem affordable is also a stab in the dark.

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And there you have hit on an important dilemma for me. Generally I model 'growth' by adding the retained earnings after the dividend is paid to the previous year's equity figure. Then I multiply that total by a representative return on equity to come up with the subsequent year's projected earnings.
But what if all of your earnings are paid out as dividends? That means no earned and retained capital available for future growth, right? Now what happens when you regularly pay out more than your earnings in dividends?

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Originally Posted by Aaron

Looking at the cash dividend history back to 2003 I was going to say there was little growth but I suppose there has been but it has been up and down.

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FWIW I am modelling no growth in dividends, but for the dividend to vary over the business cycle.

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Originally Posted by Aaron

Current share price looks fair at around $6 with a discount rate of 7% and using an average of dividends paid over the last four years. The increased payout ratio would have helped.

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The reason why I haven't updated my figures for FY2019 is that, until Covid-19, I had considered CEN too expensive. Your $6 fair value is IMO not far from the mark. I don't use a discount rate for future earnings as my method effectively considers Contact as a fixed rate bond, but with the interest rate a combination of what happened over the last ten years, yet matched up with current dividend policy.

SNOOPY

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Originally Posted by Snoopy

The reason why I haven't updated my figures for FY2019 is that, until Covid-19, I had considered CEN too expensive. Your $6 fair value is IMO not far from the mark. I don't use a discount rate for future earnings as my method effectively considers Contact as a fixed rate bond, but with the interest rate a combination of what happened over the last ten years, yet matched up with current dividend policy.

SNOOPY

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Looking at the dividends paid out over the years I haven't included a growth rate as there shouldn't really be one if you are paying out all your cash. I guess they don't see any investing opportunities and power supply in NZ is sufficient if Rio are serious about leaving. I would assume the lockdown will also reduce power demand and therefore prices. Who knows.

Hopefully the pricing model will allow them to up their charges if inflation takes off to provide some inflation protection.

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Originally Posted by Aaron

Looking at the dividends paid out over the years I haven't included a growth rate as there shouldn't really be one if you are paying out all your cash. I guess they don't see any investing opportunities and power supply in NZ is sufficient if Rio are serious about leaving. I would assume the lockdown will also reduce power demand and therefore prices. Who knows.

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Rio are tough negotiators. Threatening to leave is exactly the same tactic they used to try and get a better deal for their renewable power aluminium plant in Iceland. Although it is possible to smelt aluminium elsewhere, the very pure aluminium that Bluff produces would IMO be difficult to replace. It is possible that more of the plant will be mothballed. But I think the full close down costs will be too high.

I don't think it is true to say that Contact cannot see any growth opportunities in NZ.

https://www.thinkgeoenergy.com/conta...thermal-field/

If they do go ahead with a new power station on the Tauhara geothermal field, they will probably have a cash issue to partly fund it (the rest of the funding would be with debt). This is what happened when they built their last power station, Te Mihi.

Some argued at the time is was dumb to keep paying out big dividends only to have to go back to the market to take cash back with a 'cash issue'. With dividends not fully imputed, such a strategy would be even dumber today. It would mean creating a large tax bill for raising new capital. I wouldn't rule out things happening that way though!

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Originally Posted by Aaron

Hopefully the pricing model will allow them to up their charges if inflation takes off to provide some inflation protection.

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Renewable power stations are their hedge against inflation. They have been built for a large fixed cost but generally have very low running costs. The power pricing system in NZ works via the mechanism of the wholesale power market price creeping higher. Once the wholesale price creeps to a certain level, building a new power station becomes economical. But a rising wholesale price 'lifts all boats' in terms of market price paid for power. Existing renewable power stations pocket all of this increase in the wholesale power price as extra profit. These improved prices usually cover inflation, and more.

SNOOPY

Thanks Snoopy.