Compute a bank's all-in funding cost twice over, once by the pooled-funds method and once by averaging historical costs.
The idea
The all-in cost of a funding source is its interest cost plus non-interest costs (processing, marketing, insurance premiums), divided by the funds it provides, net of any reserve held against it. The pooled-funds method treats every source as one pool, which equals the average of the source costs weighted by balance. Write Cost for the total cost of all sources and Funds for the total raised. Pooled = Cost ÷ Funds. The historical-average method weights the cost at which each tranche was originally raised by its amount. Here A is the amount of a tranche and c is the cost at which it was originally raised. Historical = Σ(A × c) ÷ ΣA. Because it uses old costs, it lags current conditions and understates what new money costs when rates have risen. The usual mistakes are using interest only, using a simple average that ignores the weights, and forgetting the reserve adjustment. On the exam, compute the weighted figure and read off which cost is described.
Formulas
Pooled-funds cost of funds
Pooled = Cost ÷ Funds
- Cost
- total interest and non-interest cost of all sources
- Funds
- total funds raised, net of reserves where they apply
Equals the balance-weighted average of the sources' all-in costs. A simple average of rates, or interest alone, gets it wrong.
Historical-average cost of funds
Historical = Σ(A × c) ÷ ΣA
- A
- the amount of each tranche
- c
- the all-in cost at which that tranche was originally raised
Weight by amount, not by age. It lags current conditions and understates the cost of new money when rates have risen.
A practice question
Under the pooled-funds method, a bank's cost of funds is best described as:
- The average all-in cost of all funding sources, each weighted by its share of total funds raised. - correct
- The all-in cost of the most recently raised source of funds.Why not: Describes a marginal cost approach, not a pooled average.
- The simple average of the interest rates on each source, whatever their size.Why not: Ignores the weights; large sources must count for more than small ones.
- Total interest expense divided by total assets.Why not: Leaves out non-interest costs and uses assets rather than funds raised as the base.
The pooled-funds method treats all sources as one pool: total interest and non-interest cost divided by total funds, which equals a balance-weighted average of source costs.
A harder one
A bank's funding is shown below as amount in USD millions, interest rate and non-interest cost rate: transaction deposits 400, 1.0% and 2.5%; time deposits 300, 3.5% and 0.8%; federal funds purchased 100, 4.5% and 0.1%; commercial paper 100, 4.8% and 0.3%. Closest to the pooled-funds all-in cost of funds?
- 2.64%Why not: Weights interest rates only and omits non-interest costs.
- 4.38%Why not: Takes a simple average of the four all-in costs instead of weighting by balance.
- 4.07% - correct
- 3.45%Why not: Takes a simple average of the interest rates only, ignoring both weights and non-interest cost.
Cost: 400 x 3.5% = 14.0; 300 x 4.3% = 12.9; 100 x 4.6% = 4.6; 100 x 5.1% = 5.1. Total 36.6 over 900 = 4.07%.
The hardest tier
A bank has transaction deposits of USD 500 million (interest 0.5%, non-interest 3.0%, 10% reserve requirement), time deposits of USD 400 million (3.8%, 0.6%, 3% reserve) and federal funds purchased of USD 100 million (4.6%, 0.05%, no reserve). Reserves earn nothing. Pooled all-in cost = total interest and non-interest cost / total usable funds (funds less reserves). Closest to the pooled all-in cost?
- 3.98%Why not: Divides total cost by the gross funds of USD 1,000 million and ignores reserves (39.75 / 1,000).
- 4.24% - correct
- 4.36%Why not: Adjusts each source for its reserve but averages the three adjusted costs without weights.
- 4.42%Why not: Applies the largest reserve ratio of 10% to all funds instead of each source's own ratio.
Total cost = 500 x 3.5% + 400 x 4.4% + 100 x 4.65% = 17.5 + 17.6 + 4.65 = 39.75. Usable funds = 450 + 388 + 100 = 938. Cost = 39.75 / 938 = 4.24%.
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