Davistown Enterprises has assets currently worth $1,600. In one year the assets will be worth either $1,400 or $1,900. The company has a zero coupon bond issue outstanding with a total face value of
$1,200. The bonds are due in one year. The risk-free rate of return is 3%. What is the value of the
Equity in Davistown Enterprises?
A) $0
B) $234.95
C) $400.00
D) $434.95
E) $734.95

Question

Quizplus · Accepted Answer

We can use the asset pricing formula:
Asset value = Equity value + Bond value
We know the total face value of the bonds is $1,200, and it is a zero coupon bond, meaning that the bond value is equal to the face value, discounted by the risk-free rate:
Bond value = $1,200 / (1 + 3%) = $1,165.05
We can now solve for the equity value, using the different possible scenarios for asset value:
If asset value is $1,400:
Equity value = $1,400 - $1,165.05 = $234.95
If asset value is $1,900:
Equity value = $1,900 - $1,165.05 = $734.95
So the range of possible equity values is between $234.95 and $734.95. However, we need to consider the probability of each scenario occurring. Based on the information given, we don't know the probability of each scenario, so we can take a simple average to get the expected equity value:
Expected equity value = ($234.95 + $734.95) / 2 = $484.95
Therefore, the closest answer is D, $434.95, which is within the range of possible equity values but not the exact expected value.

Davistown Enterprises Has Assets Currently Worth $1,600