Wraparound loans suppose a property owner named smith

Suppose a property owner named Smith has an existing loan with a balance of $90,000
and monthly payments of $860.09. The interest rate on the loan is 8 percent and the
remaining loan term is 15 years. From the time Smith originally obtained this loan, the
property has risen in value to $150,000. Smith’s current loan balance is 60 percent of the
current value of the property. He would like to borrow an additional $30,000, which would
increase his debt to $120,000, or 80 percent of the property value.
Assume that the current effective interest rate on a first mortgage with an 80 percent loan-
to-value ratio is 11.5 percent with a term of 15 years, and the current effective interest rate
on a second mortgage for an additional 20 percent of value ($30,000) would be 15.5 percent
for a term of 15 years.
A lender different than the holder of Smith’s existing loan is willing to make a
wraparound loan for $120,000 at a 10 percent rate for a 15-year term. Payments on this loan
would be $1,289.53 per month. If Smith makes this loan, the wraparound lender will take
over the payments on Smith’s current loan; that is, Smith will pay $1,289.53 to the
wraparound lender, and the wraparound lender will make the $860.09 payment on the
original loan. Thus, Smith’s payment would increase by $429.44 ($1,289.53 – $860.09) per
month. Because the wraparound lender is taking over the payments on the old loan, Smith
will actually receive only $30,000 in cash (the $120,000 amount for the wraparound loan
less the $90,000 balance of Smith’s current loan).
Is the wraparound loan a desirable alternative for Smith to obtain an additional $30,000?

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What is the cost of the incremental $30,000? This is analogous to determining the