Question

Halliford Corporation expects to have earnings this coming year of $3.35 per share. Halliford plans to retain all of its earnings for the next two years. For the subsequent two​ years, the firm will retain 50% 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 24.21% 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 9.2%​ what price would you estimate for Halliford​ stock?

​Note: Remember that growth rate is computed​ as: retention rate times ×rate of return.

I need help figuring out how calculate the EPS and Growth rate. I have tried reading the many similar problems on here and the "experts" just give the spread sheet w/ these calculated w/out saying how excel calculated them. Please explain exactly which number multiplies to get the answer.

Answer 1

Answer :

Calculations for first year :

EPS in first year = $3.35 per share

Halliford plans to retain all of its earnings in first and second year

So, Retention rate for first year = 100%

Retained earnings for first year = EPS in first year x Retention rate for first year

= $3.35 x 100% = $3.35 per share

Dividend for first year = EPS in first year - Retained earnings for first year

= $3.35 - $3.35 = $0

Calculations for second year :

Expected rate of return = 24.21% per year

Growth rate for second year = Retention rate for first year x  Expected rate of return

= 100 x 24.21% = 24.21%

EPS in second year = EPS in first year + (Growth rate for second year x EPS in first year)

=  $3.35 + (0.2421 x 3.35)

= $3.35 + 0.811

= $4.161

Halliford plans to retain all of its earnings in first and second year

So, Retention rate for second year = 100%

Retained earnings for second year = EPS in second year x Retention rate for second year

= $4.161 x 100% = $4.161 per share

Dividend for second year = EPS in second year - Retained earnings for second year

= $4.161 - $4.161 = $0

Calculations for third year :

Expected rate of return = 24.21% per year

Growth rate for third year = Retention rate for second year x  Expected rate of return

= 100 x 24.21% = 24.21%

EPS in third year = EPS in second year + (Growth rate for third year x EPS in second year)

=  $4.161 + (0.2421 x 4.161)

= $4.161 + 1.0074

= $5.1684

Halliford plans to retain 50% of its earnings in third and fourth year

So, Retention rate for third year = 50%

Retained earnings for third year = EPS in third year x Retention rate for third year

= $5.1684 x 50% = $2.5842 per share

Dividend for third year = EPS in third year - Retained earnings for third year

= $5.1684 - $2.5842 = $2.5842 per share

Calculations for Fourth year :

Expected rate of return = 24.21% per year

Growth rate for Fourth year = Retention rate for third year x  Expected rate of return

= 50x 24.21% =12.105%

EPS in EPS in fourth year = EPS in third year + (Growth rate for fourth year x EPS in third year)

= $5.1684 + ( 0.12015 x 5.1684)

.= $5.1684 + 0.62098

= $5.79406

Halliford plans to retain 50% of its earnings in third and fourth year

So, Retention rate for fourth year = 50%

Retained earnings for fourth year = EPS in fourth year x Retention rate for fourth year

=5.79406 x 50% = $2.897

Dividend for fourth year = EPS in fourth year - Retained earnings for fourth year

= $5.1684 - $2.897 = $2.897 per share

Calculations for Fifth year :

Growth rate for Fifth year = Retention rate for Fourth year x  Expected rate of return

= 50x 24.21% =12.105%

EPS in EPS in Fifth year = EPS in fourth year + (Growth rate for Fifth year x EPS in fourth year)

= $5.79406 + (0.12105 x 5.79406)

= 5.79406 + 0.70137

= $6.4954

Halliford plans to retain 20% of its earnings from fifth year onwards :

So, Retention rate for fifth year = 50%

Retained earnings for Fifth year = EPS in Fifth year x Retention rate for Fifth year

=6.4954 x 20% = $1.299

Dividend for Fifth year = EPS in Fifth year - Retained earnings for Fifth year

= $6.4954 - 1.299

= $5.1964

Calculations for sixth year :

Growth rate for Sixth year = Retention rate for Fifth year x  Expected rate of return

= 20 x 24.21% = 4.842%

EPS in EPS in Sixth year = EPS in Fifth year + (Growth rate for Sixth year x EPS in Fifth year)

= $6.4954 + ( 0.4842 x 6.4954)

= $6.4954 + 0.3145

= $6.8099

Retained earnings forSixth year = EPS in Sixth year x Retention rate for Sixth year

= $6.8099 x 20%

= $1.36198

Dividend for Sixth year = EPS in Sixth year - Retained earnings for Sixth year

= $6.8099 - 1.36198

= $5.44792

Growth rate for Sixth year = 4.842%

Cost of capital = 9.2%

Price of stock at year 5 = Dividend for yer 6 / (Cost of capital - Growth rate for Sixth year )

= $5.44792 / ( 0.092 - 0.04842)

= $5.44792 / 0.04358

= $125

Calculation of Net present value :

Year	Dividend	Present Value factor @ 9.20%	Present Value of dividend
1	0	0.90800	0.0000
2	0	0.82446	0.0000
3	2.5842	0.74861	1.9346
4	2.89703	0.67974	1.9692
5	5.19634	0.61720	3.2072
5 Price of stock	125	0.61720	77.1506
Total			84.2616

So, the estimated stock price  for Halliford​ stock = $84.2616