Question

Please show the formulas for each step. Consider a bond with a coupon rate of 3%, a YTM of 4%, and a face value of $1000. Coupon payments are made annually. The bond matures in 3 years. Please document the bond value, current yield, and capital gains yield each year for the bond. Explain what is happening to bond value, current yield, and capital gains yield as the bond reaches maturity.

Answer 1

The formulas for calculating bond value, current yield, and capital gains yield are provided. The bond value, current yield, and capital gains yield are calculated for each year of the bond's maturity period. As the bond reaches maturity, the bond value approaches its face value, the current yield remains relatively stable, and the capital gains yield decreases.

Step-by-step explanation:

The bond value, current yield, and capital gains yield each year can be calculated using the provided information:

1. Year 1:
   • Bond Value = Coupon payment + Present value of Face Value = $30 + $988.85 = $1018.85
   • Current Yield = (Coupon payment / Bond Value) * 100 = (30 / 1018.85) * 100 = 2.95%
   • Capital Gains Yield = (Bond Value - Purchase Price) / Purchase Price * 100 = (1018.85 - 1000) / 1000 * 100 = 1.89%
2. Year 2:
   • Bond Value = Coupon payment + Present value of Face Value = $30 + $977.52 = $1007.52
   • Current Yield = (Coupon payment / Bond Value) * 100 = (30 / 1007.52) * 100 = 2.98%
   • Capital Gains Yield = (Bond Value - Purchase Price) / Purchase Price * 100 = (1007.52 - 1000) / 1000 * 100 = 0.75%
3. Year 3:
   • Bond Value = Coupon payment + Present value of Face Value = $30 + $966.13 = $996.13
   • Current Yield = (Coupon payment / Bond Value) * 100 = (30 / 996.13) * 100 = 3.01%
   • Capital Gains Yield = (Bond Value - Purchase Price) / Purchase Price * 100 = (996.13 - 1000) / 1000 * 100 = -0.39%

As the bond approaches maturity, the bond value approaches its face value of $1000. The current yield remains relatively stable around the coupon rate of 3%, while the capital gains yield decreases towards zero, indicating that there are fewer capital gains as the bond approaches its maturity.