1 answer

Halliford Corporation expects to have earnings this coming year of $3.07 per share. Halliford plans to...

Question:

Halliford Corporation expects to have earnings this coming year of $3.07 per share. Halliford plans to retain all of its earnings for the next two years. For the subsequent two​ years, the firm will retain 51% 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 20.86% 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 8.8%​, what price would you estimate for Halliford​ stock?


Answers

Let's revisit the following concepts before we get into solving this question:

  • Growth rate in any period is a function of Return on equity (ROE) and retention ratio (RR) in the prior period.
  • Growth, gn+1 = ROE x RRn where gn+1 = growth rate in Earnings per share (EPS) in the period n+1 and RRn = Retention ratio in the period n
  • EPSn+1 = EPSn x (1 + gn+1)
  • Free cash flow to the equity holder, FCFE = EPS x (1 - RR)
  • Terminal value of FCFE at the end of period N = FCFETV, N = FCFEN+1 / (Ke - gN+1) where Ke = Cost of equity capital and gN+1 = terminal growth rate or growth rate from period N+1 onwards
  • Share price today = PV of all the future FCFE = PV of future FCFE over the period t = 1 to t = N + PV of terminal value of FCFE at the end of period N.

Once these concepts are understood, we can synthesize these into the table below. Please see the column "Linkage" to understand how each row has been calculated.

Year, (n)

Linkage

1

2

3

4

N = 5

N+1 = 6

EPS

EPSn

3.0700

3.7104

4.4844

4.9615

5.4893

5.7183

Retention Ratio

RRn

100.00%

100.00%

51.00%

51.00%

20.00%

20.00%

ROE

ROE

20.86%

20.86%

20.86%

20.86%

20.86%

20.86%

Growth rate

gn+1 = ROE x RRn

20.86%

20.86%

10.64%

10.64%

4.17%

FCFE

EPSn x (1 - RRn)

-

-

2.1974

2.4311

4.3914

4.5747

Terminal growth rate

gN+1 = g6

4.17%

Cost of equity

Ke

8.80%

Terminal Value of FCFE at the end of year 5

FCFETV,5 = FCFE6 / (Ke - g6)

98.8472

PV factor

(1+Ke)-n

0.9191

0.8448

0.7764

0.7136

0.6559

PV of FCFE

FCFE x PV factor

-

-

1.7061

1.7350

2.8805

PV of Terminal Value

TV x PV factor for year 5

64.8366

Share Price

Sum of PV of FCFE and PV of TV

71.1581

Hence, estimated price for Halliford​ stock = $ 71.16 per share

.

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