Question

1. 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?

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

3. 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?

5. Return to the start of 2018, given the 2017 retained earnings as stated in question 3. 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?

6. 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

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?

Market value = Book value x (1 + premium) = 50 x (1 + 20%) = $ 60 million

Book value = $ 50 million

Market value per share = market value / number of shares outstanding = 60 / 1 = $ 60

Book value-per-share = Book value / number of shares outstanding = 50 / 1 = 50

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

ROE = After tax profits / Book value of Equity at the beginning of the year = 10 / 50 = 20%

EPS = After tax profits / number of shares outstanding = 10 / 1 = $ 10

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?

ROE = After tax profits / Book value of Equity at the beginning of the year 2018 = 10 / (50 + 5) = 18.18%

EPS = After tax profits / number of shares outstanding = 10 / 1 = $ 10

Return to the start of 2018, given the 2017 retained earnings as stated in question 3. 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?

Market value = Book value x (1 + 20%) = (50 + 5) x 1.20 = $ 66 mn

Book value = 50 + 5 = $ 55 mn

Market value per share = market value / number of shares outstanding = 66 / 1 = $ 66

Book value-per-share = Book value / number of shares outstanding = 55 / 1 = $ 55

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?

Market value = $ 66 mn + $ 100,000 x 66 x (1 - 2%) / 1,000,000 mn = 66 + 6.47 = $ 72.47 millon

Book value = $ 55 mn + $ 100,000 x 66 x (1 - 2%) / 1,000,000 mn = 55 + 6.47 = $ 61.47 million

Market value per share = market value / number of shares outstanding = 72.47 / (1 + 0.1) = $ 65.88

Book value-per-share = Book value / number of shares outstanding = 61.47 / (1 + 0.1) = $ 55.88