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A one-year zero-coupon bond yields 4.0%. The two- and three-year zero-coupon bonds yield 5.0% and 6.0% respectively.

A four-year corporate bond with a 7% coupon has a Z-spread of 200 bps. Assume a flat
yield curve with an interest rate for all maturities of 5% and annual compounding. The bond will most likely sell _______________.

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Final answer:

The four-year corporate bond with a 7% coupon and a 200 bps Z-spread, in a market with a flat 5% interest rate, would theoretically sell at its face value because the coupon rate equals the sum of the yield curve rate and the Z-spread.

Step-by-step explanation:

The student's question pertains to the pricing of a four-year corporate bond with a 7% coupon and a Z-spread of 200 basis points, assuming a flat yield curve with an annual interest rate of 5%. Given the flat yield curve, the yields for one-, two-, and three-year zero-coupon bonds are provided for context but are not directly used in pricing this particular bond.

When considering the yield of a bond, we take into account both interest payments and potential capital gains or losses. With interest rates set at a flat 5%, a corporate bond paying 7% would typically be more attractive to investors and, as a result, sell for more than its face value. However, this bond has an additional Z-spread of 200 basis points (or 2%), indicating extra yield required by investors due to credit risk or other factors. This spread must be added to the yield curve (in this case, the flat 5% rate), making the bond's total yield comparison rate 7%.

Since the corporate bond's coupon matches the combined yield curve and Z-spread rate, it should theoretically sell at face value because its coupon rate is compensating exactly for the risk-free rate plus the additional credit risk premium. However, in practice, market demand, liquidity, and other factors can influence the final price.

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