Price is the sum of the discounted cash flows.
Value of the coupon payments...
use Present Value ordinary annuity "PVoa"
coupon rate: 0.10 / 2 semi-annual periods = 0.05
coupon (PMT): 44m * 0.05 = 2.2m
r = 0.08 / 2 = 0.04
n = 8 yrs * 2 times per yr = 16
PVoa = PMT[(1 - (1 / (1 + r)^n)) / r]
= 2.2m[(1 - (1 / 1.04^16)) / 0.04]
= 2.2m[(1 - 0.53391) / 0.04]
= 2.2m[11.6523]
= $25,635,050.34
PV of par: 44,000,000 / 1.04^16 = 23,491,959.73
Add the two together for Price: $49,127,010.07
You need to determine the PV of $44 mil, N 16, R 4% (23,491,960) plus the PV of an Annuity of 2.2 mil, also with N 16, R 4%. ( 25,635,050) Total PV and Price = 49,127,010
On January 1, 2012, Water World issues $44 million of 10% bonds, due in 8 years, with interest payable semiannually on June 30 and December 31 each year.
If the market rate is 8%, will the bonds issue at face amount, a discount, or a premium? Calculate the issue price
