The determination of the selling price of bonds is important because it helps the bondholders know the yield they will receive if they were to purchase the bond.
Bonds can be issued at par, premium and at a discount. A Bond is said to be issued at par if the yield is equal to the coupon rate. If the current market yield is more than the coupon rate stated on the bond, then, that bond has been issued at premium. If the coupon rate is more than the yield rate currently earned by similar bonds in the market (Sheth, 2007, Slide 23, chapter 12).
Bondholders receive periodic payments of interest amount, which is constant over the life of bond. Therefore the price of the bond is arrived at by discounting all these payments i.e. the selling price is the present value of all periodic payments plus the present value of the maturity amount, which is the principle amount of the bond. (Englard, 1992, Page 6, chapter 1).
The formula for calculating the price of the bond is as shown below.
Bond price= (PV) =p (1+r)-2 + p (1+r)-2 +¦. +p (1+r)-n + m (1+R)-n
Where =p= period receipt/payment
r=required yield effective
M=maturity value (principle amount)
The periodic receipts of interest amount are constant over the bond period and therefore are annuity in nature.
Therefore to calculate the present value of the interest payments the annuity formula is used.
Present value interest payments= Constant interest receipts* (1-(1 +r) n
The maturity amount (principle) is received as a single amount at the end of the bond period, thus is a single amount discounted using the single amount formula.
Present value maturity value =m (1+r)-1
Therefore, the total selling price is the sum of present value of interest and principal amount.
2) Presentation of bonds in balance sheet
When a bond is issued, the following factors are considered in accounting for the bonds.
Recording the issue or purchase of the bond
Recording the interest received during the life of the bond.
-Accounting for the retirement (through calling, refinancing or conversion) of the bond. (Sheth, 2007, Slide 16, Chapter 12)
As seen earlier bonds can be issued at par, discount or premium.
Bond issued at par- the bonds were issued between interest dates.
Bond payable xxx
Interest payable (1 month) xxx
Cash (amount of bond) xxx
Bond issued at a discount
Bonds payable xxx
Discount on bonds payable xxx
Cash (less discount on bond) xxx
Bonds issued at a premium
Bonds payable (plus premium) xxx
Cash (including premium) xxx
The buyers balance sheet will be as follows
Investments in bond xxx
Interest accrued (1 month) xxx
Cash (amount of bond) xxx
Investment in bond (less discount) xxx
Bond investment (plus premium) xxx
Cash (plus premium) xxx
B) Income statement items
The items that will be included in the income statement of Norris co. for the year 2008 include
-Adjustment to interest expenses (amortization)
The amount of interest is determined using the par value and the coupon rate and not effective rate. (Englard, 1992, page 2-3)
Using the example of Norris co. bond assuming that it was issued at par, then the interest will be 1000*xx%= interest.
Payment- interest = xx%*1000
Interest amount = yy% *(1000-discount)
The difference between the interest payment and interest amount is amortization of discount.
Interest payment =xx% * 1000
Interest amount= yy% * (1000 +premium)
The difference between the interest payment and the interest amount is the amortization of premium.