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?

the answer is 4.60%

But when I do the CFs on my calculator its wrong. Can you please help:

CFo= -1,600,000

CF1= 7638.64

FO1= 35

CF2= 1,549,857.84

F02= 12 (because it's last year)

Please let me know if my inputs are incorrect.

Explanation / Answer

Note: I have checked your inputs, the following corrections is needed.

CF0 = -1,600,000

CF1 = 7,638.64

FO1 = 36

CF2 = 1,542,219.20 [Loan carrying value after 3 years is 1,511,979.61 x 102% = $1,542,219.20]

FO2 = 1

By pressing IRR you will get 0.38% and multiplying that rate by 12 for annual conversion gives 4.60%

Loan carrying value after 3 years can be determined by following,

N = 324 [27 yrs remaining x 12]

I/Y = 4%/12 = .3333

PMT = 7638.64

Press CPT + PV result is 1511979.61 and applying 2% penalty it would be 1542219.20 last cash flow after 3 years.

If need any further help, please ask in comment.

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