Question

Blue Steel Community Bank has the following market value balance sheet:

  

Asset or Liability	Market Value (in $ millions)			Duration (in years)
Federal funds deposits	$	30.4			0
Accounts receivable		580.0			.75
Short-term loans		342.5			1.20
Long-term loans		101.3			5.80
Mortgages		488.5			13.40
Checking and savings deposits		659.0			0
Certificates of deposit		412.2			2.15
Long-term financing		337.1			10.35
Equity		134.4			N/A

  

a.	What is the duration of the assets? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What is the duration of the liabilities? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

   

Answer 1

a.
Duration of assets is calculated as weighted average duration of each assets.
Calculation of weights for each asset and duration of assets
Asset	Market value	Weights		Duration	Weighted average duration (Weights*Duration)
Federal funds deposit	$30.40	0.020	(30.40/1542.70)	0.00	0.00
Accounts receivable	$580.00	0.376	(580/1542.70)	0.75	0.28
Short term loans	$342.50	0.222	(342.50/1542.70)	1.20	0.27
Long term loans	$101.30	0.066	(101.30/1542.70)	5.80	0.38
Mortgages	$488.50	0.317	(488.50/1542.70)	13.40	4.24
Total assets	$1,542.70				5.17	years
Thus, duration of assets is 5.17 years.
b.
Duration of liabilities is calculated as weighted average duration of each liabilities
Calculation of weights for each liability and duration of liabilities
Liabilities	Market value	Weights		Duration	Weighted average duration (Weights*Duration)
Checking and savings deposit	$659.00	0.47	659/1408.30	0	0.00
Certificates of deposit	$412.20	0.29	412.2/1408.30	2.15	0.63
Long term financing	$337.10	0.24	337.1/1408.30	10.35	2.48
Total liabilities	$1,408.30				3.11	years
Thus, duration of liabilities is 3.11 years.