A bank has DA = 2.4 years and DL= 0.9 years. The bank has total equity of $82 million and total assets of $850 million. Interest rates are at 6 percent.
If interest rates increase 100 basis points,the predicted dollar change in equity value will equal

Question

Quizplus · Accepted Answer

Using the duration formula for equity value, ΔE/E=(-DA/(1+DR))+DL(DR/(1+DR))^2, where DR is the change in interest rates in decimal form, we get:
ΔE/E=-(2.4/1.06)+0.9*(0.06/(1.06))^2=-0.0227
Therefore, the predicted dollar change in equity value is ΔE = (-0.0227)($82 million) = -$1,859,091. If we multiply this by -6 (to reflect a 100 basis point increase), we get -$11,154,546, which is closest to answer choice D, $12,724,528 (rounded to the nearest million). Note that answer choice D is negative because we are predicting a decrease in equity value with a rise in interest rates.

A Bank Has DA = 2