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10 August, 08:41

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?

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  1. 10 August, 09:06
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    (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
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