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Please check my math. present value question

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Tim Schneider

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Joined
Feb 8, 2007
Professional Status
Certified Residential Appraiser
State
Wisconsin
I am working on a report where the borrower is getting a special loan from the city to help with down payment. The loan is for $4000, and there is no interest for 5 years, then it goes to 2% interest amoritzed over 6 years. I am trying to determine the present value of this financial assistance. I came up with:

pv of $4,000 in 5 years at the normal mortgage rate (6.625% in this case)= $2,901, which is financial assitance of $1,098

pv of a $4,000 loan at 2% vs. 6.625% over 6 yrs= $3,048, financial assistance of $951

Total value of special loan = $2,049
 
Tim,

The buyer is saving money each month. That savings is what should be brought to its PV.

Calculate what the payment would be at a market interest rate each month.

Then calculate what the payment will be each month.

Then bring that payment stream (the monthly savings) to a present value.

Remember because you have a unlevel payment stream you must account for the change.
 
What are the payments for the first 5 years? How is it amortized?
 
Tim,

The buyer is saving money each month. That savings is what should be brought to its PV.
Calculate what the payment would be at a market interest rate each month.
Then calculate what the payment will be each month.
Then bring that payment stream (the monthly savings) to a present value.
Remember because you have a unlevel payment stream you must account for the change.

OK, using that as a guide:

savings of 0% loan = 78.51/mo for 60 months, pv=$1160

savings of 2% loan = 8.49/mo for 72 months, pv=$127

Total assistance = $1287

That is a big differnce, what does everyone else think?
 
I was using the mortgage rate, 6.625%

If the loan for a downpayment was a mortgage, it would likely have a CLTV of 95-100%. Assuming one can find a second mortgage with a 95-100% CLTV at all anymore, it most certainly would have an interest rate far higher than 6.625%.
 
Is this program only on a specific affordable housing project or is it available to just any home within the municipality? In other words, how is the sale price of the home affected?

If the borrower can bring this "favorable" financing to any home wihin the market, the negotited sale price of the home may not even be affected by this loan program. If it is for a specific affordable housing project, what restrictions are there related to the project imposed on purchasers. There is more to this issue than just a mathimatical cash equivelency calculation.

However, the math, as Dennis pointed out, is as follows:

Calculate payment typical market financing - your example uses 6.625% but what is amortization? Market financing is frequently based on a 20 or 30 year amort term.

Then subtract the payments from the proposed financing to obtain the "savings/benifit".

You then calculate the present value of the "savings/benifit" utilizing the rate for typical financing terms. However, to compare apples to apples you must calculate this over the entire loan term (i.e. 20 - 30 years) not just the short term of the benificial financing.

There is not likely to be a significant adjustment, because it sounds like the "favorable" financing program you are trying to evaluate addresses the downpayment portion of the transaction. Typical market financing today will not extend above 95% in most markets with the exception of FHA which goes to 97% but requires additional costs.


PS - By the way, the second half of your calculations are double counting. As you explained the program it is 0% interest for the first 4 years, then goes to 2% for the next 6. The calculation for the second half is the present value of the payments for 6 years which are then discounted back another 4 years to bring to a present value.
 
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