Problem
(a) Arbitrage Financial is offering an investment with the following cash flows:
|
Year
|
1
|
2
|
3
|
4
|
|
Cash flow
|
$200
|
$400
|
- $100
|
$500
|
(note that the cash flows in Years 1, 2, and 4 are positive, and the cash flow in Year 3 is negative.)
You observe the following prices of pure discount (i.e., zero-coupon) bonds, which pay a single cash flow of $100 at maturity:
|
Price, $
|
Maturity, years
|
|
95.24
|
1
|
|
89.85
|
2
|
|
83.96
|
3
|
|
77.73
|
4
|
What is a fair price (to the nearest dollar) for the investment from Arbitrage Financial?
(b) Arbitrage Financial offers another product called a "mystery coupon" bond. This bond has a face value of $1,000 and a maturity of five years. The bond pays an annual coupon, but the amount of the coupon is unknown. However, you know that the price of the bond is $1,052.30, and bonds of similar risk and maturity currently have a yield to maturity of 6.25%. What is the annual coupon payment (to the nearest dollar) on this bond?