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12 September, 02:51

Jallouk Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $3,000 every six months over the subsequent eight years, and finally pays $3,300 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the bond. The required return on both these bonds is 10 percent compounded semiannually.

What is the current price of bond M and bond N?

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  1. 12 September, 03:12
    0
    Current Price of Bond M is $28,406.72

    Current Price of Bond N is $2,840.91

    Explanation:

    BOND M

    PV of par paid at maturity is:

    = Face Value / (1 + r) ^ n

    where

    r is rate which is 5% because it is semiannually so, in this the rate will be:

    = 10 / 2

    = 5%

    n is number of years which is 40 because it is semiannually, so the number of years got doubled

    = 20,000 / (1 + 0.05) ^ 40

    = $2,840.92

    PV of the 16 will be computed by using the Present Value annuity:

    PVOA = PMT [ (1 - {1 / (1 + i) ^ n}) / i ]

    where

    Pmt is $3,000

    n is 16 years

    i is 0.05

    = 3,000 [ (1 - {1 / (1 + 0.05) ^ 16}) / 0.05]

    = 3,000 [ (1 - 0.45811) / 0.05]

    = 3,000 * 10.8378

    = $32,513.4

    PV at t = 0

    = 32,513.4 / 1.05 ^ 12

    = $18,104.68

    PV of the 12 year

    where

    pmt is $3,300

    t = 14

    = 3300 [ (1 - {1 / 1.05 ^12) } / 0.05]

    = 3300 [ 0.44316 / 0.05]

    = $29,248.56

    PV at 12

    = 29,248.56 / 1.05 ^12

    = $7,461.12

    PV of Bond M = $2,840.92 + $18,104.68 + $7,461.12

    = $28,406.72

    BOND N

    The Present value of Bond N is computed by using the excel formula of present value:

    =-PV (rate, nper, pmt, fv, type)

    where

    rate is 5%

    nper is 40 because it is semiannually, so the number of years got doubled

    pmt is 0

    Fv is $20,000

    Putting the values in the formula:

    =-Pv (5%,40,0,20000,0)

    = $2,840.91
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