Question

1. A firm reinvests 60% of its earnings in projects with return on equity of 10%. The market capitalization rate is 15%. If the expected year-end dividend is $2/share and paid-out earnings of $5/share, find out the growth rate and present value of the growth opportunity.                              

2. Given:

Long-term government bond rate                                                       4%

Historical risk premium on the market                                                7%

Beta estimate of Sylvia’s Separates                                                   0.95

Price range of Sylvia’s Separates’ share price                                 $5 - $9

Proportion of earnings retained                                                          0.6

Average return on retained earnings                                                 12%

Proposed dividend per share next year                                             $0.30

Current annual interest on company’s loan from bank                  6%

Tax rate                                                                                                    25%

Based on the information given above,

1. find out the required rate of return using CAPM                 

2. find out the growth rate and calculate the required rate of return based on Gordon’s dividend growth model (DGM)                

3. Explain the Gordon growth model as a technique for the valuation of common stocks and discuss what kind of stocks this model is more appropriate for valuing.                                                              

4. Discuss how PE ratio can be used in equity valuation and its pitfalls.

                                                                                                                

Answer 1

a]

growth rate = retention ratio * ROE = 60% * 10% = 6%

PVGO = current share price - (earnings / cost of equity)

current share price = next year dividend / (cost of equity - growth rate)

current share price = ($2 + 6%) / (15% - 6%) = $23.56

PVGO = $23.56 - ($3 / 0.15) = $3.56

b]

i]

required return = risk free rate + (beta * market risk premium) = 4% + (0.95 * 7%) = 10.65%

ii]

growth rate = retention ratio * ROE = 0.6 * 12% = 7.2%

required return = (next year dividend / current share price) + growth rate = ( $0.30 / $7) + 0.072 = 0.1149, or 11.49%

(current share price is taken as the average of the price range of $5 to $9)

c]

Gordon growth model values stocks as the present value of future dividends. The future dividends are assumed to grow at a constant rate perpetually. value of stock is calculated as : next year dividend / (required return - constant growth rate)

This is nothing but the mathematical formula for the present value of a growing perpetuity.

This model is appropriate for valuing stocks with stable, growing dividends