QUESTION 1 Trust Bankers just paid an annual dividend of $1.9 per share. The exp

Question

QUESTION 1

Trust Bankers just paid an annual dividend of $1.9 per share. The expected dividend growth rate is 6.1 percent, the discount rate is 12 percent, and the dividends will last for 9 more years. What is the value of the stock?

QUESTION 2

A share of stock will pay a dividend of $1.4 one year from now, with dividend growth of 5.6 percent thereafter. According to the constant dividend growth model, if the required return is 14.8 percent, what should the value of the stock be 3 years from now?

QUESTION 3

A share of stock just paid a dividend of $1.2, with an expected dividend growth of 4.6 percent forever. According to the constant perpetual growth model, if the required return is 14.8 percent, what should the value of the stock be 2 years from now?

QUESTION 4

If the return on equity for a firm is 18 percent and the retention ratio is 28 percent, what is the percentage sustainable growth rate of earnings and dividends?

QUESTION 5

The dividend for Weaver, Inc., is expected to grow at 19 percent for the next 4 years before leveling off at a 5.9 percent rate indefinitely. If the firm just paid a dividend of $1.27 and you require a return of 12 percent on the stock, what is the most you should pay per share?

QUESTION 6

Bill’s Bakery expects earnings per share of 5 = $5 next year. Current book value is $4.3 per share. The appropriate discount rate for Bill's Bakery is 12.2 percent. Calculate the share price for Bill's Bakery if earnings grow at 4.3 percent forever.

Explanation / Answer

Question 1:

Dividends in coming 9 years= $1.90 per share growing by 6.10% per annum

Dividend per share after end of Year 1= $1.90 + ($1.90 * 0.0610)= $2.0159

Dividend per share after end of Year 2= $2.0159 + ($2.0159 * 0.0610)= $2.13887

Dividend per share after end of Year 3= $2.13887 + ($2.13887 * 0.0610)= $2.269341

Dividend per share after end of Year 4= $2.269341 + ($2.269341 * 0.0610)= $2.407771

Dividend per share after end of Year 5= $2.407771 + ($2.407771 * 0.0610)= $2.554655

Dividend per share after end of Year 6= $2.554655 + ($2.554655 * 0.0610)= $2.710478

Dividend per share after end of Year 7= $2.710478 + ($2.710478 * 0.0610)= $2.875817

Dividend per share after end of Year 8= $2.875817+ ($2.875817 * 0.0610)= $3.051242

Dividend per share after end of Year 9= $3.051242 + ($3.051242 * 0.0610)= $3.237368

Current Stock Value= Summation of disccounted future expected dividend cash inflows

Plottting the above cash inflows of dividends for 9 years in MS Excel spreadsheet, we get the summation= $13.17389= $13.17 per share of common stock= Current Stock Value

Question 2:

A share of stock will pay a dividend of $1.40 one year from now= Div1

Div2= $1.40*(1+0.056)= $1.4784 per share of common stock

Div3= $1.4784*(1+0.056)= $1.56119 per share of common stock

Div4= $1.56119*(1+0.056)= $1.648617 per share of common stock

Value of Common Stock per share three years from now= Div4 / (r - g)......... As per Gordon's constant   dividend growth model

r= Discount rate %

g= Dividend constant growth rate %

Thus,

Value of Common Stock per share three years from now= $1.648617 / (0.148 - 0.056)= $17.91975 per share of common stock

Question 3:

Dividend just paid= $1.20 per share of common stock

Div1= $1.20*(1+0.046)= $1.2552 ........................ at end of year 1 from now

Div2= $1.2552*(1+0.046)= $1.312939 ..................... at end of year 2 from now

Div3= $1.312939*(1+0.046)= $1.373334 ................ at end of year 3 from now

Thus, Value of common stock per share at end of year 2= Div3 / (r - g)= $1.373334 / (0.148 - 0.046)

= $13.46406 per share of common stock.

QUESTION 4:

Sustainable Growth Rate, SGR= Return on Equity * Retention Ratio= 0.18 * 0.28= 0.0504 ==> 5.04% per annum

This growth rate represents permanent sustainable growth rate in earnings and dividends of a company's business in future till perpetuity..

QUESTION 5:

Dividend per share at the end of year 4= $1.27*(1+0.19)4= $2.546781

Div5= $2.546781*(1+0.059)= $2.697041 per share of common stock

Value per share of common stock at end of year 4= Div5 / (0.12 - 0.059)= $44.21379 per share

Thus, Value per share of common stock as of today= $44.21379 / (1+0.12)4= $28.09866

===> $28.10 per share of common stock is the most that I should pay per share..

QUESTION 6:

Here, SGR rate% is given= 4.30% per annum and RoE= current EPS / current book-value per share

current EPS= $5 / (1+0.043)= = $4.793864;

Thus, RoE= ($4.793864 / $4.30) * 100= 111.4852%

Thus,

SGR rate= RoE * (1-Dividend-Payout ratio)

4.30= 111.4852 * (1-(Div0 / current EPS))

4.30= 111.4852 * (1 - (Div0 / 4.793864))

Solving the above equation for Div0, we get, Div0= $4.608964 per share of common stock= current year's dividend

Dividend Payout ratio= $4.608964 per share / $4.793864= 0.96143 ===> 96.143%

EPS at end of next year= $5 per share ......... Given in the problem

Thus, Div1= Dividend Payout ratio * Next year's EPS............assuming that company keeps both, the dividend policy and the dividend-payout ratio as same in the future

Div1= 0.96143 * $5.00 per share= $4.807149

Thus, Dividend Growth rate in next year= [(Div1 - Div0) / Div0] *100= [($4.807149 - $4.608964)/ $4.608964] * 100

= 4.29999 ====> 4.30% per year

We can assume this to be constant growth rate in company's dividend per share in future till perpertuity= g

Here, r= 12.20% per annum .............. Given in the problem

Thus current share price / share value of Bill's Bakery as per Gordon's constant Dividend Growth model=

Div1 / (r -g)= $4.807149 / (0.122-0.043)= $60.84999 ========> $60.85 per share of common stock..... ANSWER

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