Question

XYZ Company had $50 million in owners’ equity at the start of 2017. A million shares were outstanding then, with a price at 20% premium to book value (i.e., market value-per-share is 20% above book value-per-share). What were its market value and book value; market value-per-share and book value-per-share?

XYZ earned $10 million in (after-tax) profits during 2017. What was its ROE and earnings-per-share (eps)?

XYZ retained $5 million of its 2017 earnings. Suppose the company makes the same profits in 2018. What are the new ROE and eps? Can you explain the different behaviors of these two measures relative to 2017?

Return to the start of 2018, given the 2017 retained earnings as stated in question What were XYZ’s market value and book value; market value-per-share and book value-per-share on Jan 2 2018, assuming the same relationship (i.e., 20% premium) between market and book value-per-share as in question 1? On Jan 3 2018 XYZ issues an additional 100,000 shares at a 2% discount to its Jan 2 price. What are its market and book values; market value-per-share and book value-per-share on that date?

Answer 1

1)Book value in total=$50 million,Total no of shares=1 million

so book value per share=$50 million/1 million=$50

Market value is 20% more than book value,so market price per share=$50*120%=$60

So total market value=$60*1 million=$60 million

2)After tax earnings in total=$10 million,So ROE=$10 million/$50 million*100=20%

EPS=$10 million/1 million=$10

3)The company earns same profit in 2018 i.e $10 million and Equity=$50 million+$5 million =$55 million

as out of 2017 earnings $5 million becomes retained and that became part of equity base.

so new ROE=$10 million/$55 million*100=18.18%

and EPS will be same as $10 as no. of shares are same $1 million so $10 million/1 million.

4)Book value per share in Jan 2, 2018=$55 million/1 million=$55 since total book value as shown in point 3=$55 million.

so market value per share given the same relationship=$55*120%=$66

total market value=$66*1 million=$66 million.

5)On 3rd Jan,2018 additional 1,00,000 i.e 0.1 million shares issued at 2% discount of 2nd Jan's price. i.e issue price becomes=$55*98%=$53.9

Total book value becomes=$55 million+($53.9*0.1 million)=$60.39 million

so book value per share=$60.39 million/(1+0.1) million=$ 54.9

market value per share assuming that 20% relationship still holds good=$54.9*120%=$65.88

total market value becomes=$65.88*1.1 million=$72.47 million.