Bonds ?

When a bond is first issued, it is generally sold at par, which is the face value of the bond. For instance, the par value of a bond with a face value of $1,000 is $1,000. The par value is the principal, which is received at the end of the bond’s term. Sometimes when the demand is higher or lower than an issuer expected, the bonds might sell higher or lower than par. In the secondary market, bonds almost always trade for either more or less than par, because interest rates change continuously. When a bond trades for more than par, then it is selling at a premium, and when it is selling for less, it is selling at a discount. The main determinant of most bond prices in the secondary market is the prevailing interest rates. When interest rates rise, bond prices decline, and vice versa.

When bond prices are listed, the convention is to list them as a percentage of par value, regardless of what the face value of the bond is, with 100 being equal to par value. Thus, a bond with a face value of $1,000 which is selling for par, sells for $1,000, and a bond with a face value of $5,000 that is also selling for par will both have their price listed as 100, which means their prices are equal to 100% of par value, or $100 for each $100 of face value.

This pricing convention allows different bonds with different face values to be compared directly. For instance, if a $1,000 corporate bond was listed as 90 and a $5,000 municipal bond was listed as 95, then it can be easily seen that the $1,000 bond is selling at a bigger discount, and, therefore, has a higher yield. To find what the bond’s price actually is, the listed price must be multiplied as a percentage by the face value of the bond, so the price for the $1,000 bond is 90% x $1,000 = 0.9 x $1,000 = $900, and the price for the $5,000 bond is 95% x $5,000 = .95 x $5,000 = $4,750.

A point is equal to 1% of the bond’s face value. Thus, a point's actual value depends on the face value of the bond. Thus, 1 point = $10 for a $1,000 bond, but $50 for a $5,000 bond. So a $1,000 bond that is selling for 97 is selling at a 3 point discount, or $30 below par value, which equals $970.

No commission is charged when buying or selling bonds. A bond dealer makes money through the spread—the difference between the bid price, which is what the dealer is willing to pay for a bond, and the ask price, which is what the dealer is selling the bond for. To keep the spread further apart, bond prices are generally listed in 1/32 increments of a point, or a higher multiple, although some Treasuries have price differentials as low a3E

Price of Security that pays interest only at maturity = PRICEMAT (settlement, maturity, issue, rate, yield,basis)

Settlement = Date in quotes of settlement.

Maturity = Date in quotes when bond matures.

Rate = Nominal annual coupon interest rate in decimal form.

Yield = Annual yield to maturity in decimal form.

Issue = Issue date of the security.

Price = Price of security as a percent of par value.

Redemption = Value of security at redemption per $100 of face value. Most often, redemption will equal 100.

Frequency = Number of coupon payments per year.

1 = Annual

2 = Semiannual

4 = Quarterly

Basis = Day count basis.

0 = 30/360 (U.S. NASD basis). This is the default if the basis is omitted.

1 = actual/actual (actual number of days in month/year).

2 = actual/360

3 = actual/365

4 = European 30/360

Examples—Using Microsoft Office Excel For Calculating Bond Prices And Discounts

The following basic facts—where they apply—will be used for each of the example calculations for a 10-year bond originally issued in 1/1/2008 with a par value of $1,000:

Settlement date = 3/31/2008

Maturity date = 12/31/2017

Issue date = 1/1/2008

Coupon rate = 6%

Yield to maturity = 8%

Price (per $100 of face value) = 21.99

Redemption = 100

Frequency = 2 for most coupon bonds.

Basis = 1 (actual/actual)

What is the price of a bond selling for a yield to maturity of 8%?

Bond Price =PRICE("3/31/2008","12/31/2017",0.06,0.08,100,2,1) = 86.62092 = $866.21

What is the discount price of a zero coupon bond with a par value of $1,000 yielding 8%?

Price Discount = PRICEDISC ("3/31/2008","12/31/2017",0.06,0.08,100,1) = 21.99288 = $219.93

What is the interest rate of a discounted zero coupon bond selling for $219.90 that pays $1,000 at maturity?

Interest Rate of Bond Discount = DISC("3/31/2008","12/31/2017",21.99,100,1) = 0.080003 = 8%

Note that the price found with the PRICEDISC function has been rounded and plugged into the DISC function as a way to verify values. (21.99 = $219.90 for a bond with a $1,000 par value).

The last function, PRICEMAT, calculates the price of a security that pays all of its interest at maturity, which includes negotiable money market certificates of deposit (CD).

What is the price of a negotiable, 90-day CD originally issued for $100,000 on 3/1/2008 paying a rate of 8% with a current yield of 6% and a settlement date of 4/1/2008? Here we use the Microsoft Excel Date function, which takes the format DATE(year,month,day) to do some calendar arithmetic. We also use the banker's year of 360 days, so we choose a basis of 0, which we could have omitted, since it is the default.

Market Price of CD = PRICEMAT (DATE (2008,4,1), DATE (2008,3,1) +90, DATE (2008,3,1),0.08,0.06,0) = 100.3181 per $100 of face value = $100,318.10