Int rate swap's effect on balance sheet

CFA Level III Derivatives
#1

Spoiler alert, don’t read on if you haven’t done but are planning to do Schweser practice test #1.

In Schweser practice test #1, question #44 of afternoon session, the company in the question is doing a swap to be the fix receiver and float payer, in order to offset its existing fixed debt. The question askes if the following comment is correct:

“By entering into the swap, the absolute duration of Worth’s long-term liabilities will become smaller, causing the value of the firm’s equity to become more sensitive to changes in interest rates.”

The answer gives it as correct.

But the text book says that it’s the fix payer/float receiver whose equity will fluctuate more, as its liability how has longer duration so will fluctuate more as interest rates change. This seems to contradict what the answer to question 44 is saying.

Am I missing something here?

#2

Equity will have longer duration than it used to. Think of it this way:

A * DA = L * DL + E * DE where A = assets, L = liabilities, E = equity, D = “duration of”.

A * DA, L and E are constant (no change in assets or their duration, amount of liability and equity) so if you decrease DL then DE has to go up.