Question

Halliford Corporation expects to have earnings this coming year of

$ 3.22 per share. Halliford plans to retain all of its earnings for the next two years. For the subsequent two? years, the firm will retain 47% of its earnings. It will then retain 17% of its earnings from that point onward. Each? year, retained earnings will be invested in new projects with an expected return of 22.22% per year. Any earnings that are not retained will be paid out as dividends. Assume? Halliford's share count remains constant and all earnings growth comes from the investment of retained earnings. If? Halliford's equity cost of capital is 9.3%?, what price would you estimate for Halliford?stock?

The price per share is $__?

? (Round to the nearest? cent.)

Answer 1

Year 1:

E₁ = $3.22, D₁ = 0

Year 2:

E₂ = $3.22 * 1.2222 = 3.935484

(Since 100% earnings retained, g=22.22%)

D₂ = 0

Year 3

E₃ = E₂ * 1.2222 = $3.935484 * 1.2222 = 4.809948545

(Since 100% earnings retained, g=22.22%)

D₃ = (1-47%) * 4.809948545 = 2.549272729

Year 4

g = Retention Ratio * Returns = 47% * 22.22% = 10.4434%

E₄ = E₃ * 1.104434 = 4.809948545 * 1.104434 = 5.312270711

D₄ = (1-47%) * 5.312270711 = 2.815503477

Year 5

g = Retention Ratio * Returns = 47% * 22.22% = 10.4434%

E₅ = E₄ * (1+g) = 5.312270711 * 1.104434 = 5.86705239

D₅ = (1-17%)*5.86705239 = 4.869653484

sustainable growth g_s = Retention Ratio * Returns = 17% * 22.22% = 3.7774%

Terminal Value at year 4 = TV₄ = D₅/(r-g_s) = 4.869653484/(0.093-0.037774) =88.17682765

Price P₀ = D₁/(1+r) + D₂/(1+r)² + D₃/(1+r)³? + (D₄+TV₄)/(1+r)⁴?

= 0 + 0 + 2.549272729/1.093³ + (2.815503477+88.17682765)/1.093⁴

= $65.71 (rounded)