Answer:
A. Alternative 1
B. No
C. No
Explanation:
a) Calculation to determine Which alternative should the borrower choose
First step is to calculate the EMI of Alternative 1 and Alternative 1 using this formula
EMI=[P∗R∗(1+R)^N]/[(1+R)N^−1]
Where:
P represent principal = $180,000
R represent interest rate per month = 9%/12 = 0.0075
N represent number of months = 240
Let Plug in the formula
EMI=[180000∗0.0075∗(1+0.0075)^240]/[(1+0.0075)^240^−1]....(1)
EMI=$1,619.51
EMI of the second mortgage in Alternative 2 = $468.63
Second step is to calculate the Total EMI
Total EMI=$1,619.51+$468.63
Total EMI=$2,088.14
Third step is to assume that the average cost of debt in Alternative (2) = R
$2,088.14=[220000∗R/12∗(1+R/12)^240]/[(1+R/12)^240−1]...(2)
Now let solve for the value of R in (2)
R=9.76%
Based on the above calculation we can that Alternative 2 which is 9.76% is greater that Alternative 1 which is 9.5% which means that the borrower should choose ALTERNATIVE 1 $220,000 loan at 9.5 percent for 20 years
b) Calculation to determine if your answer would change if the borrower plans to own the property for only five years
First step is to calculate the loan balance in Alternative 2 after 5 years
Ending balance Loan 1 in Alternative 2 = $159,672.69
Add Ending balance Loan 2 in Alternative 2= $37,038.78
Total balance $196,711.47
Now let assume that the cost of debt in Alternative 2 = R
Hence,
$220,000=$2,088.14∗PVIFA (60payments,R/12)+$196,711.47/(1+R/12)^60....(3)
Let solve for R in the equation (3)
R=9.74%
NO. Based on the above calculation my answer would NOT change if the borrower plans to own the property for only five years reason been that the cost of debt is greater in Alternative 2 which means that Alternative 1 will be preferable.
c) Calculation to determine if your answers to (a) and (b) would change if the second mortgage had a 10-year term
First step is to calculate EMI in the case of 10 year term in Alternative 2
First mortgage EMI $2,280.16
Add Second mortgage EMI $597.24
Total EMI $2,877.40
($2280.16+ $597.24)
Second step is to consider that R is the cost of debt
Hence,
$2,877.40=[220000∗R/12∗(1+R/12)^120]/[(1+R/12)^120−1]...(4)
R = 9.75%
Based on the above calculation Alternative I is preferable because of the lower cost of debt.
Let calculate the ending balance after 5 years in Alternative 2
Ending balance Loan 1 in Alternative 2 109,843.19
Add Ending balance Loan 2 inAlternative 2 26,248.89
Total balance $136,092.08
Now let assume that the cost of debt in Alternative 2= R
Hence,
$22,000=$2,877.40∗PVIFA(60 payments,R/12)+$136,092.08/(1+R/12)^60....(4)
Let solve for R in equation (3)
R=9.74%
NO. Based on the above calculation my answers to (a) and (b) would NOT change if the second mortgage had a 10-year term reason been that the cost of debt is greater in Alternative 2 which means that Alternative 2 will be preferable.
