Question

Shortly after its recent bankruptcy, a new store of Macys (to be known as Macy Ways)...

Shortly after its recent bankruptcy, a new store of Macys (to be known as Macy Ways) is being formed. You have the opportunity to invest in “Macy Ways”. If you invest $200 today, you will receive a zero-coupon bond that will pay $1,000 (face value or principal) at the end of 20 years. To be adequately compensated for the risk of this bond, you know that you should expect a spread (relative to comparable Treasury securities of at least 765 basis points. We also know that that yield for a 90-day Treasury bill is 0.50%, the yield for a 5-year Treasury note is 1.00%, the yield for a 10-year Treasury bond is 1.95%, the yield for a 20-year Treasury bond is 2.35%, and the yield for a 30-year Treasury bond is 3.05%. Provide calculations to identify whether the “Macy Ways” bond appears to be a good investment. B. How much reinvestment rate risk does this bond have?

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Answer #1

a]

Fair value of bond = $1,000 discounted at appropriate rate for 20 years

Appropriate rate = yield for a 20-year Treasury bond + spread = 2.35% + 7.65% = 10.00%

Fair value of bond = $1,000 / (1 + 10%)20 = $148.64

Cost of bond today is $200

The bond is overpriced as the cost is higher than its fair value

b]

The bond has no coupon payments because it is a zero-coupon bond

Hence, there is no risk that the coupon payments would have to be reinvested a lower rate

The reinvestment rate risk is zero

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