Question

You know that the assets of a firm BIG are today worth 100mil. You reasonably feel that in a year they will be either worth 110mil or 90mil. You also know that a riskless zero coupon bond maturing in one year is offering today a yield of 5%. The firm has issued a zero-coupon bond that matures in one year and has a face value of 100mil.

What should be the value of this corporate bond today?

What should be its yield to maturity?

What should be the value of the equity of the firm?

Can you do a further analysis of this problem? How are the above affected by the yield of the one year zero and the volatility of the asset value?

Answer 1

After 01 Year :

Probability of Asset Value in Good Scenario = 110 mil

Bad Scenarion = 90 Million

Expected Futue Value of the Asset (After 01 Year) = Average of the Asset Value in both scenario

= ( 110 + 90 ) / 02 = 100 mil

Now

Future value of Bond = Face Value (FV) = 100 mil

Present Value of Bond = Future Value / ( 1 + Interest Rate) ^ Year

= 100 / ( 1 + 5% ) ^ 01  

= 100 / 1.05 = 95.238

Ans:  The value of this corporate bond today = $ 95.238 mil

As it is a zero-coupon bond its Yield to maturity should be equal to the interest rate.

Ans: Yield to maturity of this bond = 5%

Future Value of

( Equity + Bond ) = Asset

Equity = Asset - Bond

Now Expected Future value of the Asset = 100mil

Future value of the Bond = 100mil

Equity = 100 - 100 = 0

Ans: the value of the equity of the firm = 0

Value of Equity dependent on The volatility of Asset Value. As per the given scenario Expected Future Value of the Asset is 100 mil. If it goes higher suppose the value of Assets in good condition increases, So the current value of the equity will have some value instead of zero.

Suppose Future Value of Assets become = 110 mil Future value of equity = Asset - Debt = 110 - 100 = 10 million

Now Yield of one year zero is used as a discount factor. So it will affect the current price of the bond. If yield goes higher current price will be reduced.