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Present Value of Bonds

Lesson
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When bonds are first sold, or issued, they need a price.

Fortunately, the price is the result of two types of calculations that you likely already know:

  • Present value of a sum - This represents the money invested, that will be returned at the end of the time period.
  • Present value of an annuity - This represents the money that will be paid on each payment date.

Even though it seems simple, many students get confused when deciding which interest rates to use in which parts of the problem.

  • Bond interest rate - Used to calculated the dollar value of the payment at the end of each period.
  • Market interest rate - Used for everything else.
Question
Zero Morals, inc., the mysterious dishwasher vendor, bought a bond for $100,000.00 with a 5 year duration. The bonds pay 5% at the end of each year, and the market rate of interest is 6%.

You've been provided with the following information:

  • The present value factor for an ordinary annuity at 6% for 5 years is 4.21236

  • The present value factor for an annuity due at 6% for 5 years is 4.46511

  • The present value factor for an annuity due at 5% for 5 years is 4.54595

  • The present value factor for an ordinary annuity at 5% for 5 years is 4.32948

What is the present value of the bond?
Answer
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👉 Answer:

  • $95,787.64

👩‍🎓 This is how we solve it:

  1. First, figure out the formula for the bond's interest payment
    BOND INTEREST PAYMENT = ISSUE PRICE OF BOND * PERCENT BOND INTEREST
  2. Let's plug in the numbers
    $5,000.00 = $100,000.00 * 5%
  3. Discount the interest payments to the market rate. Always use the market rate, not the bond rate for this step - many students use the wrong value here.
    DISCOUNTED BOND INTEREST PAYMENT = BOND INTEREST PAYMENT * PRESENT VALUE FACTOR OF MARKET
  4. Let's fill in the numbers.
    $21,062 = $5,000.00 * 4.21236
  5. Discount the bond price the market rate.
    DISCOUNTED BOND FACE = BOND ISSUE PRICE / ((1 + MARKET RATE) ^ NUMBER OF YEARS)
  6. Let's fill in the numbers
    $74,725.82 = $100,000.00 / ((1 + 0.06) ^ 5)
  7. There are two items that must be summed to arrive at the answer
    PRESENT VALUE OF BOND = PRESENT VALUE OF BOND PRICE + PRESENT VALUE BOND PAYMENTS
  8. Let's plug in the numbers
    $95,787.64 = $74,725.82 * $21,062
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