A bond with 3% coupon and 30 year term is brought with 3% YTM. After 1 year, one coupon payment is collected and the bond is sold for 10% YTM. Without calculator, what is the IRR of this investment?
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Without a calculator, you can see that the answer is clearly negative: for this to have a positive IRR for the original buyer, the bond must be sold for at least for at least $97 (IRR can only be positive if the undiscounted sum of cash inflows is greater than the undiscounted outflow). A 29-year bond with a 3% coupon does not have a 10% yield unless its price is much lower than 97. A quick check in Excel shows that its price will be ~35, resulting in an IRR of ~(37)% for the original holder.
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