Question

A fast growth share has the first dividend (t=1) of $2.33. Dividends are then expected to grow at a rate of 9 percent p.a. for a further 2 years. It then will settle to a constant-growth rate of 3.1 percent. If the required rate of return is 13%, what is the current price of the share? (to the nearest cent)

a. $25.95

b. $45.88

c. $23.54

d. $45.62

Answer 1

Dividend in 1st Year (D1) = $2.33

2 Year Growth Rate = 9%

Dividend in 2nd Year (D2) = $2.33 * (1 + 9%) = 2.54

Dividend in 3rd Year (D3) = $2.54 * (1 + 9%) = 2.77

Stable Growth Rate (g) = 3.1%

Required Rate of Return (Ke) = 13%

As per Gordan Growth Model,

Expected Price of Stock in Year 3 = Dividend in Year 3 * (1 + g) / (Ke - g)

Expected Price of Stock in Year 3 = 2.77 * (1 + 3.1%) / (13% - 3.1%)

Expected Price of Stock in Year 3 = $28.83

Stock Price today would be present value of expected cashflow in future.

Stock Price today = D1 / (1 + Ke)¹ + D2 / (1 + Ke)²+ (D3 + Expected Stock Price in Year 3) / (1 + Ke)³

Stock Price today = 2.33 / (1 + 13%)¹ + 2.54 / (1 + 13%)²+ (2.77 + 28.83) / (1 + 13%)³

Stock Price today = 2.06 + 1.99 + 21.90 = $25.95

Stock Price today should be $25.95. So, Option (a) is correct.