Question

Suppose a company has a book value of equity of $25 million, and has 1 million shares outstanding. The company is expected to earn a net income of $5 million next year, and plans to plow back 20% of its earnings indefinitely to grow. The company has no debt and the firm’s equity holders require a return of 10% on their investment. With this information, answer the following three questions. (i) If we assume the company will grow at a constant rate forever, what is the value per share? (ii) Is the intrinsic value per share smaller or larger than the book value, and why? And at what P/E- ratio would the company trade in the market today if the stock is priced correctly? (iii) Now assume that the company will pay a lower dividend of $2 per share next year, and grow this dividend at 12% for 2 years. After this period, the company will pay a dividend of $5.22, which will then grow at a rate of 4% indefinitely. How would this policy affect the value per share?

Answer 1

All financials in $ million. Number of shares in million and per share data in $.

ROE = Net income / Book value of equity = 5 / 25 = 20%

Retention ratio = RR = plow back ratio = 20%

Ke = required return of 10% on their investment by equity holder

(i) If we assume the company will grow at a constant rate forever, what is the value per share?

The constant growth rate forever, g = RR x ROE = 20% x 20% = 4%

Hence, total equity value = Net income x (1 - RR) / (Ke - g) = 5 x (1 - 20%) / (10% - 4%) = $  66.67 mn

Number of shares, N = 1 mn

Hence, value per share = Equity value / N = 66.67 / 1 = $ 66.67 per share

(ii) Is the intrinsic value per share smaller or larger than the book value, and why? And at what P/E- ratio would the company trade in the market today if the stock is priced correctly?

Book value per share = Book value of equity / N = 25 / 1 = $ 25 / share.

So, the intrinsic value per share = $ 66.67 > $ 25 = book value per share.

Hence, the intrinsic value per share is larger than the book value.

Book value is usually not the right reflection of the true worth of the company. Book value of equity is usually the equity stated at cost and it doesn't reflect the true potential or intrinsic value of the firm. Hence, intrinsic value per share is usually larger than book value per share.

P / E = Equity Value / Net income = $ 66.67 mn / $ 5 mn = 13.33

(iii) Now assume that the company will pay a lower dividend of $2 per share next year, and grow this dividend at 12% for 2 years. After this period, the company will pay a dividend of $5.22, which will then grow at a rate of 4% indefinitely. How would this policy affect the value per share?

D₁ = $ 2; D₂ = D₁ x (1 + g₁) = 2 x (1 + 12%) = $ 2.24; D₃ = D₂ x (1 + g₁) = 2.24 x (1 + 12%) = $ 2.51, D₄ = $ 5.22 and then terminal growth rate, g = 4%

Horizon value of future dividends from year 4 onward, at the end of year 3 = D_{HV, 3} = D₄ / (Ke - g) = 5.22 / (10% - 4%) = 87.00

Hence, intrinsic value per share = D₁/ (1 + Ke) + D₂ / (1 + Ke)² + (D₃ + D_{HV, 3}) / (1 + Ke)³ = 2 / (1 + 10%) + 2.24 / (1 + 10%)² + (2.51 + 87) / (1 + 10%)³ = $ 70.92 / share

Hence, the new policy will positively impact the value per share. The new value per share = $ 70.92 which is higher than the earlier intrinsic value of $ 66.67 / share. The new policy will enhance the value per share.