Question

In class, we discussed the fact that “Mortgages are bonds and bonds are mortgages”. Thus, we can use the basics of bond pricing and yield to maturity to evaluate across lending options in mortgages. Assume you have two mortgage home loans to choose from: a. $400,000 @ 4.5% (with monthly compounding) for 30 years with $20,000 in finance fees (aka: points) b. $400,000 @ 6.5% (with monthly compounding) for 15 years with no finance fees (aka: points) Further assume both loans are fully amortizing and that you plan to remain in the property for 7 years. Using Effective Yield (EY) (as calculated in class), explain which loan is preferable due to a lower effective yield.

Answer 1

Mortgaging option of $400,000 @ 4.5% (with monthly compounding) for 30 years with $20,000 in finance fees, costs as:
$729,626.85 as overall payments made in 30 years + $20,000 in finance fees = $   749,626.85
With monthly installments = $2,026.74
Mortgaging option of $400,000 @ 6.5% (with monthly compounding) for 15 years with no finance fees, costs as:
$627,197.24 as overall payments made in 15 years + $0 finance fees = $627,197.24
With monthly installments = $3,484.43
After 7 years payments made as per 30 years payback plan = 7x12x$2,026.74+$20,000 = $190,246.16
After 7 years payments made as per 15 years payback plan = 7x12x$3,484.43 = $292,692.12
Difference in payments = $292,692.12 - $190,246.16 = $102,445.96
Effective yield in 30 year payback option = $190,246.16/400,000 x100 = 47.56%
Effective yield in 15 year payback option = $292,692.12/$400,000 x100 = 73.13%
So as per the Effective yield factor, Option with 30 Years term with 4.5% is more feasible as a buyer when we stay in the property for 7 years.