Question 4

Halliford Corporation expects to have earnings this coming year of $3.15 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 20% of its earnings from that point onward.

Each year, retained earnings will be invested in new projects with an expected return of 21.36% 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 10.5% p.a., what price would you estimate for Halliford stock?

Answer: $52.77

Show Solution

Step 1: Determine the earnings growth rate

The growth in earnings comes from reinvesting retained earnings:

\[ g = \text{Retention Ratio}(b) \times \text{Return on Investment in New Projects}(ROE) \]

Therefore:

  • When retention is 100% in Years 1 and 2:

\[ g = 1.00 \times 21.36\% = 21.36\% \]

  • When retention is 53% in Years 3 and 4:

\[ g = 0.53 \times 21.36\% = 11.3208\% \]

  • When retention is 20% from Year 5 onward:

\[ g = 0.20 \times 21.36\% = 4.272\% \]

Step 2: Forecast EPS and dividends

Item Year 1 Year 2 Year 3 Year 4 Year 5 Year 6
Earnings Growth Rate
\(g_t = b_{t-1} \times ROE\) 		— 21.36% 21.36% 11.32% 11.32% 4.27%
EPS
\(EPS_t = EPS_{t-1}(1+g_t)\) 		3.15 3.82 4.64 5.16 5.75 5.99
Retention Ratio
\(b_t = \text{Proportion of earnings retained}\) 		100% 100% 53% 53% 20% 20%
Dividend Payout Ratio
\(1-b_t\) 		0% 0% 47% 47% 80% 80%
Dividend
\(D_t = EPS_t(1-b_t)\) 		0.00 0.00 2.18 2.43 4.60 4.80

Step 3: Calculate the terminal value

Starting from Year 6, Halliford maintains a constant retention ratio of 20%.

The sustainable growth rate is therefore:

\[ g = 20\% \times 21.36\% = 4.272\% \]

The Year 6 dividend is approximately:

\[ D_6 = 5.9949 \times 80\% = 4.7959 \]

The share price at the end of Year 5 is:

\[ P_5 = \frac{D_6}{r_E-g} \]

Therefore:

\[ P_5 = \frac{4.7959}{0.105-0.04272} = 77.0055 \]

Step 4: Discount the cash flows to today

The investor receives:

  • no dividend in Years 1 and 2;
  • $2.1805 in Year 3;
  • $2.4274 in Year 4;
  • $4.5994 in Year 5; and
  • the stock value of $77.0055 at the end of Year 5.

Therefore:

\[ P_0 = \frac{2.1805}{(1.105)^3} + \frac{2.4274}{(1.105)^4} + \frac{4.5994+77.0055}{(1.105)^5} \]

\[ \boxed{P_0 \approx \$52.77 \pm 0.01} \]