Incremental borrowing cost Incremental borrowing cost is the marginal cost of borrowing additional amount.
Ex. A borrower have two loan choices:
A. $80,000, 25 yr, 12%
B. $90,000, 25yr, 13%
Which loan is better?
The answer depends on the marginal cost of borrowing the additional $10,000.

Computing incremental cost:

Computing incremental cost Loan amount Monthly Pmt
$90,000 1,015.05
A. $80,000 842.58
B-A $10,000 172.47
What is the interest rate on the $10,000 if the monthly pmt is 172.47 for 300 months?
Answer: 20.57%
Unless the borrower can earn more than 20.57% on $10,000 of his own money, he should put that $10,000 into the house and not to borrow the additional $10,000.

Incremental cost with early pay-off:

Incremental cost with early pay-off What if the loan is paid off at the end of 5th year?
Loan amount Pmt Bal.
$90,000 1,015.05 86,639.88
A. $80,000 842.58 76,522.56
B-A $10,000 172.47 10,117.32
What is the interest rate on the $10,000 if the loan is paid-off in five years?
Answer: 20.83%
Early pay-off causes higher incremental borrowing cost.

Incremental cost with points and fees:

Incremental cost with points and fees What if the lender charges 2 points and the loan is paid off at the end of 5th year?
Loan - points Pmt Bal.
$90,000 x.98 1,015.05 86,639.88
A. $80,000 x.98 842.58 76,522.56
B-A $9,800 172.47 10,117.32
What is the interest rate on the $9,800 if the loan is paid-off in five years?
Answer: 21.48%
Points and fees cause higher incremental borrowing cost.

Incremental cost and second mortgage:

Incremental cost and second mortgage In the previous example, the borrower can obtain a second mortgage for the additional $10,000 needed.
If second mortgage rate is less than incremental cost, it is preferred.
The cost on second mortgage can be used for pricing of loans with various LTV ratios.

Pricing loan of higher LTV ratio:

Pricing loan of higher LTV ratio A house costs $100,000 can be financed with two loans:
1st loan: $80,000, 25 yr, 12%
2nd loan: $10,000, 25yr, 18%
Alternatively, the borrower can borrow one loan in the amount of $90,000.
What should the interest rate be on the $90,000, 25yr loan so that the borrower will be indifferent between the two alternatives?

Pricing loan of higher LTV ratio:

Pricing loan of higher LTV ratio Amount Payment
1st loan: $80,000 842.58
2nd loan: $10,000 151.74
Total: $90,000 994.33
What should the interest rate be on the $90,000, 25yr loan with monthly payment of 994.33?
Answer: 12.69%
The proper interest rate on 90% LTV loan should be 12.69% for the borrower to be indifferent.
Note: The answer also depends on the expected pay-off date and the fees and points charged by the lender.

Second loan with different maturity:

Second loan with different maturity A house costs $100,000 can be financed with two alternatives:
A. $80,000, 15yr, 11.5%, 1pt
B. $90,000, 20yr, 12%, 2pt
If the house will be sold in 18 years, what is the incremental cost of B?

Second loan with different maturity:

Second loan with different maturity Loan – point Pmt(1-180) pmt(181-216) Bal.
A. $80,000 x.99 934.55 0 0
B. $90,000 x.98 990.98 990.98 21,051.72
B – A 9,000 56.43 990.98 21,051.72
Set CFo=-9000, CF1=56.43, F01=180, CF2=990.98, F02=35, CF3=21051.72+990.98=22042.70, compute IRR.
Answer: 14.52%
Note: For some calculators, F01 can not exceed 99, in that case, set CFo=-9000, CF1=56.43, F01=90, CF2=56.43, F02=90, CF3=990.98, F03=35, CF4=21051.72+990.98=22042.70, compute IRR.

Loan Refinancing:

Loan Refinancing Refinancing occurs when market rate is sufficiently less than the rate of an existing loan.
Benefit: smaller payment and interest saving.
Cost: all expenses associated with paying off existing loan and acquire a new loan.
If PV-benefit > PV-cost, refinance
PV-benefit < PV-cost, no refinance

Loan refinancing example:

Loan refinancing example Existing loan (at end of yr5): Refinancing option:
$100,000, 30 yr, 10% FRM 25 yr, 7.5%, 4 points.
Payment = 877.57 713.67
Balance = 96,574
Prepay Penalty = 3% (b.f. yr 8) no penalty
1. If new loan is to be held to maturity:
Cost: 96,574 x (0.03 + 0.04) = 6,760 occurred today
Benefit: (877.57 - 713.67)PVAIF(7.5/12, 25) = 22,178
Net saving = 22,178 - 6,760 = 15,418
Should refinance.

Loan Refinancing:

Loan Refinancing 2. If new loan is to be held for only 8 years (pay off at end of yr13):
Existing loan : Refinancing option:
$100,000, 30 yr, 10% FRM 25 yr, 7.5%, 4 points.
Payment = 877.57 713.67
Balance = 85,934 82,153
Prepay Penalty = 3% no penalty
Cost: 96,574 x (0.03 + 0.04) = 6760 occurred today
Benefit: payment saving: (877.57 - 713.67)PVAIF(7.5/12, 8x12) =11,805
balance saving: (85,934 - 82,153)PVIF (7.5/12, 8x12) =2,078
Net saving = (11805+2078) - 6760=7,124
Should refinance.

Another view of refinance:

Another view of refinance The cost of refinance can be viewed as an investment that provides the cash flows equal to the payment and balance savings.
What is the return on this investment?
In previous example, set PV=-6760, N=8x12=96, pmt= 877.57 - 713.67 = 163.90, FV= 85,934 - 82,153=3,781. Compute interest rate to get I/YR= 2.29x12=27.54%
This is a fairly high return. Unless the borrower can invest the $6760 somewhere else to earn higher rate than this, he should refinance.

Borrowing the refinance cost:

Borrowing the refinance cost If the refinance cost can be borrowed, the borrower will get a loan of $96574 + $6760 = $103,334 at 7.5% for 25 years. His new payment will be $763.63 per month, which is lower than the old payment of $877.57. So he should refinance.
If the new loan will be held for only 8 years, the balance will be 87,903.87. If we view the cost of $6,760 as points of the new loan, the effective borrowing amount is still
$-96,574 (PV), Pmt=763.63, N=96, FV=87,903.87, compute interest rate I/YR=0.725x12=8.71%.
This is the effective cost of the new loan. Since it is less than the 10% on the old loan, he should refinance.

Lender Inducement:

Lender Inducement When the interest on a loan is below market, lender may offer discount to induce the borrower to repay the loan early.
E.g. An 8% mortgage with payment of 716.74 per month has 5 year to mature. If the market rate is 12%, and the lender offers a $2000 discount for the borrower to pay off the entire balance now. Should the borrower accept the offer?

Lender inducement:

Lender inducement Consider paying off the balance as an investment, the reward is the saving of monthly payment. The decision depends on the return on this investment.
The current loan balance: $35,348
Less discount: 2,000
Net pay off: 33,348
Set PV=-33,348, pmt=716.74, N=60, CPT I/YR,
I/YR=0.875x12=10.5%
If the borrower can earn more than 10.5% somewhere else with $33,348, he should not pay off the loan now.

Market value of a loan:

Market value of a loan Another way to look at the problem is to find out the market value of the mortgage as if an investor were to buy it.
This investment offers $716.74 per month for 60 months. Given market rate of 12%, its value is the PV of these payments.
Set pmt=716.74, N=60, I/YR=12%/12=1%, find PV=$32,221. This is the market value of the loan.
So the borrower should not pay $33,348 for it.
Note: This assumes the borrower can earn 12% on other opportunities of same risk.

Property Value and Loan Assumption:

Property Value and Loan Assumption An assumable loan is one whose existing terms and balance can be transferred to a buyer along with the physical property.
Assumable loan is valuable if its interest rate is well below current market rate of comparable loans.
The selling price of a property is affected by the financing terms attached to it.

Assumable Loan:

Assumable Loan Assume a house is worth $100,000 if purchased with all cash. The existing 9% loan has monthly payment of $700, and remaining term of 15 years.
If current market rate for a 15 year loan is 11%, how much may a buyer pay for the house if the existing loan is assumable?

Assumable Loan:

Assumable Loan The remaining balance of the existing loan is:
Bal. = 700 PVAIF(9%, 180) = 69,533
To obtain a new loan of this amount:
New Pmt = 69,533 MC(11%, 180) = 783
By assuming the loan buyer can save 783-700 =83 per month for 15 years. The saving is worth
PV(Saving) = 83 PVAIF(11%, 180) = 7,369
The buyer may be willing to pay up to 100,000 + 7369 = 107,369 to be indifferent with all-cash buy for $100,000.
The additional $7,369 is a financing premium.

Assumable Loan:

Assumable Loan The value of the property if purchased with all cash is known as the property’s Cash Equivalent Value ($100,000 in previous example).
The Cash Equivalent Value of a loan is the loan’s market value.
In essence, if a property has an assumable loan, its sale includes the sale of both equity and debt.
A loan with below-market rate can increase selling price but not property value.

Wraparound loans:

Wraparound loans Wraparound can be used to obtain additional finance. Original
Lender Borrower $A Existing loan Wrap loan Wraparound lender $A+$B $A

More creatively:

More creatively Wraparound can be used when a seller of a house keeps the existing loan and at the same time make another loan to a buyer. Lender Seller Buyer $A Existing loan Wrap loan house Escrow $A+$B $A $B $

In the latter case…:

In the latter case… Wraparound may be used if:
interest rate on the existing loan is well below market rate.
the seller can not prepay the existing loan at the time of sale.
the buyer can buy the house with smaller down payment.
Wraparound can be prevented with “due-on-sale” clause.

Buydown Financing:

Buydown Financing A fixed-rate mortgage in which seller prepays some of the interest to help the borrower get below-market financing at the early period of the loan.
May be used when a seller (typically a builder) promotes home sales during a high interest rate period.
The seller’s buydown payment is added to home price.

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By: aysaremail (45 month(s) ago)

very good to know the key concept for taking decision process