Question

Fin-Tech, a finance and technology firm, floated its shares today. The IPO prospectus notes that Fin-Tech does not plan to pay any dividend in the foreseeable future and reported annual earnings of $4 per share (this is the earning as of today). Fin-Tech’s Return on Equity is 15% and expected to stay the same forever. Investors agree that the appropriate discount rate is 10% and that in 4 years the firm will start distributing a dividend keeping the payout ratio constant after that.

Fin-Tech’s share price closed at $52.56. This trading price is the consensus valuation among investors and analysts.

1. What is the payout ratio on and after year 4 implied by investors’ valuation?

2. What is the implied PVGO?

Show all of your calculations and explain your approach.

Answer 1

Growth rate in the first four years = g = Retention ratio x ROE = 100% x 15% = 15%

Hence, EPS in year 4 = EPS₄ = EPS₀ x (1 + g)⁴ = 4 x (1 + 15%)⁴ = $  7.00

Let P be the payout ratio. Hence, Dividend in year 4 = D₄ = EPS₄ x P = 7P

Growth rate in long run, g* = Retention ratio x ROE = (1 - P) x 15% = 0.15 x (1 - P)

Ke = 10% = 0.10

Hence, price of the share at the end of year 3 = D₄ / (Ke - g*) = 7P / [0.10 - 0.15 x (1 - P)] = 7P / (0.15P - 0.05)

Hence, price of the share today = price of the share at the end of year 3 / (1 + Ke)³ = (1 + 0.10)^-3 x 7P / (0.15P - 0.05) = 5.26P / (0.15P - 0.05)

Hence, 52.56 = 5.26P / (0.15P - 0.05)

Hence, 7.884P - 2.628 = 5.26P

Hence, P = 2.628 /(7.884 - 5.26) =  1.00 = 100%

the payout ratio on and after year 4 implied by investors’ valuation = P = 100%

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Value of the firm in the absence of growth = Value of stock – (earnings / cost of equity) = 52.56 - 4 / 10% = $ 12.56