Question

Ann is looking for a fully amortizing 30 year Fixed Rate Mortgage with monthly payments for $4,500,000. Mortgage A has a 4.38% interest rate and requires Ann to pay 1.5 points upfront. Mortgage B has a 6% interest rate and requires Ann to pay zero fees upfront.

(A) Assuming Ann makes payments for 30 years, what is Ann’s annualized IRR from mortgage A?

(B) Assuming Ann makes payments for 30 years, what is Ann’s annualized IRR from mortgage B?

Answer 1

A)

Calculation of installment amount for mortgage A:

No of Installments (N) = 30 years x 12 months = 360 months

PV = 4,500,000

Interest rate = 4.38% p.a. = 4.38/12 = 0.365% per month

Using financial calculator or PMT function in excel,

Installment amount = 22,481.11

Processing fees = 1.50%

Net inflow = 4,500,000 - (1-0.015%) = 4,432,500

PV = 4,432,500

N=360

PMT=22,481.11

Using financial calculator or rate function in excel,

Interest rate = 0.3757% per month

Annualized interest rate = (1+0.3757%)¹² - 1

Annualized interest rate = 4.60% p.a.

B),

Since there is no processing fees, we can directly calculate annualized interest rate.

monthly interest rate = 6%/12 = 0.50%

Annualized interest rate = (1+0.50%)¹² - 1 = 6.168% p.a.

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