Question

Tim wants to buy an apartment that costs $2,225,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 3.75%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. The index was 1% at the time of origination. Tim also had to pay 1 point for this loan. Suppose the index rate will remain 1% for the life of the loan.

Compute the annualized IRR for this loan assuming Tim will prepay in 5 years.

Answer 1

	a	Cost of apartment	$2,225,000
	b	Loan to Value (LTV)	85%
	Pv=a*b	Loan amount	$1,891,250
	Rate	Teaser rate per month=(3.75/12)%	0.31%
	Nper	Number of months of mortgage	360	(30*12)
	PMT	Monthly payment for first 3 years	$8,759	(Using PMT function with Rate=0.31%, Nper=360, Pv=-1891250)
	FV	Future value of Loan after 3 years(36 months)	$2,116,074	(Using FV function with Rate=0.31%, Nper=36, Pv=-1891250)
	FV1	Future value of repayment after 3 years(36 months)	$333,183	(Using FV function with Rate=0.31%, Nper=36, Pmt=-8759)
	FV-FV1	Loan Balance at end of 3 years	$1,782,892
		Interest rate after 3 years =1+3=4%
	Rate	Monthly interest after 3 years=(4/12)%	0.3333%
	Nper	Number of months of further repayment=27*12	324
	Pv	Loan Balance at the beginning of year 4	$1,782,892
	PMT	Monthly payment	$9,007	(Using PMT function with Rate=0.3333%, Nper=324, Pv=-1782892)
	FV	Future value of Loan after further 2 years(24 months)	$1,931,126	(Using FV function with Rate=0.333%, Nper=24, Pv=-1782892)
	FV1	Future value of repayment after further 2years(24 months)	$224,668	(Using FV function with Rate=0.333%, Nper=24, Pmt=-9007)
	FV-FV1	Loan Balance at end of 5 years	$1,706,458
		Terminal Cash Flow at end of 5 years	$1,706,458
		Cash Flow at the beginning:
		Loan Amount	$1,891,250
		Less: Payment of 1 point =1%*1891250=	$18,913
		Net Cash Flow at the beginning	$1,872,338
		Cash Flow at the end of 60 months =1706458+9007	$1,715,465
		MONTHWISE CASH FLOWS
		Month	Cash Flow
		0	($1,872,338)
		1	$8,759
		2	$8,759
		3	$8,759
		4	$8,759
		5	$8,759