American Real Windows has decided to issue bonds payable to finance the acquisition of a new factory. The total bond issue will be $1,000,000. The bond is offering a 10 year term with semi-annual payments of interest at an annual rate of 5%. At the time of issuance the market rate for a similar offering with similar risk was 8%.

Required: Calculate the issue price of the bonds. As part of your answer indicate if this is a discount or a premium on the face value of the bond.

Present value factors are shown below:
Present Value of a single sum for 10 periods at 5% is : .614
Present Value of a single sum for 20 periods at 5% is : .377
Present Value of a single sum for 10 periods at 8% is : .463
Present Value of a single sum for 20 periods at 8% is : .215
Present Value of a single sum for 10 periods at 4% is : .676
Present Value of a single sum for 20 periods at 4% is : .456

Present Value of an Annuity for 10 periods at 5% is : 7.722
Present Value of an Annuity for 20 periods at 5% is : 12.462
Present Value of an Annuity for 10 periods at 8% is : 6.710
Present Value of an Annuity for 20 periods at 8% is : 9.818
Present Value of an Annuity for 10 periods at 4% is : 8.111
Present Value of an Annuity for 20 periods at 4% is : 13.590

OK...

FV = 1,000,000
n = 10 yrs x 2 = 20
I = 8%/2 = 4%
PMT = .05/2 x 1,000,000 = 25,000
PV = ?

PV of the 1,000,000
1,000,000 x .456 = 456,000

PV of the Payments...
25,000 x 13.590 = 339,750

Therefore, PV of Bond is 456,000 + 339,750 = $795,750

Bonds are sold in denominations of $1,000 (rule of thumb)

So each individual bond is sold at a discount of 795.75