Question

A judge has ordered those meddling kids at Mystery, Inc. to pay $6000 one year from today and $9500 two years from today. To match the obligations, the Mystery, Inc. crew plans to purchase bonds today. The following bonds are available for purchase today: \bullet One-year zero-coupon bonds with 8% yield \bullet Two-year 4% par-value bond with annual coupons and 7% yield Find the total purchase price of the bonds today to exactly match the obligations:

P = $ (3 decimal place)

Answer 1

Mystery needs the cash flows

Year 1: $6,000

Year 2: $9,500

At the end of year 2, we will get 4% coupon from bond 2 and FV of bond 2. Let the FV of bond 2 be x.

x + 0.04x = 9,500 implies x = $9,134.62

Coupon = $365.38

Price of this bond (assuming yield to be 7%) = 365.38/1.07 + 9500/1.07^2 = $ 8,639.668

After first year, we will receive $ 365.38 as coupon from second bond. The remaining (6,000-365.38 = ) $5,634.61 will come from Zero Coupon Bonds.

Price of ZCB = 5634.61/1.08 = $5,217.236

Total Price = $ 13,856.385