Under SFAS 114, the creditor must recognize a loss equal to the difference between the carrying value of the loan and the present value of the restructured payment stream discounted at the original rate (effective interest rate). Thus a 12% coupon loan with a face value of $100,000 and three years remaining to maturity is restructured by reducing the interest rate to 8%, the creditor recognizes a loss of $9,610 as the new carrying cost of the loan is $90,390*. ($100,000 - $90,390 = $9,610) * If we assume annual payments, the present value of a three year annuity of $8,000 discounted at 12% + present value of $100,000 in three years discounted at 12% equals $90,390. When I attempt to calculate this annuity I get a loss of $13,497 instead of the $9,610 the vignette above says I should get. Can anyone show me how the text above arrived at the carrying ocse of $90,390 for the loss of $9,610
Hi Nittany Lion First of all I think the unmentioned assumption is that the loan was issued at par and with no significant upfornt commissions, thus making the effective interest rate (XIRR) equal oto the initial coupon rate of 12%. Then if you compute the new carrying value as the PV of the new remaining 8% coupons + PV of the $100,000 face value , both discounted at the initial XIRR of 12%, you should get ~ $90,392. (this is what my excel gives using PV formula, so pretty close to the 90,390 value in the text). Thus the difference betwen current carrying value and new value is $9,608 . How do you obtain your $13k loss value?
I found my problem shortly before I saw your response. I was calculating for the FV instead of the PV. After taking a break and coming back to the problem, it was obvious why I was screwing up the problem. Thanks for your help.