Why the Funding Choice Matters
Refinancing has two distinct funding needs: the amount required to settle the old loan and the costs of arranging the replacement loan. The borrower may pay those costs in cash at closing or, if the lender permits, add some or all of them to the replacement loan principal. Financing costs can reduce the cash required immediately, but it leaves the borrower with more debt. These calculations identify the closing cash and revised debt; they do not by themselves determine which choice has the lower total cost over time.
The payoff \(M\) is the amount needed to settle the old loan on the specified date; it is not automatically the old loan’s original principal. It may reflect the payoff calculation applicable on that date. The costs \(C\) are separate closing uses, such as hypothetical appraisal, legal, or loan-origination charges. This tutorial treats them as amounts due at closing and assumes that financed costs are added to principal dollar for dollar, with no separate fee for financing them.
Balance the Closing Sources and Uses
A reliable way to organize the calculation is to list what must be paid and then identify which amounts come from the replacement loan and which come from the borrower. In the basic case, closing uses are \(M+C\). If the replacement loan supplies \(M+F\), the borrower supplies the remaining \(C-F\).
This identity is a useful check, not an extra assumption: the amounts on the right must fund the amounts on the left. If no costs are financed, \(F=0\). If all costs are financed, \(F=C\). Between these extremes, the borrower pays the unfunded portion \(C-F\) in cash.
Use the specified old-loan payoff amount \(M\) for the refinancing date.
Add the costs due at closing to obtain \(C\), keeping them distinct from the payoff.
Set \(F=0\) for costs paid entirely upfront, \(F=C\) if all costs are financed, or calculate the permitted partial amount subject to the lender’s limit.
The replacement principal is \(M+F\), and cash toward payoff and costs is \(C-F\). Confirm that loan proceeds plus cash equal \(M+C\).
Why the Formulas Hold
The formulas follow from the closing balance. The old loan requires \(M\) dollars and the costs require \(C\) dollars, so total uses are \(M+C\). The new loan covers the payoff \(M\) plus the financed portion \(F\), giving proceeds of \(M+F\). The costs not included in those proceeds are \(C-F\), which must be paid in cash. Adding the two sources gives
Thus paying all costs upfront means \(F=0\), so the new principal is \(M\) and the borrower brings \(C\) dollars for costs. Financing all costs means \(F=C\), so the new principal is \(M+C\) and no cash is needed for those costs. These conclusions assume the lender actually advances the stated principal and that the borrower does not use loan proceeds for unrelated purposes.
Worked Examples
Worked Example: Comparing Full Upfront Payment With Full Financing
A borrower’s old-loan payoff is $148,500. Hypothetical refinancing costs due at closing total $2,400. The replacement lender will advance enough to cover the payoff and, if requested, all the costs. Compare the new principal and cash required under the two choices.
Method. Apply the sources-and-uses equation once with \(F=0\) and once with \(F=C\). The key distinction is that the costs are either cash uses or additional loan principal.
Step 1: Identify the amounts. \(M=\$148{,}500\) and \(C=\$2{,}400\). Total closing uses are
Step 2: Pay all costs upfront. Here \(F=0\), so the replacement principal is
The borrower contributes \(C-F=\$2{,}400-\$0=\$2{,}400\) toward closing costs.
Step 3: Finance all costs. Here \(F=C=\$2{,}400\), so the replacement principal is
The borrower contributes \(C-F=\$2{,}400-\$2{,}400=\$0\) toward those costs.
Check. With upfront payment, \(\$148{,}500+\$2{,}400=\$150{,}900\). With full financing, \(\$150{,}900+\$0=\$150{,}900\). Each choice funds the same closing uses. The common mistake is to call the financed costs “free”: the borrower avoids paying them in cash at closing, but owes an additional $2,400 as loan principal.
Worked Example: Applying a Maximum Replacement-Loan Amount
A hypothetical refinance requires an old-loan payoff of $236,800. Closing costs are $1,250 for an appraisal, $875 for legal work, and $1,575 in other lender charges. The replacement lender will advance at most $239,000 and permits eligible costs to be included in the loan. Find the greatest amount of costs that can be financed and the borrower’s cash requirement.
Method. First total the costs. Then subtract the payoff from the loan limit to find the capacity remaining for financing costs.
Step 1: Total the costs.
Step 2: Find the loan capacity for costs. The limit leaves
above the payoff. Since the lender permits costs to be financed, no more than $2,200 of the costs can be included. Thus \(F=\$2{,}200\), which is less than the full $3,700 cost.
Step 3: Calculate the new principal and cash. The replacement principal is \(M+F=\$236{,}800+\$2{,}200=\$239{,}000\), exactly the lender’s limit. The borrower must pay the unfunded costs:
Check. Loan proceeds plus cash are \(\$239{,}000+\$1{,}500=\$240{,}500\). Closing uses are \(\$236{,}800+\$3{,}700=\$240{,}500\). The common mistake is to treat the $239,000 loan limit as if it covered all costs as well as the payoff. It covers the payoff and only $2,200 of costs, leaving $1,500 due in cash.
Worked Example: Testing Whether the Cash Available Is Enough
A borrower must pay off an old loan for $196,000 and has $4,800 of hypothetical refinancing costs. The lender’s maximum replacement-loan amount is $199,500. The borrower has $3,000 available in cash for closing. Determine whether paying all costs upfront is feasible, and find the cash requirement if the lender finances the maximum permitted costs.
Method. Compare the required upfront cash with available cash, then use the loan limit to calculate the largest financed portion. Keep the total closing uses separate from the borrower’s cash budget.
Step 1: Test the upfront option. If costs are paid entirely in cash, the replacement principal is $196,000 and the cash required for costs is $4,800. The shortfall against the borrower’s available $3,000 is
Therefore, this option is not feasible using only the stated cash.
Step 2: Calculate the maximum amount financed. The loan limit permits costs of up to
to be added to the payoff. Because \(C=\$4{,}800\), this $3,500 is less than the total costs. The new principal is $199,500, and the cash required for the remaining costs is
Step 3: Check affordability and balance. The borrower has \(\$3{,}000-\$1{,}300=\$1{,}700\) left after paying the unfunded costs. Total sources are \(\$199{,}500+\$1{,}300=\$200{,}800\), equal to uses of \(\$196{,}000+\$4{,}800=\$200{,}800\).
The maximum-financing choice is feasible. The common mistake is to compare the $199,500 loan principal directly with the borrower’s $3,000 cash; the principal is a source of funds, not a cash payment by the borrower at closing.
Generalizing to a Loan Limit
When the loan limit is \(L\), the borrower needs at least \(M\) of proceeds to cover the payoff. If \(L\geq M\) and the lender permits costs to be financed, the largest feasible financed portion is the smaller of the total costs and the capacity remaining after the payoff:
The corresponding replacement principal is \(M+F\), and the cash required for the costs is \(C-F\). This rule assumes the lender’s limit applies to the total replacement principal, the payoff is fully covered, and all costs considered are eligible for financing. If \(L<M\), the loan limit does not even cover the payoff; the borrower must provide at least \(M-L\) in addition to any costs not financed. If some costs are ineligible, only eligible costs can be included when determining \(F\).
| Choice | Financed portion \(F\) | Replacement principal | Cash toward costs |
|---|---|---|---|
| All costs paid upfront | \(0\) | \(M\) | \(C\) |
| Some costs financed | Between \(0\) and \(C\) | \(M+F\) | \(C-F\) |
| All costs financed | \(C\) | \(M+C\) | \(0\) |
Common Mistakes and What the Comparison Does Not Tell You
- Combining the payoff and costs too early. Keep \(M\) and \(C\) separate until the financing choice is known. The payoff determines the base amount needed to replace the old debt; costs determine how much additional financing may be requested.
- Subtracting financed costs from the payoff. Financed costs increase the replacement principal: \(N=M+F\). They do not reduce the amount needed to settle the old loan.
- Calling a financed cost a cash payment. If a cost is included in the replacement principal, it is funded by loan proceeds at closing, not by the borrower’s closing cash. It remains debt.
- Ignoring the lender’s limit or eligibility rules. A request to finance all costs does not mean the lender will approve that amount. Calculate the available capacity and finance only permitted costs.
- Assuming lower closing cash means a better deal overall. These calculations compare funding at closing. They do not compare interest on the added principal, future loan payments, or other consequences over the loan’s life. A complete financial comparison requires those cash flows and applicable loan terms.
Check Your Understanding
For each problem, assume costs are due at closing, financed costs are added dollar for dollar to replacement principal, and no other closing cash items apply. Compare sources and uses to check your calculation.
- A payoff is $124,600 and refinancing costs are $1,900. The lender permits all costs to be financed. State the replacement principal and the cash toward costs if they are all paid upfront and if they are all financed. (Answer: Upfront: principal $124,600 and cash $1,900; financed: principal $126,500 and cash $0.)
- A payoff is $210,750, costs are $2,450, and the maximum replacement principal is $212,000. The lender allows eligible costs to be financed. Find the maximum costs financed, the replacement principal, and the cash needed. (Answer: $1,250 financed; principal $212,000; cash $1,200.)
- A payoff is $87,300. Costs are $640, $910, and $1,250. The lender’s maximum principal is $88,900 and all listed costs are eligible. Find the costs financed and the borrower’s cash requirement. (Answer: Total costs $2,800; $1,600 financed; principal $88,900; cash $1,200.)
- A payoff is $305,400 and costs are $4,600. The lender’s limit is $308,000. Compare the all-upfront choice with financing the maximum permitted costs, giving principal and cash toward costs for each. (Answer: All upfront: principal $305,400 and cash $4,600; maximum financing: $2,600 financed, principal $308,000, and cash $2,000.)
- A payoff is $149,250, costs are $3,600, the lender’s limit is $151,000, and the borrower has $2,500 available for costs. Determine the maximum-financing cash requirement and how much cash remains. (Answer: $1,750 financed; principal $151,000; cash required $1,850; $650 remains.)