FIRST NATIONAL CORP /VA/ (FXNC) stock intrinsic value fair value estimate & owner earnings analysis

First National Corporation is the holding company for First Bank, based in Strasburg, Virginia, a roughly $2.0 billion community bank with 33 branches across the Shenandoah Valley, south-central Virginia, the Richmond and Roanoke areas and northern North Carolina. It holds about $1.8 billion of deposits and has about $1.45 billion of loans, mostly to small and mid-sized businesses and households. It has grown mainly by buying other banks for stock and some cash: The Bank of Fincastle (July 2021, six Roanoke Valley branches) and Touchstone Bankshares (October 2024, 12 branches, about $46.8 million of stock). As a result, weighted diluted shares rose from about 4.96 million in 2018 to about 9.0 million in 2025, and cash earnings per share have gone sideways even as the bank doubled in size. What we measured. For a bank we count the cash the business generates after real costs: operating cash flow, minus working-capital swings, minus stock compensation, minus the part of capital spending that merely maintains branches and systems, and minus loan-loss provisions, which we treat as a normal recurring cost rather than something to add back. Interest paid to depositors is an operating cost, so we subtract no separate debt; the holding company's small borrowings (about $8.3 million of subordinated debt, $9.3 million of junior subordinated debt and $25 million of other borrowings at year-end 2025) are already paid for inside earnings. On that basis cash earnings per share for 2016 through 2025 were $1.52, $1.79, $2.15, $2.04, $1.76, $1.70, $2.94, $1.36, $0.32 and $1.92. The ten-year median is about $1.77. 2024 was distorted by $8.1 million of merger costs, a $3.8 million day-one loan-loss provision on Touchstone's loans, and a $38.6 million reduction in other liabilities that the filing does not explain (it is close to the $39.3 million of short-term borrowings Touchstone brought with it, but the filing does not say so). We strip working-capital movements out, so that item does not change our figures. Because the bank was transformed in late 2024, we judge today's earning level mainly from 2025, adjusted two ways: adding back $2.2 million of merger costs (about +$0.19 a share after tax) and charging credit losses at a normal $4.5 million a year, about 0.31% of loans, instead of the $2.9 million booked (about -$0.14). Net charge-offs were $4.4 million in 2025 and $3.8 million in 2024, so the 2025 provision was flattered by a reserve release. That gives about $1.96, and we use $1.95 as the starting level. First-half 2026 points the same way: net income was $10.6 million ($1.17 a share) against $6.6 million a year earlier, and cash earnings ran about $1.24 a share for the half, but that half carried only $0.9 million of provisions, so we do not lift the level on two quarters. Growth. Cash earnings per share rose from $1.36 in 2023 to $1.92 in 2025 (+41%); the comparison with 2024 is meaningless because of the distortions above. The base case starts at +1.5% in year one, below that trailing figure and below the roughly 2.6% a year from 2016 to 2025, so no reversal of a slowdown has to be argued. Loans actually shrank $15 million in 2025 and deposits were flat, so we credit no loan-growth acceleration, no margin expansion beyond the 3.88% reached in 2025 (3.51% in 2024) and no further acquisitions. The 1.5% rests on the bank retaining about two thirds of earnings (dividends were $5.5 million on $17.7 million of 2025 net income) and on a record of positive cash earnings per share through the 2020 shutdown, the 2023 funding-cost squeeze and two acquisitions. Core deposit intangibles from acquisitions amortize at about $1.8 million a year; we add that back as a sunk cost and leave the modest growth rate to absorb the run-off of acquired deposits. Base case, $36.54 a share: $1.95 growing 1.5% a year for ten years (to about $2.26), then held flat. Beyond year ten we assume no growth; what persists is a 33-branch deposit franchise that produced positive cash earnings in every year of our 2016-2025 data. Depositors are owed their deposits as the raw material of the business, and the only separate claims are the borrowings above, so nothing further is deducted. If our starting level is 10% too high the base falls to about $32.89; with no growth at all it is $32.50. Bear case, $20.24 a share: a full credit cycle of the 2008-2010 kind, when US bank net charge-offs peaked around 2.5% of loans. Scaled to a community bank, we assume the net interest margin falls about 0.28 points to roughly 3.6% (about $5.4 million pre-tax, $0.47 a share), then provisions of about 0.9%, 1.5%, 1.5% and 0.9% of roughly $1.49 billion of loans in years two to five (about 4.8% cumulative: $13 million, $22 million, $22 million and $13 million), a 10% hit to pre-provision earnings in years three and four and 5% in year five, and a $7 million provision in year six. Cash earnings per share run $1.48, $0.70, -$0.27, -$0.27, $0.60 and $1.26, then settle at $1.48 with no growth and no credit given for acquisitions. The six years still add up to a small cumulative profit of about $3.49 a share, so existing capital (common equity tier 1 ratio of 12.59% at year-end 2025) absorbs the losses without new shares. The bear value sits slightly above tangible book value of $19.71 per share (June 30, 2026) because even after the cycle the bank earns about 8% on tangible equity from a sticky local deposit base, which is worth a little more than its capital. Close to half of 2025's charge-offs, and most of 2024's, came from commercial loans bought through a third-party lending program, so a worse outcome than this bear case is possible if that book or commercial real estate performs worse than the industry did. Bull case, $47.62 a share: the Touchstone cost savings (systems converted February 2025) are fully in the run rate and credit costs stay near 0.2% of loans, supporting $2.35 a share; that grows 2.5% a year for ten years (to about $3.01) and then holds flat. We leave out margin expansion, share repurchases and new deals because none is secured. Margin-of-safety price, $15.00. We are fairly sure of the starting level, about $1.95, because it rests on a ten-year record and on 2025 and first-half 2026 results that already include the Touchstone integration. We are less sure that credit costs stay low: provisions were $6.2 million in 2023 and $7.9 million in 2024, and in 2025 net charge-offs exceeded the provision. The worst plausible outcome is the bear case plus heavier losses in the purchased-loan program; the bank would come through it with capital intact because the balance sheet is plain (nonperforming assets 0.32% of loans at year-end 2025, no preferred stock, borrowings of only about $43 million against $1.8 billion of deposits). If we are wrong on the starting level by 10% and growth is zero, the shares are worth roughly $29; if credit losses run beyond the bear case, tangible book value is the only firm floor, and losses would erode it. Another stock-funded deal that leaves per-share earnings unchanged, as Fincastle and Touchstone did, would add nothing but also would not destroy value. The price assumes about a three-year holding period, during which the bank pays about $0.68 a share a year and retains the rest. At $15.00 the bank's earnings of about $1.95 are a 13% cash earnings yield on the price, of which 4.5% is paid as a dividend. A 20% annual return over three years with the dividends implies a share value of only about $24, below the roughly $25 of book value per share the bank should have by then if it retains about two thirds of roughly $2 a year. A higher price leaves less cushion for the credit and acquisition risks above and would imply less than 20% a year if those risks show up. Comparison with earlier work: our earlier figures for this company were produced on a different basis and are not comparable. What has changed in the business since then is that first-half 2026 earnings rose to $10.6 million from $6.6 million, and tangible book value per share rose from $18.83 at year-end 2025 to $19.71 at June 30, 2026.