Question

Doolittle Co.just paid a dividend of $4.2 this year (to). Doolittle is expected to pay 0.73 of its earnings as dividends and will have an ROE of 0.1 until the fourth year (ta). After that, its dividend payout ratio will increase to 0.79 and the ROE is expected to decrease to 0.04. Applying the cost of equity of 0.13 and the multistage growth model, compute the intrinsic price of Doolittle.

Answer 1

1). g1 = ROE * (1 - Payout Ratio) = 0.1 * (1 - 0.73) = 0.027

gC = ROE * (1 - Payout Ratio) = 0.04 * (1 - 0.79) = 0.0084

D1 = D0 * (1 + g1) = $4.2 * (1 + 0.027) = $4.3134

D2 = D1 * (1 + g1) = $4.3134 * (1 + 0.027) = $4.4299

D3 = D2 * (1 + g1) = $4.4299 * (1 + 0.027) = $4.5495

D4 = D3 * (1 + g1) = $4.5495 * (1 + 0.027) = $4.6723

D5 = D4 * (1 + gc) = $4.6723 * (1 + 0.0084) = $4.7116

P4 = D5 / [r - gC]

= $4.7116 / [0.13 - 0.0084] = $4.7116 / 0.1216 = $38.75

P0 = [D1 / (1 + r)] + [D2 / (1 + r)2] + [D3 / (1 + r)3] + [(D4 + P4) / (1 + r)4]

= [$4.3134 / (1 + 0.13)] + [$4.4299 / (1 + 0.13)2] + [$4.5495 / (1 + 0.13)3] + [($4.6723 + $38.75) / (1 + 0.13)4]

= $3.82 + $3.47 + $3.15 + $26.63 = $37.07

2). Sustainable growth rate (g) = ROE * plow-back ratio

= 0.14 * 0.49 = 0.0686, or 6.86%

Dividend payable at year 1; D1 = EPS*(1+g) *(1-plowback ratio)

= $7.5*(1 + 0.0686)*(1 - 0.49)

= $4.087

Stock price P0 = D1/(k-g)

= $4.087/(0.12 - 0.0686)

= $4.087 / 0.0514 = $79.52

EPS in year 1 = EPS0 * (1 + g)

= $7.5 * (1 + 0.0686) = $8.0145

So, PVGO = P0 - [E1 / k]

= $79.52 - ($8.0145/0.12)

= $79.52 - $66.79

= $12.73