Question

A company’s market-to-book-value ratio at the beginning of this year was 2.5, its price-per-share was 26 and it has 100,000 shares outstanding.

a) What was its book value and book value-per-share at the beginning of the year?

b) The company’s assets were valued then at $3 million. How much debt did it have?

c) Suppose its assets today are $3.6 million. It borrowed a half million dollars from its bank since the beginning of the year; no other changes in its debt. It also did not issue any new shares. What must be its retained earnings so far this year?

Answer 1

(a)

Compute the book value per share, using the equation as shown below:

Book value per share = Market price/ Market-book ratio

                                   = $26/ 2.5

                                   = $10.40

Hence, the book value per share at the beginning of the year is $10.40.

Compute the total book value, using the equation as shown below:

Total book value = Book value per share*Shares outstanding

                            = $10.40*100,000 shares

                            = $1,040,000

Hence, the total book value at the beginning of the year is $1,040,000.

(b)

Compute the value of debt, using the equation as shown below:

Debt value = Total assets – Total book value

                   = $3,000,000 - $1,040,000

                   = $1,960,000

Hence, the value of debts at the beginning of the year is $1,960,000.   

(c)

Compute the total book value at the end of the year, using the equation as shown below:

Total book value = Total assets – Debt at the beginning – Additional debts

                            = $3,600,000 - $1,960,000 - $500,000

                            = $1,140,000

Hence, the total book value at the end of the year is $1,140,000.

Compute the retained earnings at the end of the year, using the equation as shown below:

Retained earnings = Book value at the end – Book value at the beginning

                              = $1,140,000 - $1,040,000

                              = $100,000

Hence, the retained earnings are $100,000.