Question

(Please show all work)   

  1.The following assumptions are made:

The purchase price is $1,100,000.

Potential gross income (PGI) for the first year of operations is projected to be $171,000.

PGI is expected to increase at 4 percent peryear.

No vacancies areexpected.

Operating expenses are estimated at 35 % of effective gross income. Ignore capital expenditures.

The market value of the investment is expected to increase 4 percent peryear.

Selling expenses will be 4 percent.

The holding period is 4 years.

The appropriate unlevered rate of return to discount projected NOIs and the projected NSP is 12 percent

There are no prepaymentpenalties.

a.         Calculate net operating income (NOI) for each of the four years.

b.         Calculate the net sale proceeds from the sale of the property.

c.         Calculate the net present value of this investment, assuming no mortgage debt.  Should you purchase?  Why?

d.         Calculate the internal rate of return of this investment, assuming no debt.  Should you purchase?  Why?

For a $700,000 loan for 25 years at 8%, with monthly payments

Calculate the loan balance at the end of 15 years?

Calculate the amount of total principal reduction achieved over the 25?

Calculate the total interest paid over the 15 years?

When is the loan 60% paid off?

3.Calculate the mortgage payment for a $240,000 level payment mortgage loan amortized for 25 years at 8% interest, if the payments are made annually

How much of the first year’s payment would be principal and how much would be interest

If the mortgage is for 25 years with MONTHLY amortizing, what are the MONTHLY payments

If the payments are monthly, what is the total annual debt service?

How much of the first month’s payment is principal prepayment and how much is interest

4.For a $240,000 loan with monthly payments, at 8% interest for 25 years, the borrower had to pay 2 points in origination fees at the time the loan was made. If that loan is paid off in 5 years what is the effective yield of the loan, including the origination fees

5. (using info from question 2) Now presume that in addition to the points at the origination above, the borrower also has to pay 1 point in prepayment penalty at the time the loan is paid off. What is the EFFECTIVE yield including the origination fees and the prepayment penalty

Answer 1

a)	Calculation of NOI :
	Yrs	1	2	3	4
	PGI(Potential Gross Income)	171000	177840	184953.6	192351.744
			(171000*104%)	(177840*104%)	(184953.6*104%)
	Less:operating Expenses(35% *PGI)	59850	62244	64733.76	67323.1104
	Net Operating Income	111150	115,596.00	120,219.84	125,028.63
b)	Calculation of net sale proceeds:
	Value of investment today	1100000
	Growth Rate	4%	(Assumed Compunded Growth Rate)
	At the end of 4 yrs MV	1100000*(1+4%)^4
		1,286,844.42
	Selling Expenses (4%)	51,473.78
	Net Sale Proceeds At the end of 4 yrs	1,235,370.64
c)
	Calculate the NPV:	PV of Future Inflow+PV of Sale proceeds of Property-Initial Outflow
	Yrs	1	2	3	4
i	PV of Future Inflow@12%
	NOIs	99,256.95	92,130.01	85,596.53	79,518.21
		(111150*0.893)	(115596*0.797)	(120219.84*0.712)	(125028.63*0.636)
		356,501.70
ii	Pv of sale Proceeds	785695.727
		(1235370.64*0.636)
iii	Initial Outflow	1100000
	NPV=	PV of Future Inflow+PV of Sale proceeds of Property-Initial Outflow
		42,197.42
	ADVICE: yes project should be Purchased Due to Positive NPV
d)	Calculation OF IRR:
	A rate where Future Inflows are equal to initial Outflow i.e. NPV=0
	PV of Future Inflow (+) PV of Sale proceeds of Property = Initial Outflow
		Inflows	PVF(15%)	PVF(13%)
	1	111,150.00	0.87	0.885
	2	115,596.00	0.756	0.783
	3	120,219.84	0.658	0.693
	4	125,028.63	0.572	0.613
	4	1,235,370.64	0.572	0.613
	Total Of Inflows		1041344	1106116.52
	Using Interpolation Technique:
	but we need to pay 1100000 only	{(1106116.52-1100000)/(1106116.52-1041344)}*2%
		0.00189
		Approx 13.002%
	IRR	13.002%
	Advice: yes project should be accepted b.coz IRR>Unleverd ROI
	i.e13.002%>12%
	i.e we actually earn more than what we are expecting.