A firm is worth $50 or $180 with equal probability and is financed with debt that has a face value of
$60. The cost of capital for all securities is 12%. If the firm issues new debt with a face value of
$40 that has the same priority as the $60 debt being sold today, what effect will it have on the
Value of the existing debt?

Question

Quizplus · Accepted Answer

The first step is to calculate the current value of the firm: 
Expected value = (0.5 x $50) + (0.5 x $180) = $115
Value of debt = $60
Value of equity = $55
Using the WACC of 12%, the required return on the debt can be calculated as: 
$60 = $5(PVIFA12%,1) + $60(PVIF12%,1)
$5.48 = Interest payment per year
Therefore, the existing debt has a yield to maturity of 9.14%. 
Now, if the firm issues new debt worth $40 at the same priority as the existing debt, the total debt of the firm will be $100. The new debt holders will share the same risk as the existing debt holders, so the yield to maturity for the new debt will also be 9.14%. 
The value of the existing debt can be calculated as follows: 
$60 = $5.48(PVIFA9.14%,3) + $60(PVIF9.14%,3)
$60 = $15.45 + $45.49
Therefore, the current value of the existing debt is $60.94. 
If an additional $40 new debt is issued, the total debt of the firm becomes $140. Using the WACC of 12%, the required return on the debt can be calculated as: 
$140 = $5.48(PVIFA12%,1) + $40(PVIF12%,1) + $60(PVIF12%,1)
$10.37 = Interest payment per year
Therefore, the yield to maturity for the existing debt becomes 8.74%. 
The value of the existing debt with the additional $40 new debt can now be calculated: 
$100 = $10.37(PVIFA8.74%,3) + $60(PVIF8.74%,3)
$100 = $28.76 + $79.16
Therefore, the current value of the existing debt is $107.92. 
The change in value of the existing debt is: 
$107.92 - $60.94 = $46.98
However, the question asks for the change in value of the existing debt if new debt of $40 is issued, not $100. So, we need to calculate the value of the existing debt if only $40 new debt is issued: 
$80 = $7.16(PVIFA9.14%,3) + $60(PVIF9.14%,3)
$80 = $20.22 + $59.34
Therefore, the current value of the existing debt is $79.56. 
The change in value of the existing debt is: 
$79.56 - $60.94 = $18.62
However, this is the change in value if new debt of $40 is issued and the risk is shared equally between the two debtholders. The question does not provide any information about the risk sharing arrangement, so it cannot be determined how much the existing debt value would increase or decrease. Therefore, option B is the best choice, since it states that the value of the existing debt will decrease, but it does not provide an exact amount without the required information.

A Firm Is Worth $50 or $180 with Equal Probability