Question

AaBbCcDd AaBbCcDd AaBCC 1 Normal 1 No Spac... Heading 1 Font Paragraph Styles The most recently paid dividend by Bridges & Associates was $0.625 per share. Its dividend is expected to grow at 20%, 25% and 35% during the coming 3 years. But after 3 years, dividend growth will slow down to a constant rate of 6% per year. The required rate of return on the stock of Bridges & Associates is 10%. 1. What is the value of the stock today? 2. What is the value of the stock 5 years from today? 3. If market is in equilibrium, what would be the total return earned on the stock in year 1? 4. If market is in equilibrium, what would be the expected dividend yield and capital gains yield for Year 5? 5. If an investor who purchased the stock at its current price expects to earn a total return of 12%. Is the stock currently over-valued or under-valued? Explain.

Answer 1

The solution to part 1)

Value of stock today using Two-stage dividend discount model will be:

Calculation of Dividend at the end of each year

D1 = D0 * (1+g%) = $ 0.625 * (1+20%) = $ 0.75

D2 = D1 * (1+g%) = $ 0.75 * (1+25%) = $ 0.94

D3 = D2 * (1+g%) = $ 0.94 * (1+35%) = $ 1.27

It is mentioned that after three years the dividend will grow at a constant rate of 6%.

Hence, as per the two-stage dividend discount model, the value of the stock will be:

= D1/(1+r)¹ + D2/(1+r)² + D3/(1+r)³​​​​​​​ + [D3*(1+g%)/(K_e - g)]/(1+r)³​​​​​​​

= $ 0.75/(1+10%)¹ + $ 0.94/(1+10%)² + $ 1.27/(1+10%)³ + [ $ 1.27*(1+6%)/(10%-6%)] / (1+10%)³

= $ 0.68 + $ 0.77 + $ 0.95 + $ 25.20

= $ 27.61

Thus, the value of the stock under two-stage dividend discount model is the US $ 27.61

The solution to part 2)

Since the dividend will grow at a constant rate until perpetuity after the 3 years, the Value of stock five years from today can be calculated using the Dividend Discount Growth Model.

According to that,

Value of Share at t=5 = D₆ / (K_e - g)

D4 = D3 * (1+g%) = $ 1.27 * (1+6%) = $ 1.34

D5 = D4 * (1+g%) = $ 1.34 * (1+6%) = $ 1.42

D6 = D5 * (1+g%) = $ 1.42 * (1+6%) = $ 1.51

Value of Share at t=5 = D₆ / (K_e - g)

= $ 1.51 / (10%-6%)

= $ 37.68