Question

1. Suppose you considering an ARM with the following characteristics:

Mortgage amount	$2,000,000
Index	1-year Treasury Bill yield
Margin	2.50
Maximum annual adjustment	2%
Lifetime interest cap	6%
Discount points	2.00
Loan maturity	30 years

1. If the Treasury Bill yield is currently 6 percent, what is the monthly payment for the first year?

2. If the index moves to 7.5 percent at the end of the first year, what is the monthly payment for year 2.

3. If the loan is paid off at the end of year 2, what is the effective cost (yield)?

2. Consider a PLAM with the following features:

Mortgage amount	$190,000
Mortgage term	30 years
Current real rate	5%
Inflation for the next 3 years respectively	2%, 3%, 5%
Mortgage payments adjusted annually

1. What are the monthly payments for each of the first 3 years?

2. What is the effective cost if the loan is repaid at the end of year 3?

3. What is the effective cost if the loan is repaid at the end of year3 and the lender charges 2 discount points up front?

Answer 1

	a.	Mortgage Amount	$2,000,000
		Annual Interest =6+2.5	8.50%
	Rate	Monthly interest=(8.5/12)=	0.7083%
	Nper	Number of months of mortgage	360	(30*12)
	Pv	Mortgage Amount	$2,000,000
	PMT	Monthly payment for the first year	$15,378.27	(Using excel PMT function with Rate=0.7083%,Nper=360, Pv=-2000000)
		Excel Command: PMT(0.7083%,360,-2000000)
	b	If Index moves to 7.5%
	FV1	Future value of Year 1 monthly payments at end of year 1	$191,901.07	(Using excel FV function with Rate=0.7083%,Nper=12, Pmt=-15378.27)
		Excel Command: FV(0.7083%,12,-15378.27)
	FV2	Future Value Mortgage Loan at end of year 1	$2,176,781.81	(Using excel FV function with Rate=0.7083%,Nper=12, Pv=-2000000)
		Excel Command: FV(0.7083%,12,,-2000000)
	FV2-FV1	Loan Balance   at end of year1	$1,984,881
		Annual Interest =7.5+2.5	10%
	Rate	Monthly interest in year2 =(10/12)=	0.8333%
	Nper	Number of months of mortgage	348	(29*12)
	Pv	Mortgage Amount	$1,984,881
	PMT	Monthly payment for the Second year	$17,516.06	(Using excel PMT function with Rate=0.8333%,Nper=348, Pv=-1984881)
		Excel Command: PMT(0.83333%,348,-1984881)
	c	If Loan is paid off at end of year2
	FV3	Future value of Year 2 monthly payments at end of year2	$220,098.84	(Using excel FV function with Rate=0.8333%,Nper=12, Pmt=-17516.06)
		Excel Command: FV(0.7083%,12,-15378.27)
	FV4	Future Value Mortgage Loan at end of year2	$2,192,715.28	(Using excel FV function with Rate=0.8333%,Nper=12, Pv=-1984881)
		Excel Command: FV(0.7083%,12,,-2000000)
	FV4-FV3	Loan Balance   at end of year2	$1,972,616.44
		Initial Cash Flow:
		Mortgage Loan	($2,000,000)
		Discount Point payment(2%)	$40,000
		Net Initial Cash Flow	($1,960,000)
		Month	Cashflow
		0	($1,960,000)
		1	$15,378.27
		2	$15,378.27
		3	$15,378.27
		4	$15,378.27
		5	$15,378.27
		6	$15,378.27
		7	$15,378.27
		8	$15,378.27
		9	$15,378.27
		10	$15,378.27
		11	$15,378.27
		12	$15,378.27
		13	$17,516.06
		14	$17,516.06
		15	$17,516.06
		16	$17,516.06
		17	$17,516.06
		18	$17,516.06
		19	$17,516.06
		20	$17,516.06
		21	$17,516.06
		22	$17,516.06
		23	$17,516.06
		24	$1,990,132.50	(17516.06+1972616.44)
		Internal Rate Of Return (IRR) per Month	0.86%	(Using IRR function of excel over cash flows)
		Effective Annual Cost (Yield) =12*0.86%=	10.33%