Question

You are considering the purchase of an apartment complex. The following assumptions are made:

•           The purchase price is $1,250,000.

•           Potential gross income (PGI) for the first year of operations is projected to be $191,000.

•           PGI is expected to increase at 4.5 percent per year.

•           5% vacancies are expected.

•           Operating expenses are estimated at 35 percent of effective gross income. Capital expenditures are estimated at 15 percent of effective gross income.

•           The market value of the investment is expected to increase 5 percent per year.

•           Selling expenses will be 4.5 percent.

•           The holding period is 4 years.

•           The appropriate unlevered rate of return to discount projected NOIs and the projected NSP is 13 percent.

•           The required levered rate of return is 14.5 percent.

•           75 percent of the acquisition price can be borrowed with a 30-year, monthly payment mortgage.

•           The annual interest rate on the mortgage will be 8.0 percent.

•           Financing costs will equal 3 percent of the loan amount.

•           There are no prepayment penalties.

a.Calculate net operating income (NOI) for each of the four years. Show all work. (2 pts)

b.Calculate the net sale proceeds from the sale of the property. Show all work. (2 pts)

c. Calculate the net present value of this investment, assuming no mortgage debt. Should you purchase? Why? Show all work. (4 pts)

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

e.Calculate the monthly mortgage payment. What is the total per year? Show all work.

f.Calculate the loan balance at the end of year 4. Show all work.

g.Calculate the levered required initial equity investment. Show all work.

h.Calculate the before-tax cash flow (BTCF) for each of the four years. Show all work. i. Calculate

i. the before-tax equity reversion (BTER) from the sale of the property. Show all work.

j. Calculate the levered net present value of this investment. Should you purchase? Why? Show all work.

k. Calculate the levered internal rate of return of this investment (assuming no debt and no taxes). Should you purchase? Why? Show all work.

Answer 1

Since, there are multiple parts to the question, I have answered the first four (a to d).

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Part a)

The net operating income for each of the four years is calculated with the use of following table:

	Year
	1	2	3	4
Potential Gross Income (PGI)	191,000	199,595 [191,000*(1+4.5%]	208,577 [199,595*(1+4.5%)]	217,963 [208,577*(1+4.5%)]
Less Vacation and Collection Loss (PGI*5%)	9,550	9,980	10,429	10,898
Effective Gross Income (EGI)	181,450	189,615	198,148	207,065
Less Operating Expenses (EGI*35%)	63,508	66,365	69,352	72,473
Capital Expenditures (EGI*15%)	27,218	28,442	29,722	31,060
Net Operating Income	$90,725	$94,808	$99,074	$103,532

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Part b)

The value of net proceeds from sale of property is arrived as below:

Sales Value [1,250,000*(1+5%)^4]	1,519,383
Less Selling Expenses (Sales Value*4.5%)	68,372
Net Sales Proceeds	$1,451,011

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Part c)

The net present value can be calculated with the use of formula given as below:

Net Present Value = -Purchase Price + Net Operating Income Year 1/(1+Unlevered Rate of Return)^1 + Net Operating Income Year 2/(1+Unlevered Rate of Return)^2 + Net Operating Income Year 3/(1+Unlevered Rate of Return)^3 + Net Operating Income Year 4/(1+Unlevered Rate of Return)^4 + Net Sales Proceeds/(1+Unlevered Rate of Return)^4

Substituting values in the above formula, we get,

Net Present Value = -1,250,000 + 90,725/(1+13%)^1 + 94,808/(1+13%)^2 + 99,074/(1+13%)^3 + 103,532/(1+13%)^4 + 1,451,011/(1+13%)^4 = -$73,370 or -$73,371

No, the apartment complex shouldn't be purchased as it is resulting in a negative NPV.

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Part d)

IRR is the minimum rate of return acceptable from a project. It can be calculated with the use of IRR function/formula of EXCEL/Financial Calculator. The basic formula for calculating IRR is given as below:

NPV = 0 =  -Purchase Price + Net Operating Income Year 1/(1+IRR)^1 + Net Operating Income Year 2/(1+IRR)^2 + Net Operating Income Year 3/(1+IRR)^3 + (Net Operating Income Year 4 + Net Sales Proceeds)/(1+IRR)^4

IRR is calculated with the use of EXCEL as below:

where IRR = IRR(B2:B6) = 11.13%

No, the apartment complex shouldn't be purchased as IRR is less than the unlevered rate of return.