The following information was available as of the close of business June 1, 2004 on government of Canada bonds. Coupon...Maturity.....Price.....Yield 5.00%......June 1, 2005......102.35......2.60 10.50%......June 1, 2006......113.91......3.26 8.50%......June 1, 2007.....107.41......3.39 Calculate the anticipated one-year interest rate
To calculate the anticipated one-year interest rate, you can use the formula for yield to maturity (YTM). YTM is the estimated annual rate of return you can expect if you hold the bond until it matures.
The formula for YTM is as follows:
YTM = (Annual interest payment + [(Face value - Purchase price) / Years to maturity]) / Purchase price
In this case, we need the annual interest payment for each bond, the face value, the purchase price, and the years to maturity. Let's calculate the YTM for each bond:
For the first bond:
Annual interest payment = 5.00% of face value = 5.00 / 100 * 100 = 5
Face value = $100
Purchase price = $102.35
Years to maturity = 1
YTM = (5 + [(100 - 102.35) / 1]) / 102.35
For the second bond:
Annual interest payment = 10.50% of face value = 10.50 / 100 * 100 = 10.50
Face value = $100
Purchase price = $113.91
Years to maturity = 2
YTM = (10.50 + [(100 - 113.91) / 2]) / 113.91
For the third bond:
Annual interest payment = 8.50% of face value = 8.50 / 100 * 100 = 8.50
Face value = $100
Purchase price = $107.41
Years to maturity = 3
YTM = (8.50 + [(100 - 107.41) / 3]) / 107.41
Now, let's plug in the values and calculate the YTMs:
For the first bond:
YTM = (5 + [(100 - 102.35) / 1]) / 102.35 = (5 + [(-2.35) / 1]) / 102.35 = (5 + (-2.35)) / 102.35 = 2.65 / 102.35 ≈ 0.0259 or 2.59%
For the second bond:
YTM = (10.50 + [(100 - 113.91) / 2]) / 113.91 = (10.50 + [(-13.91) / 2]) / 113.91 = (10.50 + (-6.955)) / 113.91 = 3.545 / 113.91 ≈ 0.0312 or 3.12%
For the third bond:
YTM = (8.50 + [(100 - 107.41) / 3]) / 107.41 = (8.50 + [(-7.41) / 3]) / 107.41 = (8.50 + (-2.47)) / 107.41 = 6.03 / 107.41 ≈ 0.056 or 5.60%
Therefore, the anticipated one-year interest rates for the three bonds are approximately 2.59% for the first bond, 3.12% for the second bond, and 5.60% for the third bond.