Charles Davies is a Certified Mortgage Analyst with 15 years of experience in loan performance review and detailed annual cost modeling, ensuring accurate comparison of non-recoverable expenditures.
The **Total Sunk Cost Comparison Calculator** compares the total non-recoverable expenses between two different mortgage scenarios (A and B) over a fixed **Comparison Period (Q)** of 12 months. This linear model relates the **Total Sunk Cost Difference** (F) to the **Monthly Sunk Cost Differential** $(P-V)$. Enter any three variables—Total Difference (F), Higher Monthly Sunk Cost (P), Lower Monthly Sunk Cost (V), or the fixed Time Period (Q=12)—to solve for the unknown fourth value.
Total Sunk Cost Comparison Calculator
Total Sunk Cost Comparison Formula
The core relationship modeling the annual sunk cost difference is:
$$ F = Q \times (P – V) $$
Four Forms of the Formula:
Where $\mathbf{(P – V)}$ is the **Avg. Monthly Sunk Cost Differential**.
\(\mathbf{F} (\text{Total Diff}) = Q \times (P – V)\)
\(\mathbf{Q} (\text{Months}) = F / (P – V)\)
\(\mathbf{P} (\text{Higher Cost}) = (F / Q) + V\)
\(\mathbf{V} (\text{Lower Cost}) = P – (F / Q)\)
Variables Explained:
- F: Total Sunk Cost Difference (Currency) – The cumulative dollar difference in non-recoverable costs (Interest, Taxes, Insurance, MI) between the two scenarios over the 12-month period.
- Q: Comparison Period (Months) – Fixed at 12 months for annual comparison, aligning with fiscal or calendar years.
- P: Avg. Higher Monthly Sunk Cost (Currency) – The average monthly non-recoverable cost for the more expensive scenario (A).
- V: Avg. Lower Monthly Sunk Cost (Currency) – The average monthly non-recoverable cost for the less expensive scenario (B).
Related Calculators
To accurately determine the sunk cost components (P and V) being compared, consult these essential tools:
- Total Cost of Ownership Calculator: A deeper analysis of total sunk costs vs. equity growth over many years.
- Interest Rate Savings Calculator: Quantify the savings from a lower interest rate, which is the largest sunk cost component.
- Property Tax Budget Calculator: Isolate the property tax portion of the sunk cost.
- PMI Reduction Cost Calculator: Compare scenarios where one includes PMI (a sunk cost) and the other does not.
What is Total Sunk Cost Comparison?
In homeownership, “sunk costs” are non-recoverable expenses that do not build equity. These primarily include interest payments, property taxes, homeowners insurance, and mortgage insurance premiums (PITI & MI components, excluding Principal). **Total Sunk Cost Comparison** involves analyzing the difference in these non-recoverable expenses between two financial decisions, such as comparing the sunk costs of a 15-year loan versus a 30-year loan, or a loan with 7.0% interest versus 6.0%.
By using a fixed period of 12 months ($\mathbf{Q}=12$), this calculator provides the cumulative annual difference ($\mathbf{F}$) in these sunk costs. This analysis is crucial because while a borrower may accept a higher payment for a greater return, comparing the total *sunk* expenditure highlights the true, non-productive financial burden of each scenario. A positive result for F means Scenario P costs F dollars more in irrecoverable costs annually than Scenario V.
How to Calculate Avg. Higher Monthly Sunk Cost (Example)
Let’s find the required **Avg. Higher Monthly Sunk Cost (P)** that results in a $3,000 annual sunk cost difference, given the lower cost.
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Step 1: Identify Known Variables.
Total Sunk Cost Difference (F) = $3,000. Comparison Period (Q) = 12 months. Avg. Lower Monthly Sunk Cost (V) = $1,400. We need to solve for P.
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Step 2: Calculate Required Monthly Sunk Cost Differential.
Monthly Differential Needed $ = F / Q = \$3,000 / 12 = \$250$ per month.
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Step 3: Apply the Formula for P.
The Higher Sunk Cost (P) must cover the Lower Sunk Cost plus the Differential: $P = V + (\text{Monthly Differential}) = \$1,400 + \$250 = \$1,650$.
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Step 4: Conclusion.
To incur a $3,000 annual sunk cost difference, the average Higher Monthly Sunk Cost (P) must be $1,650.
Frequently Asked Questions (FAQ)
A: The Monthly Sunk Cost should include all non-equity components: Monthly Interest, Monthly Property Taxes, Monthly Home Insurance, and any applicable Monthly Mortgage Insurance (PMI/MIP). Exclude the principal payment component.
Q: What happens if the Lower Sunk Cost (V) is higher than the Higher Sunk Cost (P)?A: If $V > P$, the calculated Total Sunk Cost Difference (F) will be negative. This means Scenario B (V) is actually the more expensive option in terms of non-recoverable expenses. The absolute value of F still represents the magnitude of the annual difference.
Q: Why is the Comparison Period (Q) set to 12 months?A: Q is set to 12 months to provide an *annual* comparative metric, which is the standard period for reviewing financial performance and preparing tax documents. The total interest cost reported on Form 1098 is a primary component of the annual sunk cost.
Q: Does this calculation include closing costs?A: No. Closing costs are typically a one-time, upfront sunk cost. This calculator focuses on the ongoing monthly cash flow difference (P-V) multiplied by the monthly term (Q), providing a measure of the *recurring* annual sunk cost differential.