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    Bond Values and Stock Prices

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    Part a

    Assume you hold a corporate bond with a $1,000 par value paying a 7 ⅝ coupon rate that has two years left until maturity. Calculate the value of the bond if the current market interest rate on a bond of this risk is 9 %.

    Part b

    Assume that you hold a share of common stock that will pay a dividend of $5.00 per share for the next three years. At the end of the third year, you expect the price per share to be $50. Calculate the value of the stock if your required rate of return is 11 %.

    Part c

    Calculate the price of a share of stock that is expected to pay a $15 dividend in perpetuity if the stock is priced to yield an 11.5% rate of return.

    © BrainMass Inc. brainmass.com October 6, 2022, 9:04 am ad1c9bdddf
    https://brainmass.com/economics/bonds/bond-values-stock-prices-18683

    SOLUTION This solution is FREE courtesy of BrainMass!

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    Bond Values and Stock Prices
    Part a

    Assume you hold a corporate bond with a $1,000 par value paying a 7 ⅝ coupon rate that has two years left until maturity. Calculate the value of the bond if the current market interest rate on a bond of this risk is 9 %.

    7 5/8 = 7.625%
    Discount rate= 9.000%
    We assume that the bond pays semi annual interest
    To calculate the price of the bond we need to calculate / read from tables the values of
    PVIF= Present Value Interest Factor
    PVIFA= Present Value Interest Factor for an Annuity
    Price of bond= PVIF * Redemption value + PVIFA * interest payment

    Price of bond
    Coupon rate= 7.625%
    Face value= 1000
    Payment S Semi Annual
    No of years= 2
    No of Periods= 4
    Discount rate annually= 9.00% annual
    Discount rate per period= 4.50%
    n= 4
    r= 4.50%

    Interest payment= 38.125 Semi Annual =(7.625%/2)*1000
    Redemption value= 1000

    PVIF 4 periods, 4.5% rate= 0.8386
    PVIFA 4 periods, 4.5% rate= 3.5875

    Price of bond=PVIFA X Interest Payment+PVIF X Redemption value
    PVIFA X Interest Payment= 136.77 =3.5875*38.125
    PVIF X Redemption value= 838.6 =0.8386*1000
    Total 975.37 =Price of bond

    The price of the bond= $975.37

    Answer:Value of the bond= $975.37

    There is an alternative way of solving the problem

    We discount the cash flows

    Discount rate= 9.00% Annual

    No of periods Cash flow Present value factor at 4.5%= 1/(1+4.5%)^no of periods Discounted cash flow
    Coupon Principal Total
    1 38.125 38.125 0.9569 36.482 =38.125*0.9569
    2 38.125 38.125 0.9157 34.911 =38.125*0.9157
    3 38.125 38.125 0.8763 33.409 =38.125*0.8763
    4 38.125 1000 1038.125 0.8386 870.572 =1038.125*0.8386
    $975.37

    Price of bond= $975.37

    If instead we assume that interest payments are annual

    Price of bond
    Coupon rate= 7.625%
    Face value= 1000
    Payment A Annual
    No of years= 2
    No of Periods= 2
    Discount rate annually= 9.00% annual
    Discount rate per period= 9.00%
    n= 2
    r= 9.00%

    Interest payment= 76.25 Annual =7.625%*1000
    Redemption value= 1000

    PVIF 2 periods, 9.% rate= 0.8417
    PVIFA 2 periods, 9.% rate= 1.7591

    Price of bond=PVIFA X Interest Payment+PVIF X Redemption value
    PVIFA X Interest Payment= 134.13 =1.7591*76.25
    PVIF X Redemption value= 841.7 =0.8417*1000
    Total 975.83 =Price of bond

    The price of the bond= $975.83

    Answer:Value of the bond= $975.83

    There is an alternative way of solving the problem

    We discount the cash flows

    Discount rate= 9.00% Annual

    No of periods Cash flow Present value factor at 9% = 1/(1+9%)^no of periods Discounted cash flow
    Coupon Principal Total
    1 76.25 76.25 0.9174 69.952 =76.25*0.9174
    2 76.25 1000 1076.25 0.8417 905.88 =1076.25*0.8417
    $975.83

    Price of bond= $975.83

    Part b

    Assume that you hold a share of common stock that will pay a dividend of $5.00 per share for the next three years. At the end of the third year, you expect the price per share to be $50. Calculate the value of the stock if your required rate of return is 11 %.

    We will discount ( at the required rate of return= 11 %)the dividends and the price of the bond that we will receive at the end of 3 years

    Year Cash flow Present value factor at 11 %= 1/(1+11%)^no of years Discounted cash flow
    Dividend Price of share Total
    1 5 5 0.9009 4.505 =5*0.9009
    2 5 5 0.8116 4.058 =5*0.8116
    3 5 50 55 0.7312 40.216 =55*0.7312
    $48.78

    Value of stock= $48.78

    Answer: $48.78

    Part c

    Calculate the price of a share of stock that is expected to pay a $15 dividend in perpetuity if the stock is priced to yield an 11.5% rate of return.

    Price of share= Po= Div/ r

    Div=Perpetual dividend $15
    r=required rate of return= 11.50%

    Po= Div/ r= $130.43 =15/11.5%

    Answer: $130.43

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com October 6, 2022, 9:04 am ad1c9bdddf>
    https://brainmass.com/economics/bonds/bond-values-stock-prices-18683

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