Considering the following information, what is the NPV if the borrower refinances the loan? Expected holding period: 15 years, Current loan balance: $100,000; Current loan interest: 7%; Current loan mortgage payment: $898.33; Remaining term on current mortgage: 15 years; New loan interest: 5.5%; New loan mortgage payment: $817.08; New loan term: 15 years; Cost of refinancing: $$5000. Assume that the opportunity cost is the interest rate on the new loan (5.5%).

Question

Quizplus · Accepted Answer

To calculate the NPV, we need to find the present value of all cash flows (savings and costs) using the opportunity cost as the discount rate (5.5%).

First, let's calculate the savings from refinancing:

- Current monthly payment = $898.33
- New monthly payment = $817.08
- Monthly savings = $81.25 ($898.33 - $817.08)

To calculate the present value of these monthly savings over 15 years, we can use the PV formula:

PV = PMT x ((1 - (1 + r)^-n) / r)

Where:
PMT = monthly savings = $81.25
r = discount rate = 5.5% / 12 months = 0.0045833
n = number of months = 15 years x 12 months = 180

PV = $81.25 x ((1 - (1 + 0.0045833)^-180) / 0.0045833) = $12,493.48

Next, let's subtract the cost of refinancing:

- Cost of refinancing = $5,000

To calculate the present value of this cost, we can use the same formula:

PV = PMT x ((1 - (1 + r)^-n) / r)

Where:
PMT = cost of refinancing = -$5,000
r = discount rate = 5.5% / 12 months = 0.0045833
n = number of months = 15 years x 12 months = 180

PV = -$5,000 x ((1 - (1 + 0.0045833)^-180) / 0.0045833) = -$7,536.96

Finally, we can calculate the net present value (NPV) by subtracting the present value of the cost from the present value of the savings:

NPV = $12,493.48 - $7,536.96 = $4,943.48

Therefore, the NPV of refinancing the loan is $4,943.48, making choice C the correct answer.

Considering the Following Information, What Is the NPV If the Borrower