A firm has 60% probability of being worth $100 million and a 40% probability of being worth $150 million. There is one bond outstanding that promises to pay $100 million at an interest rate of 4%. The cost of capital for the firm's projects is 8%.
-Refer to the information above. What are the current proportions of debt and equity financing used by the firm?

Question

Quizplus · Accepted Answer

Since the bond promises to pay $100 million at an interest rate of 4%, the current value of the bond is: 
$100 million / (1 + 0.04) = $96.15 million

To find the current proportions of debt and equity financing used by the firm, we need to calculate the total value of the firm at the cost of capital of 8%.

Probability of being worth $100 million: 
$100 million / (1 + 0.08) = $92.59 million 
Weighted value = 0.6 x $92.59 million = $55.55 million

Probability of being worth $150 million:
$150 million / (1 + 0.08) = $138.89 million 
Weighted value = 0.4 x $138.89 million = $55.56 million

Total value of the firm = $55.55 million + $55.56 million = $111.11 million

Therefore, the proportion of debt financing is: 
$96.15 million / $111.11 million = 0.865 or 86.5%

The proportion of equity financing is: 
(1 - 0.865) = 0.135 or 13.5%

Hence, the answer is C. To calculate the proportions of debt and equity financing, we need to know the total value of the firm. The total value of the firm is the probability-weighted sum of the two possible outcomes: 
Total value = (0.6 x $100 million) + (0.4 x $150 million) = $120 million
Therefore, the proportion of debt financing is the bond amount divided by the total value:
Debt financing = $100 million/$120 million = 83.3%
And the proportion of equity financing is the difference between the total value and the bond amount divided by the total value:
Equity financing = ($120 million - $100 million)/$120 million = 16.7%
So the answer is (C) 86.5% debt; 13.5% equity

A Firm Has 60% Probability of Being Worth $100 Million