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. 1. What should be the value of this corporate bond today? 2. What should be its yield to maturity? 3. What should be the value of the equity of the firm? 4. Can you do a further analysis of this problem?

(1) 95.23 (2) 5.008% or 5% (3) The value of equity is zero (4) The future value of the firm will be 110 mil. than Firm equity will be 110-100 = 10 mil not zero

Explanation:

Solution

Given that:

The worth in good in this example = 110 mil

Worth in bad in this example = 90 mil

The future value = (110+90) / 2

=100

Future value = 100

Now

(1) The Present value = F / (1+r) ^n

=100/1.05

=95.23

(2) the yield to maturity is given below:

YTM = (FV/PV) ^n - 1

Here

FV = future value

PV = present value

n=years

Thus

(100/95.23) ^1 - 1

=5.008% or 5%

Since the bond are zero coupon bond so interest rate is equal to YTM

(3) The total worth = 100 mil

Thus

The Debt + equity = 100

100+equity = 100

Equity = 100-100

=0

Hence the value of equity is zero.

The firm BIG is only debt firm. Firm do not have equity.

(4) The future value of the firm will be 110 mil. than Firm equity will be 110-100

=10 mil not zero