Coupon received every 6 months: Face * (rate/2) = 1,000 * .010 / 2 = $50
...you divide the interest rate by 2 because the bond pays semi-annually
...on a 10 year bond, paying 2 times per year, you receive 10 x 2 = 20 $50 payments
Par paid at maturity: Face = $1000
If you are trying to value the bond when the market rate is different from the coupon rate, use Present Value ordinary annuity "Pvoa" to value the stream of coupons, then add the PV of par paid at maturity. Add the two together to get PV of the bond (price).
For example, if the market rate is 8%...i = 0.08/2 = 0.04, PMT = $50, n = 20...
PVoa = PMT [(1 - (1 / (1 + i)^n)) / i]
= $50[(1 - ( 1 / 1.04^20)) / 0.04]
= $50[(1 - (1 / 2.19112)) / 0.04]
= $50[(1 - 0.45639) / 0.04]
= $50[0.54361 / 0.04]
= $50[13.59033]
= $679.51632
PV of par paid at maturity, n = 20, i = 0.04 <0.08/2
PV = FV / (1 + i)^n
PV = 1,000 / 1.04^20
= $456.38695
Add the two PVs together for price: $1,135.90326, round to $1,135.90
notice that the bond sells for more than par (at a premium to par) b/c the coupon rate is higher than the market rate (aka the required rate of return, the discount rate)
when coupon rate > market rate...bond sells at a premium
when coupon rate < market rate...bond sells at a discount
when coupon rate = market rate...bond sells at par
Note: If you were to use 10%, e.g. 0.10 / 2 = 0.05, as the discount rate in the above formulas your price would equal par $1000
Private Banker gave you an excellent analysis. a financial calculator does the same thing simultaneously. You can input the future $1,000 maturity value and the payments of the annuity, in one operation, as long as you understand what you are doing, which Private Banker explained nicely.
Why is it that when the market rate is less than the coupon rate of the bonds they sell at a premium? It's very simple. If you can only earn 8 percent by buying bonds, a a 10% bonds becomes available, everyone will want it. so they bid up the price to get it. The bidding stops when the bid price pays the market rate.
Similarly if a 6% bond becomes available, no one would want it. The seller would have to lower the price and sell the bond at a discount. The price would decline until it yields the market rate of interest.
To add to PrivateBanker's fine answer...
"The book shows the formula for basic bond valuation but doesn't break down how to solve it."
It may be that there is some formula there like YTM that is not "solvable" in the way that you are used to. Alas, we can't get closed form solutions to all interesting math problems and sometimes problems are solved using numerical methods (like Newton-Raphson) that would be beyond the scope of any normal finance class. Your financial calculator simply does the work for you. That's what it is for....
Please help me with this finance calculation.
On January 1st, 2010, a bond was issued at 10% coupon interest rate. It is a 10 year bond with a $1,000 par value that lays interest semiannually. Investors who buy this bond receive the contractual right to two cash flows: 1) $100 annual interest rate distributed as $50 (.50 * $100) at the end of each 6 months, and 2) the $1,000 par value at the end of the 10th year.
The book shows the formula for basic bond valuation but doesn't break down how to solve it. Please help. This is hell.
