After more than a year of crippling losses and three bailouts from Washington, Citigroup, a troubled giant of American banking, said Friday that it had done something extraordinary: it made money.
Hut the headline number—a net profit of $1.6 billion for the first quarter—was not quite what it seemed. Behind that figure was some fuzzy math. Like several other banks that reported surprisingly strong results this week, Citigroup used some creative accounting, all of it legal, to bolster its bottom line at a pivotal moment . . .

1. Suppose Citigroup had issued at par on January 1, 2005, $500 million of 10-year bonds with a fixed annual interest rate of 6% reflecting the company’s financial soundness at the time. Calculate the proceeds received by Citigroup, the interest expense recorded in 2005, and the bond carrying value on January 1, 2009, Assume cash interest payments are made on December 31 of each year.
2. Suppose the market interest rate had increased to 12% by January 1, 2009. Compute the market value of the bonds on that date.
3. At the time the news article above was published, Citigroup’s debt had lost value in the bond market because of investors’ concerns about the company’s ability to meet the required debt payments when due. Explain how this perceived increase in Citigroup’s credit risk translates into a decline in the market value of its bonds.
4. How did Citigroup account for the $2.7 billion decline in the value of its own debt?

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