Calculate Share Price question.

**Timbuk2**

Firstly apologies - I had no idea what was the most suitable forum for this, so mods feel free to move if you feel this isn't appropriate!

I'm doing an Intro to Finance module and came across this question while studying.

A company pays a divided of €10 next year.
It will continue to pay dividends in the future growing at 5% p.a. until year 4, when its growth will stop.
In year 5 and onwards, it will pay out all its earnings as dividends.

Assuming that the EPS next year will be €15, what is the share price?
The capitalisation rate is 8%

This is my attempt at a solution:
I split the dividend into the 'growing' and non-growing bit.
The price for the growing bit
[latex]P =\displaystyle{\frac{10}{1.08} + \frac{10(1.05)}{(1.08)^2} + \frac{10(1.05)^2}{(1.08)^2} + \frac{10(1.05)^3}{(1.08)^4} = €35.52}[/latex]
(edit: there should be plus signs between each fraction but I'm not sure why they aren't appearing for me!)

For the non-growing bit, I just calculated it as [latex]P = \frac{Div_1}{r} = \frac{10}{1.08} = €125[/latex]

Therefore the price should be the sum of 35.52 and 125 = €160.52

Is this even close to the solution? We've never mentioned the capitalisation rate in the lectures, so I'm not sure if I'm right using it as 'r'. Also, the question tells me the EPS is €15 which I haven't used.

Cooper1992

for a share price . 160 seems almighty high

draiochtanois

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draiochtanois

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HeinekenTicket

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Shouldn't the third denominator in your first expression be cubed? Otherwise looks okay to me.

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Regarding the second expression, the denominator should be 0.08, not 1.08 but looks like just a typo based on your calculated result.

Secondly, while your thinking about the non-growth phase is correct, you should calculate P for the fourth year and then discount to present value, i.e. calculate div4/r where where div 4 is the fourth numerator in the expression above (which will be constant thereafter) and r is 8%. My calculation of P4 is 144.70.

This gives share price as and from the fourth year so it must be discounted to present value using 8% discount rate, i.e. multiply div4/r by (1/1.08)^4. My calculation is 106.36.

Add the 106.36 to your first figure (after correcting for my first point above).

**Timbuk2**

Thank you draoichtanois and HeinekenTicket!!

And yes, sorry, I did make two typos in my original post. The 3rd fraction should be over (1.08)^3 (cubed) not squared as I have written. And for the non-growing part, it should be over (0.08) not (1.08). It won't let me edit the post now because I've posted it too long ago!

Thanks again for the answers! They were very helpful!

hivizman

**Timbuk2** wrote: »

I'm doing an Intro to Finance module and came across this question while studying.

A company pays a dividend of €10 next year.
It will continue to pay dividends in the future growing at 5% p.a. until year 4, when its growth will stop.
In year 5 and onwards, it will pay out all its earnings as dividends.

Assuming that the EPS next year will be €15, what is the share price?
The capitalisation rate is 8%

This is my attempt at a solution:
I split the dividend into the 'growing' and non-growing bit.
The price for the growing bit
[latex]P =\displaystyle{\frac{10}{1.08} + \frac{10(1.05)}{(1.08)^2} + \frac{10(1.05)^2}{(1.08)^3} + \frac{10(1.05)^3}{(1.08)^4} = €35.52}[/latex]

For the non-growing bit, I just calculated it as [latex]P = \frac{Div_1}{r} = \frac{10}{0.08} = €125[/latex]

Therefore the price should be the sum of 35.52 and 125 = €160.52

Is this even close to the solution? We've never mentioned the capitalisation rate in the lectures, so I'm not sure if I'm right using it as 'r'. Also, the question tells me the EPS is €15 which I haven't used.

The calculation for the first four years is fine, but the question says that, from year 5, the company will be paying out all its earnings as dividends. Calculating the present value of the dividends from year 5 involves three stages - this is the same calculation as the one done by HeinekenTicket but with earnings instead of dividends:

First, you need to determine what the earnings will be in year 5, given that they are assumed to be €15 in year 1. The question is badly drafted, because you are not told what the growth rate in EPS is going to be between now and year 5 - all you are told is the growth in dividends between now and year 4. But it would be reasonable to assume (a) EPS growth is 5% per annum in each year from year 1 to year 4 (hence the company pays the same proportion of earnings each year as dividends), and (b) EPS growth is zero from year 5 onwards (because all earnings are paid out as dividends, there are no retained earnings that would lead to growth in net assets and hence growth in earnings in future years - also we are told "its [i.e., the company's] growth will stop" after year 4).

On this basis, earnings in year 5 will be equal to earnings in year 4, giving EPS = 15(1.05)^3 = €17.36.

Secondly, we can then use the formula for a perpetuity to calculate the value at the end of year 4 of the future dividends, from year 5 onwards. The value of all the future dividends from year 5 onwards, as measured at the end of year 4, is [latex]\frac{17.36}{0.08} = €217.05[/latex].

Finally, we need to discount this back to today's date, as the dividend stream begins in year 5. The perpetuity formula used above assumes that the cash flows begin one year after the valuation date (year 4), so the value at time zero (the beginning of year 1) would be [latex]\frac{217.05}{(1.08)^4} = €159.54[/latex].

Adding this to the present value of the dividends for years 1 to 4 of €35.52 gives a value for each share of €195.06.

This example involves a modification of the so-called Gordon dividend growth model, developed by the economist Myron Gordon in the 1950s. In the simplest case, assuming dividends grow at a constant rate g into perpetuity, and using a discount rate of r, if the expected dividend in one year's time is d per share, the value of each share is: [latex]\frac{d}{r-g}[/latex]. On the numbers given, this would provide a value of 10/0.03 = €333.33. However, in the actual question, (a) dividend growth ceases after 4 years, but (b) in year 5 and subsequent years the dividend equals EPS rather than being based on prior years' dividends.

**Timbuk2**

Thank you Hivizman, that is an excellent explanation, thanks for taking the time to write it out