Question

The XYZ Corporation pays no cash dividends currently and is not expected to for the next five years. Its latest EPS was $18.00, all of which was reinvested in the company. The firm’s expected ROE for the next five years is 16% per year, and during this time it is expected to continue to reinvest all of its earnings. Starting in year 6, the firm’s ROE on new investments is expected to fall to 11%, and the company is expected to start paying out 30% of its earnings in cash dividends, which it will continue to do forever after. DEQS’s market capitalization rate is 24% per year. a. What is your estimate of XYZ’s intrinsic value per share? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Solving systematically, the estimated intrinsic value of XYZ's share is $297.68.

How is that so?

Given:

• The firm's expected ROE for the next five years is 16% per year.
• The firm is expected to continue to reinvest all of its earnings during the next five years.
• The firm's ROE on new investments is expected to fall to 11% starting in year 6.
• The company is expected to start paying out 30% of its earnings in cash dividends starting in year 6.
• The firm's market capitalization rate is 24% per year.

Calculations:

Expected EPS for the next five years:

Expected EPS = $18.00 * (1 + 0.16)⁵

= $29.52

Total retained earnings for the next five years:

Retained earnings = Expected EPS * 5

= $29.52 * 5

= $147.60

Expected EPS in year 6:

EPS year 6 = Expected EPS * (1 + 0.16)⁵ * (1 + 0.11)

= $29.52 * (1 + 0.16)⁵ * (1 + 0.11)

= $38.17

Expected dividend in year 6:

Dividend year 6 = EPS year 6 * 0.3

= $38.17 * 0.3

= $11.45

Expected growth rate of the dividend:

Growth rate = 0.11 * 0.7

= 7.7%

Present value of the dividends from year 6 onwards:

PV dividends = Dividend year 6 / (Market capitalization rate - Growth rate)

= $11.45 / (0.24 - 0.077)

= $202.20

Present value of the retained earnings in year 6:

PV retained earnings = Retained earnings / (1 + Market capitalization rate)^5

= $147.60 / (1 + 0.24)⁵

= $95.48

Intrinsic value per share:

Intrinsic value = PV dividends + PV retained earnings

= $202.20 + $95.48

= $297.68

Therefore, the estimated intrinsic value of XYZ's share is $297.68.

Answer 2

current intrinsic value per stock = $26.35

Step-by-step explanation:

year dividend EPS

0 0 $18

1 0 $20.88

2 0 $24.22

3 0 $28.10

4 0 $32.59

5 0 $37.81

6 $12.59 $41.97

growth rate up to year 5 = 16%

ROE growth rate starting year 6 = 11%

dividend growth rate starting year 6 = 11% x (1 - 30%) = 7.7%

cost of equity = 24%

horizon value at year 5 = $12.59 / (24% - 7.7%) = $77.24

current intrinsic value per stock = $77.24 / 1.24%⁵ = $26.35