MULTI STAGE GROWTH MODEL HELP

Hi Guys,

I appreciate this is a long winded question to try and explain but I’m falling at a certain hurdle on this. I think it’s do with the timings of my dividends. PLEASE can someone read my answer below and see where i’ve gone wrong. I know I messed something up badly.

Thanks so much!

Assume a company has earnings per share of $5 and pays out 40% in dividends. The earnings growth rate for the next 3 years will be 20%. At the end of the third year the company will start paying out 100% of earnings in dividends and earnings will increase at an annual rate of 5% thereafter. If a 12% rate of return is required, the value of the company is approximately:

A) $92.92. B) $102.80. C) $55.69.

Could someone please clarify where I am going wrong?

My steps are this:

  1. Div Y0 = 0.4 x 5 = 2.

The earnings growth rate for the next 3 years is 20% Y1= 2 x 1.2 = 2.4

Y2= 2.4 x 1.2 =2.88

Y3 = 3.5

At the end of the 3rd year the company will pay 100% of earnings which are growing at 5%

5 x 1.05 = 5.25

Price = (5.25 x 1.05) / 12 - 5 = 78.75

So therefore.

2.4/1.12 +2.88/1.12 ^2 + 3.5/1.12^3 + 78.75/1.12^4 = 56 which is roughly ans C

This is a two stage model wherein there is supernormal growth of 20% in the first 3 years and then the growth is stable at a rate of 5%. You forgot to increase the earnings for the first three years, earnings for the 4th year should have been:

5*(1.2^3)*1.05 i.e 9.072, which is the dividend for the 4th year (100% payout).

Now apply the formula. Hope I made myself clear.

You answer is correct and I came up with similar calculations. For speed purposes think that the terminal value that you calculated is 78.75 Therefore The number should be less than that since it will be discounted back. The other two answers are well above 78.75.

I’m just looking at this quick, but wouldn’t wouldnt 100% earnings in Y4 be 9.072? 5x1.02^3 x 1.05 This should then be discounted by the 1.12^3 discount rate from Y3, the last year before constant growth. It looks like you are discounting using Y4.

9.072/.07 = 129.6 129.6/1.12^3 = 92.246 plus your other CF’s gives you 101.026

What is the solution provided by the book?

The way I’m reading the question leads me to say that D3 is (3.456/0.4) = 8.64. It says at the end of the third year, not after , the dividend payout will be 100% EPS. My thoughts-- for the dividend at the end of year 3, 100% EPS is paid as a dividend and all subsequent dividends are 100% of the EPS.

I calculated D3= 1.2^3*(5). Additionally, the 5% growth comes after the third year of 20% growth, so although D3 is 100% EPS3, D4 is 1.05 times D3. Any thoughts?

D1 2.4

D2 2.88

D3 8.64

P3= (D3*1.05)/(.12-.05)= (9.072)/(0.07)= 129.6

(2.4/1.12) + 2.88/(1.12^2) + (8.64+129.6)/(1.12^3) = 102.83 which is about 102.80

I get the same answer as you.

TS, what is the offical answer?

Thanks,

Ernest

I’m going to trust the result you and I obtained. The original poster probably has a solution manual or something, though.

Thanks for the feedback. I found this qutie a weird question to be honest.

Answer was B I think, I can’t seem to find the question on my Qbank anymore though!

I think the wording here is something that makes all the difference in this and many other probelms.

Here is the official answer:

First, calculate the dividends in years 0 through 4: (We need D4 to calculate the value in Year 3)

D0 = (0.4)(5) = 2 D1 = (2)(1.2) = 2.40 D2 = (2.4)(1.2) = 2.88 D3 = E3 = 5(1.2)3 = 8.64

g after year 3 will be 5%, so

D4 = 8.64 × 1.05 = 9.07

Then, solve for the terminal value at the end of period 3 = D4 / (k − g) = 9.07 / (0.12 − 0.05) = $129.57

Present value of the cash flows = value of stock = 2.4 / (1.12)1 + 2.88 / (1.12)2 + 8.64 / (1.12)3 + 129.57 / (1.12)3 = 2.14 + 2.29 + 6.15 + 92.22 = 102.80