Gloucester County Institute of Technology



Reading: Determining the Price of a BondPresent ValueThe present value of a bond is the current worth of a future payment, taking into account the time value of money. For example, if you have $100 cash today, it’s worth $100 today because that is what is available to you now if you were to spend it today. On the other hand, if you lend it to a friend who promises to pay it back one year from today, as in the case of a bond, the present value of the amount would not be $100 because you don’t have the money today to save, spend, or lend to someone else. There’s a price to having your money tied up so that you can’t use it. There’s also a cost to the uncertainty of what might happen between now and a year from now. Will your friend refuse to pay you back? Will inflation rise so much that next year $100 only buys $75 worth of stuff?To find the present value of the $100 you will receive in a year, calculate the money that would have accrued in interest had the money remained invested for a full year.Here is an algebraic equation to help you calculate present value:present value = future amount / (1+interest rate)termRead the equation like this: The present value of your money (the value today) is equal to what it will be worth in the future, divided by 1 plus the interest rate, to the power of the amount of time you’re calculating for. Then you fill in all of the numbers you know and solve for the variable. For example, say you’re considering investing in a bond that’s going to pay $100 in one year. The interest rate the bond is paying is 5%. How much should you be willing to pay for the bond? You can use the equation to calculate the present value of the bond. Plug in the numbers you know. The future amount is $100. Divide that by 1.05 to the power of the term of the bond until it pays off—1 year. Then solve for the variable—the value of the bond today:present value = 100 / (1+ 0.05)1So the present value of the bond is $95.23, which is less than its future value of $100 because the projected interest, the money that would have been made in investment, has been subtracted.This shows us that time really is money. The value of money now is not the same as it will be in the future. By calculating present value, you can figure out whether it is in your best interest to accept the present value and have more cash now, or whether it is worthwhile to leave investments in anticipation of future payoff. Of course, if you leave the money in the investment, you have to consider investment risks, too.Questions:What is the definition of present value?If the face value of a bond is $100, what is its present value if it accrues interest at a fixed rate of 7% for five years? Please show your work.Bond PricingBonds are similar to loans. A bond purchaser (or bond holder) basically is lending money to the bond issuer (the borrower). Issuers are often national governments or government-sponsored programs such as the Federal Home Loan Mortgage Corporation (Freddie Mac), the Federal National Mortgage Association (Fannie Mae), and the Federal Home Loan Banks. Some corporations also offer corporate bonds.Unlike bank loans, bonds are traded over the counter through dealer markets, meaning that the price goes up and down with interest rates. Although the cost to issuers (the interest payment) doesn’t change, the present value (or market value) of the bond to the holder can change. The amount the company has to pay back when the bond reaches its maturity date (the face value) doesn’t change either.Since bond prices vary with the market, they are priced in terms of percentage of par value. Bonds are not necessarily issued at par (where the coupon rate and the market interest rates are perfectly equal), but all bonds reach par at yield to maturity (YTM). The market price of a bond is the present value of all future interest payments plus the principal payment of the bond. These payments are discounted to present value at the bond’s yield. The yield accounts for the current market interest rates. Yield is the measure commonly used to estimate or determine a bond’s expected return. When market rates rise, bond prices generally fall, and vice versa.If you are interested in buying a bond at a market price that is different from the bond’s payback value, there are a few numbers used to measure the annual rate of return you are getting on your investment. The first is coupon rate (interest) or the annual payout as a percentage of the bond’s par value. The second is current yield, which refers to the ratio of the annual interest payment and the bond’s current price. The third is YTM, meaning the composite rate of return off all payouts, coupon, and capital gain.There are three basic rules about bond pricing:If a bond’s current yield is less than its YTM, the bond is selling at a discount. If a bond’s current yield is more than its YTM, then the bond is selling at a premium. If a bond’s current yield is equal to its YTM, then it is selling at par. ................
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