Question

Suppose you are a stock analyst at Goldman Sachs. You forecast that Paddy plc will pay dividends of $2.50, $2.75, and $2.25 at the end of each of the next 3 years. It is expected that thereafter the firm will sustain a long-run rate of growth of 4.5%. The appropriate cost of equity for Paddy is 10%. Based on your forecasts, what is the “fair” price for Paddy?

Answer 1

Let Dividend in Year n be denoted by D_n

Given, D₁ = $2.50

D₂ = $2.75

D₃ = $2.25

Growth rate for subsequent years = g = 4.5%

Hence, D₄ = D₃(1+g) = 2.25(1+0.045) = $2.35

Cost of Equity = r = 0%

Using Gordons Growth model,

Price of Stock in Year 3 = P₃ = D₃/(r - g) = 2.35/(0.10 - 0.045) = $42.73

Hence, Price of stock now = P₀ = D₁/(1+r) + D₂/(1+r)² + D₃/(1+r)³ + P₃/(1+r)³

= 2.50/(1+0.10) + 2.75/(1+0.10)² + 2.25/(1+0.10)³ + 42.73/(1+0.10)³

= $38.34