Bob is considering acquiring a commercial property for $100,000. He expects the
ID: 2710066 • Letter: B
Question
Bob is considering acquiring a commercial property for $100,000. He expects the property will generate NOIs of $10,000 in year 1, $11,000 in year 2, $12,000 in year 3 and $12,500 in year 4. He wants you to do a three-year cash flow simulation. He expects the cap rate on the property in three years to be the same as the one at purchase. He is offered an $80,000 interest only 3-year participating mortgage with annual payments of 7% interest plus 50% kickers on any annual cash flow above $11,000 and property value at maturity above $100,000. Assume 39 years straight-line depreciation, income tax rate 30%, 15% capital gain tax, and 20% depreciation recapture tax rate. (a) What is the before tax property expected return? (b) What is the yield to maturity (YTM) on the loan assuming Bob will not default on the loan? (c) What is the before-tax and after-tax returns on Bob’s equity assuming he takes the loan? (d) The lender may be interested in offering a convertible mortgage with 7% interest payments rather than the participating mortgage. At the end of year three, the lender can choose to convert the mortgage into 70% of the property value, what is the before-tax and after tax IRR of Bob’s equity? What is the YTM of the convertible mortgage?
Explanation / Answer
a) At time of purchase ,Value of property=NOI in year 1/cap rate =>cap rate=NOI in year 1/Value of property=10,000 /100,000=.10 or 10% the same cap rate prevails after time 3yrs
after time 3yrs,Value of property=NOI in year 4/cap rate=12,500 /.10=125,000
let Before tax property expected return=r
100,000=10000/(1+r)+11,000 /(1+r)2 +(12,000+125,000-.50*1000-.50*25000)(1+r)3
In calculator enter under CF,CF0=-100000,C01=10000,C02=11000,C03=124000 finally press IRR then CPT to get the value of r=14.386% before tax property expected return.
b)Let y=yield to maturity (YTM) on the loan,interest on loan=7% of 80,000 =5600
-80,000 =5600/(1+y) + 5600/(1+y)2 +(.50*1000+.50*25000+5600+80,000 )/(1+y)3
-80,000 =5600/(1+y) + 5600/(1+y)2 +(98600 )/(1+y)3
In calculator enter under CF,CF0=-80,000 ,C01=5600,C02=5600,C03=98600 finally press IRR then CPT to get the value of r=11.824% .
c) depreciation per year=100000/39=2564
before tax cash flows for Bob's equity
yr 1 10000-5600+2564=6964,after tax=4400*(1-.3)+2564=5644
yr 2 11000-5600+2564=7964,after tax=5400*(1-.3)+2564=6344
yr 3: tax on capital appreciation=.15*(125,000-100000)=3750,tax depreciation recapture=.20*(125000-(100000-3*2564))=6538.4,income in final year=6400-(.50*1000+.50*25000)=-6600, after tax income=(1-.3)*-6600=-6599.3 thus final year after tax cash flow=-6599.3-6538.4-3750+2564+(125,000-100000)=10676,before tax cash flow=-6599.3+2564+(125,000-100000)=20964
let Before tax equity expected return=r
20,000=6964/(1+r)+7964/(1+r)2 +(20964)(1+r)3
In calculator enter under CF,CF0=-20,000,C01=6964,C02=7964,C03=20964finally press IRR then CPT to get the value of r=28.85% before tax equity expected return.
let after tax equity expected return=r
20,000=5644/(1+r)+6344/(1+r)2 +(10676)(1+r)3
In calculator enter under CF,CF0=-20,000,C01=5644,C02=6344,C03=10676 ,press IRR then CPT to get the value of r=5.84% after tax equity expected return.
d) The YTM of the mortgage shall remain the same as the lender shall not choose to convert the mortgage into 70% of the property value, since it shall be more expensive for him to convert rather than just repay the loan 80000.before and after tax return shall also remain the same.
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