Final answer:
To calculate the value of Bond L, the present value of the annuity (coupon payments) and the present value of the lump sum (face value) are determined and then summed. Using the given formulas with a market interest rate of 5%, the value of Bond L is approximately $1,583.50.
Step-by-step explanation:
Calculating the Value of Bond L
The question concerns the calculation of the present value of a bond. Bond L has a face value of $1,000, pays a 12% annual coupon, and matures in 12 years, given that the current market interest rate is 5%. To find the value of Bond L, we can use the present value formula for the bond's remaining cash flows. The bond has 12 more annual interest payments of $120 each (12% of the $1,000 face value) and the repayment of the principal at the end of the 12 years.
The formula for the present value of an annuity (the periodic interest payments) is:
PV of annuity = C * [(1 - (1 + r)^-n) / r]
And the formula for the present value of a lump sum (the face value of the bond) is:
PV of lump sum = F / (1 + r)^n
Where:
• C = annual coupon payment ($120)
• r = market interest rate (0.05)
• n = number of years to maturity (12)
• F = face value of the bond ($1,000)
When we plug in the values:
• PV of annuity = $120 * [(1 - (1 + 0.05)^-12) / 0.05] ≈ $120 * 8.55547 ≈ $1,026.66
• PV of lump sum = $1,000 / (1 + 0.05)^12 ≈ $1,000 / 1.79586 ≈ $556.84
Add the present values of the annuity and the lump sum:
Value of Bond L ≈ $1,026.66 + $556.84 = $1,583.50
Therefore, the value of Bond L, rounded to the nearest cent, is approximately $1,583.50 when the going interest rate is 5%.