A firm is equally likely to be worth $50 million, $80 million, $120 million, or $150 million. There is one bond outstanding that promises to pay $100 million at an interest rate of 6%. The appropriate cost of capital for the firm's projects is 12%.
-Refer to the information above. What is the current value of the bonds?

Question

Quizplus · Accepted Answer

The current value of the bond can be calculated using the formula: Bond value = (Coupon payment/Discount rate) x (1 - 1/(1+Discount rate)^n) + (Face value/(1+Discount rate)^n) where n is the number of years until maturity. In this case, the coupon payment is 6% of $100 million, or $6 million. The discount rate is 12%, and the bond has one year until maturity. Therefore, the bond value is:
Bond value = ($6 million/0.12) x (1 - 1/(1+0.12)^1) + ($100 million/(1+0.12)^1)
Bond value = $50 million x 0.893 + $89.29 million
Bond value = $44.65 million + $89.29 million
Bond value = $133.94 million
However, since the firm is equally likely to have different values, we need to take the expected value of the bond, which is:
Expected bond value = (0.25 x $50 million) + (0.25 x $80 million) + (0.25 x $120 million) + (0.25 x $150 million)
Expected bond value = $100 million
Therefore, the current value of the bond is equal to the expected bond value, or $100 million. None of the given choices is correct. To find the current value of the bonds, we need to discount the promised payment by the appropriate cost of capital for the firm's projects. The cash flow from the bond is $100 million, and the appropriate cost of capital is 12%. To find the present value of the bond, we use the formula: 
Present Value = Cash flow / (1 + Cost of Capital)^Time
Since the bond pays $100 million at the end of its term, we don't need to worry about time. 
Present Value = $100 million / (1 + 0.12)^1 = $89.28 million

However, we need to adjust this value based on the probability of the company being worth a certain amount. We can find the expected present value of the bond:

Expected Value = ($50 million x 0.25 + $80 million x 0.25 + $120 million x 0.25 + $150 million x 0.25) = $100 million

So, the current value of the bond is the expected present value, which is $100 million. Therefore, the answer is C.

A Firm Is Equally Likely to Be Worth $50 Million