How Does the Value of a Bond Change?
As rates increase or decrease, the discount rate that is used also changes appropriately. Let's change the discount rate in the above example to 10% to see how it affects the value of the bond.

Example: The Value of a Bond when Discount Rates Change
PV of the cash flows is: Year one = 70 / (1.10) to the 1st power = $ 63.63
Year two = 70 / (1.10) to the 2nd power = $ 57.85
Year three = 70 / (1.10) to the 3rd power = $ 52.63
Year four = 70 / (1.10) to the 4th power = $ 47.81
Year five = 1070 / (1.10) to the 5th power = $ 664.60

Value = 63.63 + 57.85 + 52.63 + 47.81 + 664.60 = $ 886.52

  • As we can see from the above examples, an important property of PV is that for a given discount rate, the older a cash flow value is, the lower its present value.
  • We can also compute the change in value from an increase in the discount rate used in our example. The change = 1,086.59 - 886.52 = 200.07.
  • Another property of PV is that the higher the discount rate, the lower the value of a bond and the lower the discount rate the higher the value of the bond.
Look Out!

If the discount rate is higher than the coupon rate the PV will be less than par. If the discount rate is lower than the coupon rate, the PV will be higher than par value.

How Does a Bond's Price Change as it Approaches its Maturity Date?
As a bond moves closer to its maturity date, its price will move closer to par. The break down on the three scenarios is as follows:

1. If a bond is at a premium, the price will decline over time towards its par value.
2. If a bond is at a discount, the price will increase over time towards its par value
3. If a bond is at par, its price will remain the same.

To show how this works lets use our original example of the 7% bond, but now let's assume a year has passed and a discount rate remains the same at 5%.

Example: Price Changes Over Time
Let's compute the new value to see how the price moves closer to par. You should also be able to see how the amount by which the bond price changes is attributed to it being closer to it's maturity date.

PV of the cash flows is: Year one = 70 / (1.05) to the 1st power = $66.67
Year two = 70 / (1.05) to the 2nd power = $ 63.49
Year three = 70 / (1.05) to the 3rd power = $ 60.47
Year four = 1070 / (1.05) to the 4th power = $880.29

Value = 66.67 + 63.49 + 60.47 + 880.29 = 1,070.92

As the price of the bond decreases, it moves closer to its par value. Theamount of change attributed to the year's difference is 15.67.

An individual can also decompose the change that results when a bond approaches its maturity date and the discount rate changes. This is accomplished by first taking the net change in the price that reflects the change in maturity, and then adding it to the change in the discount rate. The two figures should equal the overall change in the bond's price.

Computing the Value of a Zero-coupon Bond
This may be the easiest of securities to value because there is only one cash flow - the maturity value.

Value of a zero coupon bond that matures N years from now is:

Formula 14.9

Zero coupon bond value = Maturity value / (1 + I) to the power of the number of years x 2
Where I is the semi-annual discount rate.

Example: The Value of a Zero-Coupon Bond
For illustration purposes, let's look at a zero coupon with a maturity of three years and a maturity value of $1,000 discounted at 7%

I = 0.035 (.07 / 2)
N = 3

Value of a Zero = 1,000 / (1.035) to the 6th power (3 x 2)
= 1,000 / 1.229255
= 813.50

Arbitrage-free Valuation Approach

Related Articles
  1. Investing

    Understanding Bond Prices and Yields

    Understanding this relationship can help an investor in any market.
  2. Financial Advisor

    Using Excel PV Function to compute Bonds PV

    To determine the value of a bond today - for a fixed principal (par value) to be repaid in the future at any predetermined time - we can use an Excel spreadsheet.
  3. Investing

    Understanding Face Value

    Face value is the dollar value stated on a security.
  4. Investing

    Explaining Original Issue Discount

    An original issue discount is the amount below par at which a bond or other debt instrument is issued.
  5. Investing

    How To Evaluate Bond Performance

    Learn about how investors should evaluate bond performance. See how the maturity of a bond can impact its exposure to interest rate risk.
  6. Investing

    What is Par Value?

    Par value is a term used for investments that means original value. It’s also called face value or nominal value.
  7. Investing

    Are Bonds Selling At A Premium A Good Investment?

    A bond with a par value – or face value -- of $1,000 is selling at a premium when its price exceeds par.
  8. Investing

    Comparing Yield To Maturity And The Coupon Rate

    Investors base investing decisions and strategies on yield to maturity more so than coupon rates.
  9. Investing

    How Do I Calculate Yield To Maturity Of A Zero Coupon Bond?

    Yield to maturity is a basic investing concept used by investors to compare bonds of different coupons and times until maturity.
  10. Financial Advisor

    Simple Math for Fixed-Coupon Corporate Bonds

    A guide to help to understand the simple math behind fixed-coupon corporate bonds.
Frequently Asked Questions
  1. Depreciation Can Shield Taxes, Bolster Cash Flow

    Depreciation can be used as a tax-deductible expense to reduce tax costs, bolstering cash flow
  2. What schools did Warren Buffett attend on his way to getting his science and economics degrees?

    Learn how Warren Buffett became so successful through his attendance at multiple prestigious schools and his real-world experiences.
  3. How many attempts at each CFA exam is a candidate permitted?

    The CFA Institute allows an individual an unlimited amount of attempts at each examination.Although you can attempt the examination ...
  4. What's the average salary of a market research analyst?

    Learn about average stock market analyst salaries in the U.S. and different factors that affect salaries and overall levels ...
Trading Center