Question

An apartment building has the following investment characteristics:

            Year 1 NOI                 $2,500,000

            Year 2 NOI                 $2,600,000

            Year 3 NOI                 $2,704,000

            Year 4 NOI                 $2,812,000

You plan to purchase the asset at a 5% initial cap rate and to sell it 3 years later, also at a 5% cap rate. You plan to use a loan at 60% LTV to purchase the asset. The loan will be interest only (no amortization) at a 4% annual interest rate. Answer the following:

What is the purchase price?                                                                                       

What is your initial equity investment?                                                                     

What are the annual mortgage payments?                                                                 

What is the loan balance at the end of year 3?                                                          

What is your expected equity (levered) IRR?                                                           

Answer 1

Purchase price = Year 1 NOI/5% = $2500000/0.05 = $50,000,000

As LTV is 60 %, Equity required is 40% = $50 million *40% = $20 million

Annual mortgage payments (interest only loan of $30 million) = $30 million * 4% = $1.2 million

Loan Balance at the end of year 3 = $30 million + $1.2 million = $31.2 million (before paying interest)

or $30 million (after paying interest)

Cashflows to equity are as follows:

Cashflow in year 0 = -$20,000,000

Cash flow in year 1 = $2500000 - $1200000 = $1300000

Cash flow in year 2 = $2600000 - $1200000 = $1400000

Cash flow in year 3 = $2704000 - $1200000 = $1504000

Sale value at the end of year 3 = Year 4 NOI/5% = $2812000/0.05 = $56,240,000

Loan Balance to be paid = $30,000,000

Cashflow from sale in year 3 = $56240000-3000000 = $26,240,000

IRR (r) is given as

-20+1.3/(1+r)+1.4/(1+r)^2+1.504/(1+r)^3+26.24/(1+r)^3=0

Using hit and trial or SOLVER in Excel , r = 0.15868 ir 15.87%