Final answer:
To determine the price to pay for a coupon bond today, calculate the present value of annual coupons of $41.50 for 14 years and the face value of $1,000 at the end of 14 years using a discount rate of 3.50%. Sum the present values of the annuity and lump sum to get the total price to offer.
Step-by-step explanation:
To find out how much you should offer to pay for a coupon bond today, you need to calculate the present value of all future coupon payments and the face value payment at maturity, discounted at the required return rate of 3.50%. This bond pays annual coupons at a rate of 4.15% on a face value of $1,000 for the next 14 years, which means you will receive $41.50 each year for 14 years and then the face value of $1,000 at the end of the 14th year.
The present value (PV) of an annuity (regular coupon payments) formula is:
PV = C * [(1 - (1 + r)^-n) / r]
where C is the annual coupon payment, r is the required return rate, and n is the number of years.
For the face value payment, you use the present value of a lump sum formula:
PV = F / (1 + r)^n
where F is the face value.
Plugging in the values you get:
PV of coupon payments = $41.50 * [(1 - (1 + 0.035)^-14) / 0.035]
PV of face value = $1,000 / (1 + 0.035)^14
Calculating these and summing gives the price you should offer for the bond today. Using a financial calculator or spreadsheet can help to compute these values quickly.