Question

A company issued 5%, 20-year bonds with a face amount of $80 million. The market yield for bonds of similar risk and maturity is 6%. Interest is paid semiannually. At what price did the bonds sell? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Enter your answers in whole dollars.)
n=
i=
Interest = Amount?
Interest = Present Value?
Principal = Amount?
Principal = Present Value?
Price of Bonds?

Answer 1

Answer:

n = 40

i = 3% (semiannual)

face value = $80 million

coupon payment = $2,000,000

market price:

PV of face value = $80 / (1 + 3%)⁴⁰ = $24.52 million

PC of coupon payments = $2 x 23.115 (PV annuity factor, 3%, 40 periods) = $46.23 million

market value = $70.75 million

Answer 2

The bond price shows the present discounted value of future cash that is derived from purchasing a bond.

The computation of value of n semiannually

$n=20*2\\=40$

The computation of value of i semiannually

$i=\frac{6 percent}{2} \\=3 percent$

The computation of the Present Value of interest when the interest amount is 2,000,000

$80,000,000*0.05*\frac{1}{2} \\=46,229,544$

The computation of present value of principal when the principal amount is 80 million

$\frac{80}{(1+0.03)^{40} } \\=24,524,547$

The computation of bond price would be

$46,229,544+24,524,547\\=70,754,091$

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