A bond consists of two promises. It promises to pay $1,000 on the maturity date, and it promises to pay periodic interest. The interest payments are determined by the coupon rate. If the coupon rate of interest is more than the market rate, the bond will sell at a premium because it is more attractive than the rate available in the market. So it's price will be bid up. The bidding will stop when its yield to maturity equals the market interest rate. If the coupon rate is less than the market rate, the bond will sell at a discount.
By discounting the two future cash flows to the present using the market interest rate, you can find the present value of the bond, the price at which it will sell. In a diagram you have
PV - - - PMT - - - PMT - - - - - - PMT - - - PMT + $1,000
PMT is the interest payment calculated from the coupon rate. The number of payments is determined by the life of the bond. So you have variables whose values are known and you can solve for any unknown variable when you know the others. The simplest way is using a financial calculator. The variables are
Maturity value - $1,000 face value per bond
Coupon rate - determines size of PMT
PMT = periodic interest = Face value * coupon rate * time
Number of periods is usually semiannual, sometimes annual
Market rate: Used to discount future cash flows
PV = present value of the future cash flows
A bond's coupon rate is fixed and does not change during the life of the bond. But market interest change in reaction to a variety of economic conditions. So if a bond has a 5% coupon rate, and investors can now earn only 4% in the market, the 5% bond will be very attractive. Investors will all want it so they will bid for it and its price will go up. That is, when market interest rates fall below the bonds coupon rate the price of the bond will increase.
The opposite is true if market interest rates go up. The price of the bond will go down. If investors can earn 6% interest why should they buy a bond that pays only 5%. They will buy it only if the price is low enough to yield 6%. So bond prices move in opposite directions from interest rate.
For problem 1, find the present value of $1,000 10 years from now at 10% plus the present value of 10 $120 annual payments and add up the two present values to find the market price of the bond. In a financial calculator you input:
FV = $1,000
PMT = $120
N = 10,
i% = 10%
PV = ???
Your answer should be (a) $1,122.89.
For part (b) the only difference is that you have 9 periods instead of 10, so you should get $1,115.18. You can see what is happening to the bond price: It is approaching the maturity value.
A financial calculator works well for these problems, especially for 2, where you don't know the market rate. Instead of guessing at a rate and then zeroing in on the correct answer by trial and error, the calculator does just that for you. The answer is more than 12% but less than 12.5%. have fun working it out.
It is not appropriate of you to assign your homework to others. To get help you should do the work as well as you can and provide your solution so someone can help you by pointing out where you are wrong and by explaining areas where you show weaknesses.
dunno
Bond Valuation:
1.) $1,000, 12% coupon bond pays coupon annually and has 10 years remaining to maturity.
a.) What is today's price (value) if it is bought at a yield to maturity of 10%?
b.) Assuming the required yield to maturity stays constant at 10%, at what price should this bond sell one year hence, i.e., when it has a remaining life of 9 years to maturity?
c.) What should be the price of this bond at maturity (i.e. one second before it matures)? (no need for calculations here)
d.) From your anser to parts a-d, what happened to the bond price over time? That is, did it gradually rise or fall?
2.) a two year bond pays a coupon rate of 10% and has a face value of $1,000. In other words, the bond pays interest of $100 per year and its principal of $1,000 is paid off in year two. If the bond sells for $960, what is its approximate yield to maturing? Hint: This requires some trial and error calculating.
