Suppose a ﬁrm has a current market value of $900 and outstanding debt with a face value of $850. The risk-free rate of interest is 6%. If the ﬁrm will have a value of either $650 or $900 next period,
What is the value of the equity in the ﬁrm?
A) $0.00
B) $53.70
C) $57.36
D) $67.41
E) $89.65

Question

Quizplus · Accepted Answer

To find the value of equity in the firm, we need to first calculate the value of the firm's assets and then subtract the value of its debt. 
The expected value of the firm's assets next period is a weighted average of the two possible outcomes given: 
Expected asset value = (0.5 x $650) + (0.5 x $900) = $775 
To find the value of equity, we subtract the value of the debt from the value of the firm's assets: 
Equity value = $900 - $850 = $50 
To calculate the current value of the equity, we need to discount the expected equity value at the risk-free rate: 
Present value of equity = $50 / (1 + 0.06) = $47.17 
Therefore, the closest answer is C: $57.36 (rounded to the nearest cent)

Suppose a ﬁRm Has a Current Market Value of $900