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The cost of capital: relocating with different mortgage rates

There are times when a healthcare provider has to move. When interest rates are high, the move can add unexpected costs. Let's dive into a real example & what you can do to mitigate the financial hit.

Our case

Here’s an interesting and perhaps familiar situation. A physician has an initial mortgage:

30-year fixed at
2.75%

S/he will be moving and their new mortgage is:

30-year fixed at
7.00%.

Let's walk through how to make these two scenarios equal to each other.

Limitations

First, let's acknowledge that we do not know how much principal of the loan remains. That information wasn't provided. Second, let's assume the current home will be sold, but we don't know the selling price or net proceeds. We assume that proceeds are positive.

Scenarios

We will be analyzing 3 scenarios: A: the scenario of the original home A': the scenario for the new home A'': the scenario that makes A' equal to A.

Lines 1-2. Scenario A: This scenario is the current mortgage package at a stated annual interest rate (SAIR) of 2.75%. Since mortgage payments are compounded monthly, we need to convert the SAIR to a K_effective_monthly.

The stated annual interest rate for the two mortgages and their converted effective monthly interest rates (just divide SAIR by 12)

Lines 3 and 4. Now that we have the monthly interest rate, we need to convert the compounding periods from years to months. In all 3 scenarios, the term of the loan is 30 years, or 360 compounding periods.

Converting compounding periods from years to months so that the periods have the same units as the effective monthly interest rate

Line 5. Now we need to know the cost of purchasing the original home and the new home. For that, we need details that the healthcare professional did not specify but that we can determine from other data online.

Line 5, Scenario A. Without revealing his/her identity, we know the mean home price in his/her state is $234,386. Let's equate that value to the original loan amount. We'll call this value the present value of the loan at time zero (PV at t=0)

We know where the healthcare provider is moving based on his/her tweets, but we won’t reveal that information here because we want to maintain his/her anonymity

Same as above. We know where the HCP is moving and to preserve his/her anonymity, we aren’t revealing anything more than the mean home price in the destination state

Home values

Line 5, Scenario A'. Now we need the mean home value in the new state (this HCP is making an inter-state move). Again, without revealing his/her identity, we found information about this person's destination state (all publicly available).

Line 5, Scenario A'. The mean home price in the new state is $345,625. Let's assume that is the new home loan value (PV at t=0).

Line 6. We don't know if any down payment was made on the original home loan or the new home loan, and thus we assume that $0 downpayment was made for both.

An assumption that the HCP did not make a down payment in either scenario A (the current home) or scenario A’ (the new home).

Line 7. The annuity discounting factor (ADF) is what we will use to *compound* both loans. I know, I could have just calculated the annuity compounding factor (ACF), but I converted the ADF to an ACF in Line 9.

ADF and ACF are mathematically related to each other. The key is to make sure you’ve placed it in either the numerator or denominator of your calculations.

Cash flows

Line 8. This line represents the monthly payments (cash flows) that one would make on the loan terms for scenarios A and A'. We will use these cash flows to determine the future value (FV) of both loans. The FV is what you actually end up paying if you carry the loan to term.

Big difference in the monthly mortgage payments (cash flows) because of the huge difference in interest rates.

Future value of mortgages

Line 9. The future value (FV) of loans for Scenarios A and A' is what you ultimately end up paying. This value is your accounting value. Big difference between the two scenarios because of Line 2.

As above. Huge difference in what you ultimately pay (half-a-mil versus nearly 3 mil $) because of the huge interest rate. The interest rate difference is driving the huge difference in future values (line 9) a lot more than the loan amounts (line 5).

Scenario analyses

Scenario A''. Alright. Now comes the part in which we are really interested. Now that the SAIR has jumped from 2.75% to 7.00%, our new FV is really high. Really high (see Line 13 between Scenarios A and A'). We want to return the FV of the new loan back to the original loan.

Scenario A''. Scenario A'' is the new loan at 7.00% but with a FV from the original home loan (Scenario A, Line 13 = $534,336). What must the PV (at time=0) be in Scenario A'' in order to have a FV (Scenario A'') = FV (Scenario A)?

Scenario A'', Line 9. The PV (time=0) for the above to be true is $65,833. So we need a new home loan of $65,833 for a new home whose mean price is $345,625 (Line 9).

The HCP needs to borrow $65,833 at an SAIR of 7.00% for a 30-year term on a house costing $345,625 in order for the sum of his/her payments to equal what s/he would have paid in the original (current) home.

Scenario A'', Line 10 For the above to be true, we must make a down payment in Scenario A'' of $279,792. From where will this capital come? Hopefully from the sale of the original home (which we assumed is the fate of the original home).

Hopefully, the original home is sold for more than $279,792 so that the HCP makes a profit.

This calculations show you how to offset a jump in SAIR from 2.75% to 7.00%. Is this financially possible? It depends on:

a) fate of the original home (we assumed it would be sold),

b) principal on the original home (we weren't given this info & can't find it from public data sources),

c) net proceeds of the home (we have no way of knowing this from public data at this time).

Good luck to this healthcare provider. I wish him/her only the best.

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