Ann wants to buy an office building which costs $2,000,000. She obtains a 30 yea

Question

Ann wants to buy an office building which costs $2,000,000. She obtains a 30 year fully amortizing fixed rate mortgage with 80% LTV, an annual interest rate of 4%, with monthly compounding and monthly payments. The mortgage has a 2% prepayment penalty if the borrower prepays in the first 5 years. Suppose Ann makes the required monthly payment for 3 years and prepays after her final monthly payment at the end of 3 years. What is the annual IRR on Ann’s mortgage? ANSWER: 4.60% I have the answers and submitted them up there ^^ . I need the calculator solutions, not excel. Please do NOT submit incorrect responses. I already checked chegg. Either noone submitted calculator responses, or what they submitted was wrong. So please dont try to copy/paste wrong asnwers. Thanks in advance!

Explanation / Answer

Note: Calculations are done using Texas BA II plus professional calculator.

Since LTV is 80% , Loan Amount is = 0.8x2000000 = $1600,000

As there are monthly compounding and monthly payments, interest rate and number of period will be adjusted.

N= 30x12= 360

Interest rate = 4/12 = 0.333%

Step 1 will be to find the amount of the 360 equal monthly payments.

Clear time value of money memory: 2nd CLR TVM. Compounding should remain at P/Y = 1 (third row second column).

Enter Present Value: PV = 1600000
        Enter Future Value: FV = 0
        Enter number of periods: N = 360
        Enter interest rate: i (I/Y) = 4/12=0.333
        Calculate unknown: CPT PMT, answer is $7638.6447.

Step 2 will be to find the remaining balance of the loan after 3 years i.e. 36 months or 36th installment

2nd Amort (third row third column above the PV key)
P1 = 36 (ENTER, down arrow)
P2 = 36 (ENTER, down arrow)
The screen should now read BAL = -1511979.610, which is the remaining balance of the loan.
Therefore the amount paid after 36th installment will 1511979.610 + 0.02(1511979.610) as prepayment penalty is 2%

Step 3 will be to find IRR

Clear the cash flow registers first.In this case we need to press 2nd CE/C

Now press CF,

Enter CF0 = 1600000, ENTER and then press down arrow
Enter C01= -7638.6447,ENTER and then press down arrow
Enter F01 = 35   (It represents frequency of the same amount paid in subsequent periods)
Enter C02 = (1511979.610 + 0.02(1511979.610) + 7638.6447) = -1549857.847, Enter and then press down arrow   (As remaining balance was paid immediately after 36th installment, it will be considered in the same time period)
Enter F02 = 1
Press IRR and then CPT
IRR = 0.3837

As it was monthly compounding

Annual IRR = 0.3837x12 = 4.6041% which is approximately 4.60%

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