The cost-savings method values the deposit franchise year by year: the spread over alternative funding, on a balance that decays, after tax, discounted.
A core deposit intangible is the present value of what a bank saves by funding itself with its deposits rather than wholesale money, after tax, on a balance that runs off each year. On an illustrative 1,000,000 of deposits costing 2.20 per cent all-in against 4.80 per cent for alternative funding, with 15 per cent runoff a year, a 25 per cent tax rate and a 9.0 per cent discount rate over ten years, the CDI is 68,906, a premium of 6.89 per cent of the deposits.
Worked in full in Bank Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The CDI is the line that makes a bank acquisition work or not. Purchase accounting marks every asset and liability, and the deposit franchise, which the seller's balance sheet never shows, comes in as an intangible asset. The cost-savings method below is the standard way to value it, and three of its inputs carry almost all of the answer.
| Input | Value |
|---|---|
| Core deposits at acquisition | 1,000,000 |
| Interest rate paid | 1.20% |
| Servicing cost net of fee income | 1.00% |
| All-in cost of the deposits | 2.20% |
| Alternative funding rate, matched term | 4.80% |
| Runoff a year, share of opening balance | 15% |
| Tax rate | 25% |
| Discount rate | 9.0% |
| Projection horizon | 10 years |
The all-in cost includes what it costs to run the accounts, net of the fees they bring in, because that is what the bank actually pays per dollar; how to build it is in the all-in cost of deposits.
Balance at end of year t = deposits × (1 − runoff)t
Saving in year t = average balance × (alternative rate − all-in cost) × (1 − tax)
CDI = Σ savingt ÷ (1 + discount rate)t
In Excel, with the opening balance of the year in B5, the closing balance in C5 and the year number in A5: =(B5+C5)/2*(Alt-Cost)*(1-Tax)/(1+Disc)^A5, filled down ten rows and summed.
Step 1: the spread. 4.80 − 2.20 = 2.60 per cent a year on every dollar that stays.
Step 2: the first year. The balance falls from 1,000,000 to 850,000, an average of 925,000. The saving is 925,000 × 2.60% = 24,050 before tax and 18,038 after. Discounted one year at 9.0 per cent it is worth 16,548.
Step 3: the decay. Each year the balance is 85 per cent of the year before, so the saving shrinks with it and is discounted further.
| Year | Opening balance | Average balance | Saving, after tax | Discount factor | Present value |
|---|---|---|---|---|---|
| 1 | 1,000,000 | 925,000 | 18,038 | 0.9174 | 16,548 |
| 2 | 850,000 | 786,250 | 15,332 | 0.8417 | 12,905 |
| 3 | 722,500 | 668,312 | 13,032 | 0.7722 | 10,063 |
| 4 | 614,125 | 568,066 | 11,077 | 0.7084 | 7,847 |
| 5 | 522,006 | 482,856 | 9,416 | 0.6499 | 6,120 |
| 6 | 443,705 | 410,427 | 8,003 | 0.5963 | 4,772 |
| 7 | 377,150 | 348,863 | 6,803 | 0.5470 | 3,721 |
| 8 | 320,577 | 296,534 | 5,782 | 0.5019 | 2,902 |
| 9 | 272,491 | 252,054 | 4,915 | 0.4604 | 2,263 |
| 10 | 231,617 | 214,246 | 4,178 | 0.4224 | 1,765 |
| Total | 96,576 | 68,906 |
The CDI is 68,906, 6.89 per cent of the deposits acquired. After ten years 196,874 of the original balances, 19.7 per cent, are still there; extending the horizon to thirty years adds only 6,207 and takes the premium to 7.51 per cent, because what is left is small and heavily discounted. The ten-year cut-off is a modelling choice, and it is worth stating.
The buyer amortises the CDI over the deposits' expected life, and its earnings carry that charge. The full purchase-price reading of a bank, where the franchise is the only positive mark, is worked in what a buyer actually pays for a bank.
| Runoff a year | Alternative rate 3.80% | 4.80% | 5.80% |
|---|---|---|---|
| 10% | 5.12% | 8.31% | 11.51% |
| 15% | 4.24% | 6.89% | 9.54% |
| 20% | 3.56% | 5.78% | 8.00% |
| 30% | 2.58% | 4.20% | 5.81% |
A point on the alternative rate moves the premium by about 2.6 points at 15 per cent runoff; doubling the runoff from 15 to 30 per cent cuts it by about two fifths. Holding the all-in cost fixed while the alternative rate rises assumes a deposit beta of zero; a realistic beta narrows the spread as rates rise, and the deposit beta should be stated on the same deposits as the runoff, as the deposit beta article shows.
All figures are illustrative. In an acquisition the runoff is usually estimated from the bank's own account-level history, and the alternative rate from the funding the acquirer could actually raise at a matching term.
The book's bank values its deposit franchise inside the economic value of equity, with the deposit beta measured two ways; both are in the free workbooks for this case.
It depends on the gap between the deposits' all-in cost and alternative funding, and on how fast the balances leave, so no single level applies. On the same deposits the premium runs from 2.58 per cent with 30 per cent runoff and a 3.80 per cent alternative rate to 11.51 per cent with 10 per cent runoff and 5.80. Higher rates and stickier deposits both raise it.
Because the saving is the spread between what the bank would pay for wholesale money and what it pays its depositors, and deposit rates lag market rates. With 15 per cent runoff, lifting the alternative rate from 3.80 to 4.80 per cent takes the premium from 4.24 to 6.89 per cent of deposits, while the deposits themselves cost the same 2.20 per cent.
After tax, because the saving would raise taxable income. Valuing the pre-tax saving gives 91,875 instead of 68,906 on the same deposits, overstating the CDI by 22,969. Where an acquirer can also amortise the intangible for tax, a tax amortisation benefit is added on top as a separate step.
This article is one calculation from Bank Management. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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