Jallouk Corporation has two different bonds currently outstanding. Bond M has a face value of $70,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $2,800 every six months over the subsequent eight years, and finally pays $3,100 every six months over the last six years. Bond N also has a face value of $70,000 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.

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TomShelby TomShelby · Answer 1 · 2019-10-24T23:43:51+02:00

Answer:

Bonds N present market value: $ 10,405.05

Bond M present market value: $ 36.893,9‬0

Explanation:

Bond N is a zero-coupon we discount maturity at 10%:

We calculate using the present value of a lump sum:

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]

Maturity 70,000.00

time 20.00

rate 0.1

[tex]\frac{70000}{(1 + 0.1)^{20} } = PV[/tex]

PV 10,405.05

Bond M

present value of the annuity payment:

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 2,800.00

time 16 (8 years 2 payment per year)

rate 0.05 (10% annual becomes 5% semiannual)

[tex]2800 \times \frac{1-(1+0.05)^{-16} }{0.05} = PV\\[/tex]

PV $30,345.7548

Then we discount at present date using the lump sum formula:

[tex]\frac{30345.7547684816}{(1 + 0.05)^{16} } = PV[/tex]

PV 13,901.74

We do the same for the next annuity:

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 3,100.00

time 12

rate 0.05

[tex]3100 \times \frac{1-(1+0.05)^{-12} }{0.05} = PV\\[/tex]

PV $27,476.0801

[tex]\frac{27476.0800729913}{(1 + 0.05)^{16} } = PV[/tex]

PV 12,587.11

Now we add the present valeu of the maturity: which is the value of the zero-coupon bond: 10,405.05

Bond M present value: 10,405.05 + 12,587.11 + 13,901.74 = 36.893,9‬