Question

Halliford Corporation expects to have earnings this coming year of $ 2.74 per share. Halliford plans to retain all of its earnings for the next two years. For the subsequent two​ years, the firm will retain 53 % of its earnings. It will then retain 23 % of its earnings from that point onward. Each​ year, retained earnings will be invested in new projects with an expected return of 27.56 % 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 11.5 %​, what price would you estimate for Halliford​ stock? ​Note: Remember that growth rate is computed​ as: retention rate times rate of return.

Answer 1

Price of stock = present value of dividends of Years 3 and 4 + present value of terminal value at end of Year 4

(The stock does not pay any dividend in Years 1 and 2 as all the earnings are reinvested)

Growth rate of earnings = retention ratio * rate of return

Growth rate of earnings during Years 1 and 2 = 100% * 27.56% = 27.56%.

Growth rate of earnings during Years 3 and 4 = 53% * 27.56% = 14.61%.

Growth rate of earnings after Year 4 = 23% * 27.56% = 6.34%.

Terminal value at end of Year 4 = Year 5 dividend / (cost of equity capital - growth rate after Year 4)

The dividends, terminal value and their present values are calculated as below :

I 1 Year A B C D E Terminal Present Earnings Dividend Value Value O $ 2.74 1 $ 3.50 2 $ 4.46 3 $ 5.11 $ 2.40 $ 1.73 4 $ 5.86 $ 2.75 $ 92.93 $ 61.91 5 $ 6.23 $ 4.80 Total $ 63.64

A B Dividend Terminal Value Present Value 20 3 1 42 5 3 64 75 Earnings 2.74 =B2*(1+27.56%) =B3*(1+27.56%) =B4*(1+14.61%) =B5*(1+14.61%) =B6*(1+6.34%) =B5*(1-53%) =B6*(1-53%) =B7*(1-23%) =C5/(1+11.5%) A5 =(C6/(1+11.5%)^A6)+(D6/(1+11.5%)^A6) =C7/(11.5%-6.34%) Total =SUM(E5:E7)

Price of stock = $63.64