Question

Which of the following is closest to the investment cost of a 30 year bond at time zero that makes annual coupon payments at a rate of 5% if the face value payment is $100 and the bond is trading at a yield of 6%?

a) $95
b) $90
c) $100
d) $85

Answer 1

The investment cost of the 30-year bond with annual coupon payments at a rate of 5% and trading at a yield of 6% is approximately $90.

Step-by-step explanation:

When interest rates rise, the price of previously issued bonds with lower interest rates falls below face value. In this case, the bond has an annual coupon rate of 5% and a face value of $100. The bond is trading at a yield of 6%, meaning the market interest rate is higher than the bond's coupon rate. To calculate the investment cost of the bond, we can use the formula:

Investment Cost = (Annual Coupon Payment / Yield) + (Face Value / (1 + Yield)^n)

Plugging in the given values:

Annual Coupon Payment = 5% of $100 = $5

Yield = 6% = 0.06

Face Value = $100

n = 30 years

Investment Cost = ($5 / 0.06) + ($100 / (1 + 0.06)^{30})

Calculating this, we get:

Investment Cost ≈ $83.333 + $7.163 = $90.496

Therefore, the option closest to the investment cost is $90 (option b).