How much would you pay for the bond ($1,000 par, 6% coupon rate) if your required rate is 4%? Is this bond selling for a premium or discount?
The bond should be selling at a premium, if 4% is the prevailing interest rate at that time for bonds of that type, selling at par. The value of the bond will also depend upon its term (how many years before it is redeemed), which should have been specified.
I do not see why they specify what your "required rate" is. The Yield to Maturity is what matters. That isdetermined by bond quality and market conditions.
If you pay $1500 for a $1000 face value bond paying 6% coupon, you will get $60 a year interest, and that will be 4% of what you paid. HOWEVER, when the bond matures, you will be paid only $1000, and you will have suffered a $500 loss on the principal. If it was a ten year bond, you will effectively have lost another $50 a year, or about 3% annually.
That is why the maturity period of a bond sold at premium is important in determining its price.
To determine how much you would pay for the bond and whether it is selling at a premium or discount, you can use the formula for bond valuation. First, let's understand the components of the formula:
1. Bond Price: The amount you would pay for the bond.
2. Par Value: The face value of the bond, which is $1,000 in this case.
3. Coupon Rate: The annual interest rate paid by the bond, which is 6% in this case.
4. Required Rate: Your desired or required rate of return, which is 4% in this case.
The formula for bond valuation is as follows:
Bond Price = (Coupon Payment / Required Rate) + (Par Value / (1 + Required Rate)^n)
In this formula:
- Coupon Payment = Coupon Rate * Par Value
- n = Number of periods or years until the bond matures. We don't have that information, so let's assume it is 10 years.
Now, let's calculate the bond price:
Coupon Payment = 6% * $1,000 = $60
n = 10
Bond Price = ($60 / 0.04) + ($1,000 / (1 + 0.04)^10)
= $1,500 + ($1,000 / 1.4802)
= $1,500 + $675.34
= $2,175.34
Therefore, you would pay $2,175.34 for the bond if your required rate is 4%.
To determine whether the bond is selling at a premium or discount, compare the calculated bond price ($2,175.34) to the bond's par value ($1,000). Since the bond price is higher than the par value, the bond is selling at a premium.