Financial Management Question/Share Valuation?

Question

Hayden Ltd intends to make its first dividend payment 2 years(s) from now. It then intends to pay dividends annually thereafter. The company has announced it expects the first three dividends to all be of the magnitude of around 5 cents per share. Subsequent dividends will then be paid out at a set rate of 50% of earnings. Your earnings forecasts for this coming year suggest that $0.20 Earnings per Share (EPS) is the most likely outcome. You are then forecasting EPS growth of around 7% p.a. in perpetuity. What would be your valuation of Hayden Ltd's shares, given you require a 15% p.a. return?

Could someone please help me figure this out step by step ? I can only complete it to a certain degree before I get confused, have spent 3 hours trying now =\. It is a toughy (for me) doing this in Uni right now

Answer 1

This is about the net present value of all your dividend payments. The first being 0 followed by three at $0.05, subsequent dividends being 50% of earnings that are increasing at a rate of 7% per year from a starting point of $0.20 in the first year. With the required rate of return being 15% p.a. you would be discounting the cash flows by 15% p.a. hence R = 1.12. Therefore the net present value is:



NPV = $0.05 * ( 1/R^2 + 1/R^3 + 1/R^4 ) + summation of the term $0.20 * 1.07^(n-1) * 0.5 / R^n for n from 5 to infinity



This can be rewritten as:



NPV = $0.09927 + summation of the term $0.20 / ( 2 * 1.07 ) * ( 1.07 / R )^n for n from 5 to infinity



which can then be rewritten as:



NPV = $0.09927 + summation of the term $0.20 / ( 2 * 1.07 ) * ( 1.07 / R )^n for n from 0 to infintiy - summation of the term $0.20 / ( 2 * 1.07 ) * ( 1.07 / R )^n for n from 0 to 4



applying the summation of an infinite geometric sequence and the summation of a finite geometric sequence equations you get:



NPV = $0.09927 + $0.093457944 / ( 1 - 1.07 / R ) - $0.093457944 * ( 1 - ( 1.07 / R ) ^ 5 ) / ( 1 - 1.07 / R )



Therefore

NPV = $1.04



The share value has a upper bound of $1.04 because at any higher a price, you would no longer meet your required 15% p.a. required rate of return.

Answer 2

1

Answer 3

First, write down all the earnings and dividend values for the next 10 years for example. Once you know how it's structured, use equations to calculate your values.



Dividend:

Year Value

0 0.00

1 0.00

2 0.05

3 0.05

4 0.05

5 0.5 * EPS

6 0.5 * EPS

7 0.5 * EPS

n 0.5 * EPS



Earnings (EPS):

Year Value

0 ?

1 0.20

2 0.20 * 1.07

3 0.20 * 1.07^2

4 0.20 * 1.07^3

5 0.20 * 1.07^4

6 0.20 * 1.07^5

7 0.20 * 1.07^6

n 0.20 * 1.07^(n-1)



Now you should have all the nominal values (a solid number) for EPS and Dividends for every year into infinity.



Since you're using DDM (dividend discount model) I'm assuming, you're looking at the present value of all future dividends. Looking here, there are 2 parts to value separately, a 3 year annuity that's 1 year delayed into the future (eg. pays at year 2-4), and a growing (geometric) perpetuity that's 4 years delayed (eg. pays starting on year 5). This should be obvious to you, hopefully. The annuity, since it's only 3 payments, can be discounted as 3 individual payments if you feel that using a more complex equation isn't worth the effort.



It says you have a required return of 15%/year. Therefore, discount these payments by 15%.



3-year annuity:

P = R * [[(1-(1+i)^(-n)]/i] = 0.05 * [[1-(1+0.15)^(-3)]/0.15] = 0.114161



This is the value of a 3 year annuity starting today (paying year 1-3). Since it is 1 year delayed (paying yeah 2-4), we discount that back another 1 year.



0.114161 / 1.15 = 0.099271



Perpetuity:

It's complicated because it's a growing geometric series that goes on to infinity, being discounted as well. I tried out various things on excel to get the numbers I needed (excel can get you all the answers you need in real life, if you weren't trying to "prove" things... eg. just get the solution). But, here's the explanation.



You have an infinite geometric series starting with a payment of 0.2, and discounted 15%/year as well. That means at time 0 (if you were to be paid based on the annuity since time zero) the annuity would pay 0.2/1.07 = 0.186916. We will need to discount by 15% as we increase the EPS by 7%, so the growth rate of the discounted EPS is 1.07/1.15 = 0.930435.



Subbing into the geometric series equation:

P = a / (1 - r) = 0.186916 / (1- (1.07/1.15)) = 0.186916 / 0.069565 = 2.686916



This value is of the discounted geometric series starting at time 0. 2 adjustments to make: 1) remove the payments from time 0 to time 4 (as the payments we actually want start at time 5), and also 2) divide that value by 2, as you are only paid half of the EPS.



For time reasons, the results are shown below, you should be able to calculate this yourself:



Payments year 0 to 4 are:

0.186916

0.200000

0.214000

0.228980

0.245009



Discounted at 15% is:

0.186916

0.173913

0.161815

0.150558

0.140084



Sum is:

0.813286



Subtract this from the total geometric series:

2.686916 - 0.813286 = 1.873630



Divide this by 2 as you are only paid half of the EPS:

1.873630 / 2 = 0.936815



Add this to the PV of the 3 year annuity (1 year delayed):

0.936815 + 0.099271 = 1.036085



So, your valuation should be $1.036085/share.



May be a shorter method to this, but this gets it done. When I do finance questions, I always model it out on excel for verification / 'knowing the answer before I do the question'. The modeling helps layout what payments come when, and also let you quantitatively find the answer. Eg. right now i have the thing modeled for 300 years (which makes the PV of payments < 0.00000005) and i get the same answer to the 6th decimal place.

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