Question

Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $1,250,000.

Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront.

Assuming Ann makes payments for 2 years before she sells the house and pays the bank the balance, what is Ann’s annualized IRR from mortgage A?

#2 IRR from mortgage B?

I would like to know how to calculate the IRR of this in a BA II

Answer 1

Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $1,250,000. Mortgage A has a 4.38% interest rate

We first need to estimate the amount of loan taken.

This can be estimated using PV function in BAII

Loan amount = PV of all the future monthly payments. Hence, input for PV functions are:

Rate, i = interest per period = interest per month = 4.38% / 12 = 0.00365

Period, n = numbers of months in 30 years = 12 x 30 = 360

PMT = monthly payment = - $1250000

Hence, loan amount = PV (i, n, PMT) = PV (0.00365, 360, -1250000) = $ 250,210,069.6852

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We now need to know the amount of loan outstanding at the time of closing i.e. after 2 years. Loan balance after 2 years = PV of all the pending future monthly payments. We again make use of the PV function but the inputs this time will be:

Rate, i = interest per period = interest per month = 4.38% / 12 = 0.00365

Period, n = numbers of months in 30 - 2 = 28 years = 12 x 28 = 336

PMT = monthly payment = - $1250000

Hence, loan amount = PV (i, n, PMT) = PV (0.00365, 336, -1250000) = $ 241,779,990.2295

So, Ann will have to pay this much amount at t = 2 to close the loan.

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Ann to pay 1.5 points upfront

Cash flows for Ann:

At t = 0, the bank disburses the loan amount after deducting the upfront fees of 1.5% = $ 250,210,069.6852 x (1 - 1.5%) = $  246,456,918.6399

This is the money Ann receives at t = 0,

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So Ann's series of cash flows comprises of following:

• Receipt of $ 246,456,918.6399 at t = 0
• Monthly payments of $ 1,250,000 over 24 months
• Final payment of $ 241,779,990.2295 at t = 2 years = 24 months

We can calculate the IRR per period (month) of these cash flows using RATE function on BAII calculator. Inputs for RATE functions are:

Period, n = 24

Payment, PMT = -1250000

PV = 246,456,918.64

and FV = -241,779,990.2295

Hence, IRR per period = RATE (n, PMT, PV, FV)

= RATE (24,-1250000, 246456918.6399, -241779990.2295) = 0.4320%

Hence, IRR = 12 x IRR per period = 12 x 0.4320% = 0.051837125 = 5.18%