I\'ve seen these problems asked quite a bit on here but can someone break down h

Question

I've seen these problems asked quite a bit on here but can someone break down how exactly the answers are attained? This is a copy with the answers already in place, I would like to know the formulas or how exactly the answers were attained.

Taussig Technologies Corporation (TTC) has been growing at a rate of 20% per year in recent years. This            
same growth rate is expected to last for another 2 years, then to decline to gn = 6%.            
            
a.   If D0 = $1.60 and rs = 10%, what is TTC's stock worth today? What are its expected dividend            
      and capital gains yields at this time, that is, during Year 1?            
            
   1. Find the price today.            
            
D0 $1.60            
rs 10.0%           
gs 20% Short-run g; for Years 1-2 only.          
gn 6% Long-run g; for Year 3 and all following years.          
20%   6%        
Year 0 1 2 3        
Dividend $1.6000 $1.9200 $2.3040 $2.4422        
            
PV of dividends            
$1.7455            
$1.9041      $2.4422      
$50.4595   $61.0560 = Horizon value = P2 =        
      4.0% = rs - gn     
$54.1091   = P0           
            
    2. Find the expected dividend yield.            
            
Recall that the expected dividend yield is equal to the next expected annual dividend divided by the price at            
the beginning of the period.            
            
Dividend yield = D1 / P0         
Dividend yield = $1.9200 / $54.1090         
Dividend yield = 3.55%           
            
     3.   Find the expected capital gains yield.            
            
The capital gains yield can be calculated by simply subtracting the dividend yield from the expected            
total return.            
            
Cap. gain yield = Expected total return Dividend yield         
Cap. gain yield = 10.0% 3.55%         
Cap. gain yield = 6.45%           
            
b.   Now assume that TTC's period of supernormal growth is to last for 5 years rather than 2 years.             
      How would this affect the price, dividend yield, and capital gains yield?            
            
    1. Find the price today.            
            
D0 $1.60            
rs 10.0%           
gs 20% Short-run g; for Years 1-5 only.          
gn 6% Long-run g; for Year 6 and all following years.          
20%      6%     
Year 0 1 2 3 4 5 6     
Dividend $1.6000 $1.9200 $2.3040 $2.7648 $3.3178 $3.9813 $4.2202     
            
PV of dividends            
$1.7455            
$1.9041            
$2.0772            
$2.2661            
$2.4721            
      $4.2202      
$65.5102   $105.5000 = Horizon value = P5 =        
$75.9751   = P0     4.0% = rs gn     
            
            
Part 2. Find the expected dividend yield.            
            
Dividend yield = D1 / P0         
Dividend yield = $1.9200 / $75.9750         
Dividend yield = 2.53%           
            
            
Part 3. Find the expected capital gains yield.            
            
Cap. gain yield = Expected total return - Dividend yield         
Cap. gain yield = 10.0% - 2.53%         
Cap. gain yield = 7.47%           
            
d.   TTC recently introduced a new line of products that has been wildly successful. On the basis of this             
      success and anticipated future success, the following free cash flows were projected:            
            
Year FCF (in millions)           
1 $5.5           
2 $12.1           
3 $23.8           
4 $44.1           
5 $69.0           
6 $88.8           
7 $107.5           
8 $128.9           
9 $147.1           
10 $161.3           
            
     After the 10th year, TTC's financial planners anticipate that its free cash flow will grow at a constant rate            
     of 6%. Also, the firm concluded that the new product caused the WACC to fall to 9%. The market value            
     of TTC's debt is $1,200 million, it uses no preferred stock, and there are 20 million shares of common            
    stock outstanding. Use the corporate valuation model approach to value the stock.            
            
INPUT DATA: (Dollars in Millions)            
WACC  9%          
gn  6%          
Millions of shares  20          
MV of debt  $1,200           
            
Year            
0               1 2 3 4 5 6 7 8 9 10 11
FCF's $5.5 $12.1 $23.8 $44.1 $69.0 $88.8 $107.5 $128.9 $147.1 $161.3 $169.4
PV of FCF's $5.05 $10.18 $18.38 $31.24 $44.85 $52.95 $58.81 $64.69 $67.73 $68.13  
            
PV of FCF1-10 =            $169.4
HV at Year 10 of FCF after Year 10 = FCF11/(WACC – gn):            
PV of HV at Year 0 = HV/(1+WACC)10:            
            
Sum = Value of the Total Corporation     $2,806.72       
Less: MV of Debt and Preferred     $1,200.00       
Value of Common Equity     $1,606.72       
            
Number of Shares (in Millions) to Divide By:     20       
            
Value per Share = Value of Common Equity/No. Shares:     $80.34 versus  using the discounted    
        dividend model    
            

Explanation / Answer

Answer:a D 1 = D *(1+g)=$1.6*(1+20%)=$1.920

D 2 = D 1 *(1+g)=D *(1+g) 2 = $1.6*(1+20%) 2=$2.304

After 2 years, g changes to 6%

D 3 = D 2 *(1+g ) =$2.304*(1+6%)=$2.442

P2=D3/(rs-G)

=2.442/(0.10-0.06)=$61.055

Price of stock today:

Answer:2 Dividend yield = D1 / P0         
Dividend yield = $1.9200 / $54.1090         
Dividend yield = 3.55%   

Answer:3 Cap. gain yield = Expected total return Dividend yield         
Cap. gain yield = 10.0% 3.55%         
Cap. gain yield = 6.45%           

Answer:b

Year Dividend Price Cash Flow P.V.F (10%) PV 1 1.92 1.92 0.90909 1.7455 2 2.304 2.304 0.82644 1.9041 2 61.056 61.056 0.82644 50.4595 Price today 54.1091

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