Principles of Finance-fixed-rate loan

Consider the following balance sheet:

 

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ASSETS LIABILTIES

Cash 30 Core Deposits 20

Fed funds 20 Fed funds 50

Loans (floating) 105 Euro CDs 130

Loans (fixed) 65 Equity 20

TOTAL 220 220

 

Fed funds rate is 8.5%

Floating loans are 15%

Fixed rate loans selling at par, 5 year maturities, 12% annual coupon.

Core deposits fixed rate for 2 years at 8%.

Euro CDs 9% yield.

 

a. What is duration of fixed-rate loan portfolio?

 

 

b. If duration of floating rate notes is 0.36, what is duration of bank’s assets? (Cash and fed fund assets= 0)

 

 

 

 

c. What is the duration of the core deposits is they are priced at par?

 

 

 

d. If the duration of fed fund liabilities and Euro CDs is 0.401, what is the duration of the bank’s liabilities?

 

 

 

e. What is the duration gap? If all rates increase by 1% (r/(1+r))=0.01), what is the impact on equity?