Question

Denver Company (DC) expects to pay a dividend of $1.28 in exactly one year. DC has recently invested in multiple wealth increasing projects and expects its operating cash flow to increase dramatically for a few years. DC expects a dividend growth rate of 50% during years 2, 3, and 4. After that high growth period, a normal growth rate of 3.1% will occur. DC shareholders require a 14.7% return. The DC stock price is closest to: A. $45.46 B. $33.91 C. $31.82 D. $29.14

Answer 1

Let Dividend in Year n be denoted by D_n

Given, D₁ = $1.28

Growth rate of Years 2 to 4 = g₁ = 50%

Hence,

D₂ = D₁(1+g₁) = 1.28(1+0.50) = $1.92

D₃ = D₂(1+g₁) = 1.92(1+0.50) = $2.88

D₄ = D₃(1+g₁) = 2.88(1+0.50) = $4.32

Growth rate for subsequent years = g = 3.1%

Hence, D₅ = D₄(1+g) = 4.32(1+0.031) = $4.45

Required Rate of Return = r = 14.7%

Using Gordons Growth model,

Price of Stock in Year 4 = P₄ = D₅/(r - g) = 4.45/(0.147 - 0.031) = $38.36

Hence, Price of stock now = P₀ = D₁/(1+r) + D₂/(1+r)² + D₃/(1+r)³ + D₄/(1+r)⁴ + P₄/(1+r)⁴

= 1.28/(1+0.147) + 1.92/(1+0.147)² + 2.88/(1+0.147)³ + 4.32/(1+0.147)⁴ + 38.36/(1+0.147)⁴

= $29.14