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Homework answers / question archive / Problem Five years ago you purchased a house from a Housing Project

Problem Five years ago you purchased a house from a Housing Project

Finance

Problem

Five years ago you purchased a house from a Housing Project. The seller financed 105.000 TL on a 15-year fixed rate loan at 12% annually. The contract requires annual principal payments of 7.000 TL plus interest on the remaining balance (e.g. at the end of first year you paid principal of 7.000 TL and interest of 12.600 TL).

Five years have passed since the contract was signed, and interest rates have fallen. A local bank has agreed to make a new 10-year loan at annual 10% interest with equal annual repayments.

You are also informed that expenses associated with refinancing are as follows: Recording fee of 300 TL and loan origination fee of %2 of remaining principal of 70.000 TL (or 1400 TL). These expenses (total of 1.700 TL) need to be paid immediately when new agreement is signed.

Assume that after-tax discount rate or market interest rate for you is 9%. In other words, you should discount the cash outflows with 9%.

Given this information; you are asked to evaluate whether or not to refinance your loan. Calculate the parameters that help you to evaluate, show your work for both existing loan and refinancing loan, explain your logic, and discuss the results.

Hint: First, calculate cash flows for each option and then compare!

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After 5 years, Principal amount repaid = 7000 TL * 5 =35000 TL

So, Loan Outstanding after 5 years = 105000 TL - 35000 TL = 70000 TL

The loan payments under the original loan per year are shown in table below

Year Principal Due at beginning of Year Principal Paid Interest Total Payment
1 105000 7000 12600 19600
2 98000 7000 11760 18760
3 91000 7000 10920 17920
4 84000 7000 10080 17080
5 77000 7000 9240 16240
6 70000 7000 8400 15400
7 63000 7000 7560 14560
8 56000 7000 6720 13720
9 49000 7000 5880 12880
10 42000 7000 5040 12040
11 35000 7000 4200 11200
12 28000 7000 3360 10360
13 21000 7000 2520 9520
14 14000 7000 1680 8680
15 7000 7000 840 7840

Refinancing makes sense only if the present value of the payments due under original loan at the new discount rate is more than the principal amount due plus refinancing and prepayment costs

Present value of original loan payments (after 5th year)

= 15400/1.09 +14560/1.09+....+7840/1.09^10

= 78358.80 TL

So value of refinanced loan after costs = 78358.80 TL - 1700 TL = 76658.80 TL

New Loan Annual payment (A) per year for 10 years are given as   

= 70000* 0.1/(1-1/1.1^10)

=11392.18 TL

Present value of New loan payment at 9%

=11392.18/0.09*(1-1/1.09^10)

=73111.10 TL

So, the value of new loan is 73111.10 TL

Since the value of refinanced loan is higher than value of new loan

The loan must be refinanced