Fristy Corporation has a book value of equity of $5,000 at the beginning of 2005, and net income of $1,000 for year ended 2005. It pays no dividends, and its cost of equity capital is 10%. It expects return on beginning of year equity to remain constant for 2006 and 2007 and decrease to 10% thereafter. What should its price-to-book ratio be at the end of 2005 (pick closest number)?
A)1.01
B)1.05
C)1.09
D)1.19

Question

Quizplus · Accepted Answer

The price-to-book ratio at the end of 2005 can be calculated using the Gordon Growth Model, which in this case simplifies to the formula for a perpetuity since the return on equity (ROE) is expected to equal the cost of equity (10%) from 2008 onwards. The net income for 2005 is $1,000, which is also the expected net income for 2006 and 2007 since the return on equity is constant and there are no dividends paid. The book value at the beginning of 2005 is $5,000, and it increases by the net income each year due to no dividends being paid. Therefore, the book value at the end of 2005 is $6,000 ($5,000 + $1,000). The expected net income for 2008, when the ROE equals the cost of equity, would be 10% of the book value at the end of 2007, which is $6,000 + $1,000 (2006 net income) + $1,000 (2007 net income) = $8,000. Thus, the expected net income for 2008 is $800 (10% of $8,000). Using the Gordon Growth Model with a growth rate of 0 (since ROE equals the cost of equity from 2008 onwards), the value at the end of 2007 is the expected net income for 2008 divided by the cost of equity, or $800 / 0.10 = $8,000. The price-to-book ratio at the end of 2005 is then the value at the end of 2007 ($8,000) divided by the book value at the end of 2005 ($6,000), which equals approximately 1.33. However, since this option is not available, it seems there was a mistake in the calculation or interpretation of the choices provided. The correct approach involves understanding the relationship between ROE, cost of equity, and the perpetuity value of future earnings, but the final step or the interpretation of the options may need reconsideration based on the provided choices.

Fristy Corporation Has a Book Value of Equity of $5,000