Both loans hold the same $720,000 starting balance — so every dollar of difference is the rate doing the work, isolated from the noise of differing capital structures.
Holding the loan amount constant — the same $720,000 starting balance for both — produces a clean apples-to-apples view of the rate itself. No down-payment differential, no second-lien gap, no confounding capital structure. Three numbers do the work.
Two value streams matter, and they matter together. There's cash kept from paying less every month — and there's the smaller payoff balance you'd write a check for if you sold. Counted alone, each understates the benefit. Counted together, they describe the actual economic position the buyer holds at any exit point.
| Year | Cash Saved CumulativelyMonthly P&I differential, accrued | Smaller Payoff if You SellLoan B balance − Loan A balance | Total Value at ExitSum of both streams | NPV Today @ 4.31%Discounted at 10-Yr Treasury |
|---|
Two complementary curves tell the story. Cash saved grows linearly through year 25, then accelerates when Loan A is extinguished. Smaller payoff at sale peaks at year 25 and then collapses as Loan B catches up. The total rises smoothly throughout — but the NPV in today's dollars peaks at year 25 and gently declines thereafter.
Every dollar of "savings" from this assumption is contractually certain. It's not a forecast. It's not equity-like. It's not contingent on the housing market, employment, or anything else — both loans are fixed-rate, both schedules are locked, and the differential between them is mathematically guaranteed the moment the assumption closes.
Finance theory has one rule about discounting certain cash flows: discount them at the risk-free rate. The 10-Year U.S. Treasury (4.31% as of late April 2026) is the standard benchmark — it's what every CFA curriculum, every DCF textbook, and every Big Four valuation report uses as the default risk-free rate.
The mortgage rate (6.40%) sometimes used as a self-consistent discount rate is, on closer inspection, a price, not a discount rate. It bakes in lender margin, originator profit, servicing costs, and the credit risk premium for the average borrower. Discounting a riskless cash flow at a price loaded with credit-risk premia for someone else is a category error — it understates the value of the savings stream.
Equity opportunity costs (7–10%) are the wrong rate too. Comparing certain cash flows to risky cash flows requires risk-adjustment, not discount-rate inflation. Mixing the two discount rates is one of the most common amateur mistakes in DCF analysis.
| Rate | Justification | NPV at Y25 | NPV at Y30 | Peak NPV | Best Year |
|---|---|---|---|---|---|
| 4.31% | 10-Yr Treasury — risk-free benchmark (primary) | $313,988 | $316,429 | $316,623 | Y29 |
| 4.91% | 30-Yr Treasury — duration-matched alternative | $289,441 | $290,089 | $290,475 | Y28 |
| 6.40% | Market mortgage rate — self-consistent but flawed | $239,310 | $237,163 | $239,310 | Y25 |
The choice of discount rate moves the headline NPV by roughly $77,000 across this range. The lower the rate, the flatter the NPV curve over time and the later the optimal exit — because there's less penalty for waiting to capture future cash flows. At the risk-free rate, holding nearly to maturity is essentially as valuable as exiting early.
The 2.5% subsidized financing carries a quantifiable, present-value benefit of approximately $316,623 in its own right. Because no other property on the market carries this benefit, any cross-listing comparison must begin by deducting that value from the ask price before drawing any conclusions. On that adjusted comparable basis, this property sits at approximately $982,377 — directly comparable to listings near $999,000 elsewhere, without the embedded financing instrument.
The 2.5% assumable mortgage is not a courtesy or a marketing flourish — it is a financial asset that travels with the property and carries an independently quantifiable present value of approximately $316,623 when discounted at the risk-free rate. That value belongs to whoever holds the deed.
Any comparison of this property against other listings must therefore begin with a like-for-like adjustment. Other listings do not carry this financing structure. Their ask prices already represent the full economic cost of acquisition. The subject property's ask price, by contrast, includes access to a transferable financial instrument worth approximately $316,623 — a value that must be netted out before any cross-listing comparison can be made on equal terms.
On that adjusted basis, the comparable-analysis figure for this property is approximately $982,377. A buyer evaluating this property against listings near $999,000 elsewhere is, in present-value terms, evaluating two assets at the same effective comparison basis — but only one of those assets carries the specific attributes, improvements, lot characteristics, and location that distinguish the subject property. Those distinguishing features are obtained without further economic premium above the comparable basis.
The price-equivalence demonstrated in Section 06 has a direct, practical implication: for the same 30-year economic outlay, the buyer can acquire a $1,299,000 home with the assumable financing — or a $982,377 home without it. Same total cost in present-value terms. Materially different asset acquired. The case study below tests this claim by walking both paths month by month for 30 years and discounting every dollar to present value. The convergence is precise within $194.
We hold the loan amount constant at $720,000 in both paths — the only meaningful apples-to-apples basis for isolating the financing's value. Path A acquires the subject property at $1,299,000 by assuming the existing 2.5% mortgage. Path B acquires a comparable property at $982,377 with new 6.4% conventional financing — the calculated price at which the two paths cost the same in present-value terms. Each buyer holds for 30 years. We then total every dollar that leaves the buyer's pocket and discount it to present value at the 10-Year Treasury rate. The test isn't whether they cost the same. It's whether the buyer in Path A has acquired $316,623 more property at no additional economic cost.
| Component of Total Cost | Path A | Path B | Δ (A − B) |
|---|---|---|---|
| Acquisition Inputs | |||
| Purchase price | $1,299,000 | $982,377 | +$316,623 |
| Loan amount | $720,000 | $720,000 | $0 |
| Cash to close | $579,000 | $262,377 | +$316,623 |
| Loan Mechanics | |||
| Interest rate | 2.50% | 6.40% | −3.90 pts |
| Loan term remaining | 25 years | 30 years | −5 years |
| Monthly principal & interest | $3,230.04 | $4,503.64 | −$1,273.60 |
| 30-Year Cumulative Outlay | |||
| Total cash to close (paid year 0) | $579,000 | $262,377 | +$316,623 |
| Total principal repaid | $720,000 | $720,000 | $0 |
| Total interest paid | $249,012 | $901,311 | −$652,299 |
| Total nominal outlay (30 yrs) | $1,548,012 | $1,883,688 | −$335,676 |
| Present-Value View — Discounted @ 4.31% | |||
| NPV of total 30-year outlay | $1,171,556 | $1,171,361 | $194 |
| Δ as % of NPV outlay | +0.017% — convergence within statistical rounding | ||
A careful reader of the table will notice two related but distinct figures: the nominal outlay differential of $335,676 and the NPV outlay differential of essentially zero ($194). The gap between $335,676 and the $316,623 figure is approximately $19,053, and that gap deserves explanation rather than dismissal.
The principle is foundational to financial analysis: only cash flows occurring at the same point in time can be meaningfully compared. Path A and Path B distribute their costs and savings across very different timing patterns — Path A front-loads cash at closing and back-loads payment relief over decades, while Path B back-loads cost through 30 years of higher interest. Adding nominal dollars from year 0 to year 30 as if they were interchangeable would be empirically wrong, because a dollar today can earn risk-free interest while a dollar in year 30 has been waiting three decades to arrive.
Discounting at 4.31% — the 10-year Treasury — translates every future dollar into its today-equivalent. This is the same operation the Treasury market itself performs every day when it prices a 30-year bond. Once both paths are stated in the same units of measurement, direct comparison becomes valid. Only then can the equivalence claim be tested rigorously.
The $19,053 difference between nominal and NPV totals is not noise — it is the time value of waiting 25-30 years to receive Path A's payment relief. Path A's higher up-front cash outlay arrives in year 0, undiscounted. Path B's offsetting interest savings arrive over 30 years and are discounted at the risk-free rate. That asymmetry, properly accounted for, is precisely what produces the $194 NPV convergence.
If the equivalence were a nominal accounting trick, the two paths would tie at the nominal level. They do not. They tie at the NPV level — which is where economically equivalent cash-flow streams are required to tie under any rigorous valuation framework. The nominal divergence is what we should expect to see, and want to see, given the different timing structures involved.
NPV reaches $316,623 in year 29, then declines slightly in year 30. At a near-risk-free discount rate, the curve is unusually flat across the back half of the loan — meaning value continues to accrue almost all the way through the term, and there is no sharp "optimal exit" inflection that punishes a long hold. The structure rewards patience.
By year 5 you've already captured $120K NPV — over a third of the maximum — even though the loan still has 20 years to run. By year 10 you're at $206K, nearly two-thirds. The first decade does most of the heavy lifting, which matters since most American homeowners exit within 7–13 years.
Early years are dominated by faster amortization (the payoff advantage). Later years are dominated by accumulated cash savings. They cross around year 13 and reverse roles. Either stream alone understates the benefit; only together do they tell the full story.