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**Chapter 6: Residential Financial Analysis**

Incremental Borrowing Cost Two loans, one for a greater sum than the other. How should borrower compare the alternatives? Calculate marginal or incremental cost of borrowing.

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Loan 1: $80,000, 12%, 25 years = $ /mo. Loan 2: $90,000, 13%, 25 years= $ 1,015.05/mo $10, $ IRR? =PV =PMT = n IRR = 20.57% = incremental cost of extra $10,000

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**What if loan is repaid early (say after 5 years)?**

Loan 1: OLB after 5 years = 76,523 Loan 2: OLB = 86, ,117 IRR? -10,000=PV =pmt ,117=FV =OLB Differential =n IRR = 20.83%

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**If there were origination fees?**

Loan 1: 1,600 Fees Loan 2: 2,700 Fees IRR? 8,900=PV= {(90,000-80,000)-(2,700-1,600)} =pmt =n IRR = 23.18%

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**LOAN REFINANCING If interest rates fall, should loan be refinanced?**

Compare costs of refinancing to benefits or savings. Calculate IRR or NPV. Five year old loan ($80,000 orig., 30 years, 15%) vs. new loan of $78, (OLB of old loan) 25 years, 14%.

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**Loan Refinancing (con’t)**

Costs = $4,105 Benefits = pmtold - pmtnew ( = 60.87) IRR? : 4,105=PV =pmt =n IRR = 17.57% NPV = ? depends on borrower’s req’d rate of return.

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**What happens if loan is repaid early?**

Assume loans were prepaid after 15 years (old loan) or 10 years after refinancing IRR? : 4,105 = PV = pmt = FV (OLBold-OLBnew)=(72,275-71,387) =n IRR = 14.21%

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**What if refinancing costs can be financed?**

Simply compare new payments (based on OLB & refinancing costs) to old payment. If new payment is lower, refinance. Alternatively, calculate the effective cost of refinancing. IRR?: , = PV (loan disbursment) 1,000.10= pmt (OLB &Financed refinance cost)=(78, ) 300 = n IRR = 14.81%

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What if the borrower wanted to refinance for a lower interest rate, but wishes to continue making their current monthly payment? The impact of this approach would be to shorten the payback period. Let’s revisit the first refi example. The interest rate drops from 15% to 14%, and a refi fee of $4105 is charged. The original loan had 25 more years (300 months) until maturity. How long would it take to amortize the outstanding loan balance at the 14% rate?

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PV= OLB= $78,976.50 PMT= $ I= 14% N=?= months vs. the 300 months remaining on the original loan What would the lender’s yield be on the refi loan? PV= $74, = ( OLB – 4105 refi fee) PMT= $ N= months I= ? = 14.99%

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**Early Loan Repayment: Lender Inducements**

If interest rates rise, lenders would like to retire old loans. Lender might offer to discount loan if prepaid. Old loan $75,000; 8%; 15 years. 10 years later OLB is $35,348. If current rates are 12% and lender offers to accept repayment of only $33,348. What is the return to the borrower?

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**IRR?: 33,348 = PV (OLB - 2000 discount)**

= pmt (orig. loan pmt) = n IRR = 10.50% = return on “investment” to buy back the loan.

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Market Value of a Loan Simple - compute the present value of the remaining payments at the market interest rate. Old Loan of $80,000; 10%; 20 years. Five years later, the OLB is $71,842. If market rates were 15% today, what is the loan value?

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PV = ?: = pmt = n 15% = i PV = $55,161 is the “discounted” value of the loan. Makes sense if the borrower has the $$ to pay off loan and the IRR represents on attractive yield to alternative investments

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**Effective Cost of Two or more loans:**

Situations exist when borrower takes a second mortgage or perhaps assumes a loan and needs additional funds. You wish to buy a property priced at $115,000. An existing mortgage can be assumed (OLB=$75,331), payments are $ and the loan will mature in 20 years. A second mortgage for $16,669 ($115,000 x $75,331) can be obtained at 14% for 20 years. Alternatively, the purchase can be made with an 80% LTV loan ($115,000 x .80) at 12% for 20 years.

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**Is the assumption attractive**

Is the assumption attractive? IRR of combined assumption plus second mortgage? IRR?: = = pmt = n 92,000 = PV IRR = 10.75%, which is lower than cost of First mortgage financing (12%)

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**Usually second mortgages have short maturities**

Usually second mortgages have short maturities. If the above situation called for a 5 year second mortgage, would the assumption make sense? IRR?: * =1, = pmt *pmt. On 2nd mtg.,i=14% ,N=5YRS 1-5 for 1, = n 6-20 for = n 92,000 = PV IRR = 10.29%

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Wraparound Loans Used to keep an old (low interest rate) loan in place. Wrap lender makes loan for an amount equal to existing loan balance plus the additional financing required. Wrap lender pays off old note and borrower pays off wraparound loan. Can be used in lieu of assumption and second mortgage in an acquisition or as a means to borrow against equity in a property.

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**$90,000 = OLB old loan (8%, 15 years remaining)**

$ = old pmt. $150,000 = property value $30,000 = desired new financing Options: 1. New first mortgage $120,000 at 11.5% for years. 2. Second mortgage of $30,000 at 15.5% for years. 3. Wrap loan of $120,000 at 10% for 15 years.

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Obviously the wrap rate of 10% is favorable compared to a new first mortgage at 11.5%. Is the wrap better than adding a second mortgage? Calculate the incremental cost on the additional $30,000 acquired via wrap financing. Compare this rate to the second. IRR?: 30,000 = PV = pmt ( wrap loan = n pmt-860 old loan pmt) IRR = 15.46% which is slightly lower than rate on the second.

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**Original mortgagee gets screwed**

Original mortgagee gets screwed. That is why the original mortgage probably disallows further encumbrances or includes a due-on-sale clause.

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BUYDOWNS Seller (often builder) helps buyer (borrower) qualify for mortgage financing by “buying down” early mortgage payments. Used most often when interest rates are very high. Often buydowns are executed with graduated payments for 3-5 years.

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**Assume buyer seeks a $75,000 mortgage and current rates are 15%**

Assume buyer seeks a $75,000 mortgage and current rates are 15%. If loan maturity were 30 years, payments would equal $ Borrower can’t qualify at this payment, but if rate were 13% ($ pmt) they could qualify. Builder/Seller offers to “buy down” the interest rate from 15% to 13% for the first five years of the loan.

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**How much would builder pay lender to buydown the loan**

How much would builder pay lender to buydown the loan? Calculate present value of payment short fall $ ( ) at 15% over 5 years. PV = ? = pmt 15% = i 60 = n PV = $4,988.67

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