An investor has owned a property for 15 years, the value of which is now to $200

Question

An investor has owned a property for 15 years, the value of which is now to $200,000. The balance on the original mortgage is $100,000 and the monthly payments are $1,100 with 15 years remaining. He would like to obtain $50,000 in additional financing. A new first mortgage for $150,000 can be obtained at a 12.5 percent rate and a second mortgage for $50,000 at a 14 percent rate with a 15-year term. Alternatively, a wraparound loan for $150,000 can be obtained at a 12 percent rate and a 15-year term. All loans are fully amortizing. Which alternative should the investor choose?

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Explanation / Answer

The alternative, which results in the lowest monthly payments, should be selected. Hence, we need to calculate the monthly payments under every alternative.

Formula to calculate monthly payments:

Payment per period (Pmt) = Lr / (1-(1+r)-n)

The loan amount is “L”, the interest rate per period is “r” and the number of periods is “n”.

PMT = ($32,419.06*0.05) /[(1)-(1.05)37) = $5,590.21, which is closest to $5,596. So, Option 2 is correct.

Option 1: A new first mortgage for $150,000 and a second mortgage of $50,000:

First Mortgage:
Loan Amount = $150,000
r = 12.5%/12 = 0.010416667 or 1.04167%
n = 15 x 12 = 180 months

PMT = ($150,000*0.0104167) /[(1)-(1+0.0104167)-180)
=> 1562.5/(1 - 0.15484949)
=> 1562.5/0.84515051
= $1,848.78

Second Mortgage:

Loan Amount = $50,000
r = 14%/12 = 0.0116667 or 1.167%
n = 15 x 12 = 180 months

PMT = ($50,000*0.01167) /[(1)-(1+0.01167)-180)
=> 583.33/(1 - 0.123954037)
=> 583.33/ 0.876045963
= $665.87

Total Monthly Payments = $1,848.78 + $665.87 = $2,514.65

Option 2: Wraparound loan for $150,000

Loan Amount = $150,000
r = 12%/12 = 0.01 or 1%
n = 15 x 12 = 180 months

PMT = ($150,000*0.01) / [(1)-(1+0.01)-180)
=> 1500/(1 - 0.16678336)
=> 1500/ 0.83321664
= $1,800.25

Since the monthly payments on Wraparound loan (Option 2) is lower, it should be selected.

Note: There is one thing fundamentally wrong. If you see the first option, it talks about total loan of $200,000 wherein the homeowner requires only $50,000 in additional funding. So, please check it once with your professor and in case only second mortgage should be considered, just add the monthly payment of $665.87 in the current monthly payment. Which makes this alternative preferable.

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