8. Firm XYZ issued 3-year bonds that if they sold at Par would raise

$10,000,000. The bonds had a Par Value of $1,000 and a coupon rate

of 4 percent. If the market prices the bonds such that they carried a

yield-to-maturity of 5 percent, how much did the ?rm actually raise

with the new bond issue? Assume the coupons are paid annually.

Price is the sum of the discounted cash flows.

I'll do this one $1,000 bond at a time, and multiply at the end for the $10m of bonds.

since the discount rate is > coupon rate, the bonds will sell at a discount to par.

Coupon: 1,000 * 0.04 = $40

r = 0.05

n = 3 years

PV of coupons...use PV ordinary annuity "PVoa"

PVoa = PMT[(1 - (1 / 1+r^n)) / r]

= 40[(1 - (1 / 1.05^3)) / 0.05]

= 40[(1 - (1 / 1.15763)) / 0.05]

= 40[(1 - 0.86384) / 0.05]

= 40[0.13616 / 0.05]

= 40[2.7325]

= 108.92992

PV of par: 1,000 / 1.05^3 = 863.8376

add the two PVs together for price of one bond = $972.76752

for $10m of bonds, multiply by 10,000 = $9,727,675.20 (note that they sell at a discount)

not really sure, but here goes.

at the end of 3 yrs, at 4%, total returned is 11.2M (0.04M/yr x3 + 10M principal)

so if yield to maturity is 5% (total over 3 years) then 1.05x = 11.2M

and so

x = 11.2/1.05

which is 10.66666M

This is the amount raised.

Hi im doing an assignment and i am having trouble with this one...

8. Firm XYZ issued 3-year bonds that if they sold at Par would raise

$10,000,000. The bonds had a Par Value of $1,000 and a coupon rate

of 4 percent. If the market prices the bonds such that they carried a

yield-to-maturity of 5 percent, how much did the ?rm actually raise

with the new bond issue? Assume the coupons are paid annually.

Any help would be greatly appreciated