# Math Help - bonds question 2

1. ## bonds question 2

You bought a bond GMAC 8s15 on 1-1-07 at a price of 45. What is the price in dollars? How many years before it expires (assume it expired Dec 31)? How much total interest will be received from the bond by the expiration date? What is the annual yield? How much risk is associated with this bond (low, medium or high) and how do you know?

2. Originally Posted by jilllamtn
You bought a bond GMAC 8s15 on 1-1-07 at a price of 45. What is the price in dollars? How many years before it expires (assume it expired Dec 31)? How much total interest will be received from the bond by the expiration date? What is the annual yield? How much risk is associated with this bond (low, medium or high) and how do you know?
There are typically two ways to value fixed income securities: you can either use time value of money (also known as discounted cash flows), or replication (more complicated but once mastered, extremely useful for arbitrage).

I think your problem asks for TVM. In general, to price a bond, denote the following variables:

PV = present value
FV = face value
C = annual coupon payment
Y = annual yield
T = total periods that the bond will be valid (purchase date until maturity date)

Then the price of a bond is calculated as:

$PV = \frac{FV}{(1+Y)^T} + \sum_{t=1}^T \frac{C}{(1+Y)^t}$

So for example, a 3-year bond with a face value of \$100, annual coupon rate of 5%, and yield of 3% is priced as:
$PV = \frac{100}{(1+0.03)^3} + \sum_{t=1}^3 \frac{5}{(1+0.03)^t}
= \frac{100}{1.03^3} + \frac{5}{1.03^3} + \frac{5}{1.03^2} + \frac{5}{1.03^1} = 105.66
$

(In this case, this bond is sold at a premium because the PV is higher than its face value. If it's the other way around, it's at a discount).

The interest that you receive is all the coupon payments.

The annual yield is usually either given or you can solve for it according to the formula that I gave you.

Risk for bonds are reflected in their yields. Higher risk of default by the issuer of the bond results in a higher return as compensation for that risk, which results in a higher yield. A bond with yield of 6% has a higher default risk than a bond with a yield of 4%, all else held constant. For example, because corporate debt is considered to be riskier than U.S. Treasuries, corporate debt will have a higher yield than government bonds.

But keep in mind that default risk is not the only thing that affects yield. There is also liquidity, as well as other factors.

Let me know if you need further help, such on concepts of accrued interest or semiannual coupon bonds.