# Real estate problem

Assume you are considering investing in an apartment building with the following estimated financial characteristics: Net operating income (NOI) = \$64,000. Net operating income growth rate = 4% per year. Tax depreciation = \$25,000 per year. Annual interest expense = \$32,000. Annual debt service expense = \$35,000. Equity investors marginal income tax rate = 36%. Investment horizon = 2 years. Net purchase price = \$500,000. Equity investment = 30%. Gross sale price = \$650,000. Cost of sale = \$50,000. Outstanding mortgage balance at time of sale = \$385,000. The tax rate on recaptured depreciation = 28%. Long-term capital gains tax rate = 20%. Required after tax return on equity = 6%. The net present value (NPV) and internal rate of return (IRR) for this investment are closest to: NPV IRR A) \$51,977 19% B) \$99,994 47% C) \$288,905 33% D) \$61,095 27%

Initial Investment = 500,000*.3 = 150,000 Book value = 500,000 - (2*25,000) = 450,000 ERAT = 650,000 - 50,000 - 450,000 - 50,000 = 100,000 Long Term Gains tax = 100,000*.2 = 20,000 Recaptured Depreciation Tax = 50,000*.28 = 14,000 ERAT = 650,000 - 50,000 - 385,000 - 20,000 - 14,000 = 181,000 ATCF1 = 64,000 - 32,000 - 25,000 = 7,000*36 = 2,520 in taxes 64,000 - 35,000 - 2,520 = 26,480 CFAT ATCF2 = 64,000*1.04 = 66,650 - 32,000- 25,000 = 9,560*.36 = 3,441.60 in taxes 66,650 - 35,000 - 3,441.60 = 28,208.40 CFAT t0 = -150,000 t1 = 26,480 t2 = 28,208.40 + 181,000 = 209,208.40 r = 6% NPV = 61,175.86 IRR = 27.25% D with probably some rounding error?

Niblita… Why didnt you add back Dep. to get your CF number?

chadtap Wrote: ------------------------------------------------------- > Niblita… > > Why didnt you add back Dep. to get your CF number? Depreciation is not a CF (tax saving tkanks to depreciation is a CF and Niblia incorporated it)

^ I see what I was doing now…thanks

I originally did, I forgot when calculating CFAT, you must find out the taxes you pay and then incorporate that into NI - principal repayment - taxes. I’ve done both and you get close to the answer, I think off by 6,000 or so for the NPV.

good job, Niblita. Very impressive!

wow that’s a pretty intense problem. great practice, thanks maratikus. Just as soon as you think you know a topic, leave it to AF to crush your confidence.

Zombie71 Wrote: ------------------------------------------------------- > wow that’s a pretty intense problem. great > practice, thanks maratikus. > > Just as soon as you think you know a topic, leave > it to AF to crush your confidence. exactly what i was thinking

> > ERAT = 650,000 - 50,000 - 450,000 - 50,000 = > 100,000 > i dont get this part… its 650 (gross sale) - 50 (cost of sale) - 450 (book val) - 50 (???) = 100 what is the other 50? thanks

mike0021 Wrote: ------------------------------------------------------- > 650 (gross sale) - 50 (cost of sale) - 450 (book > val) - 50 (???) = 100 is that re-captured depreciation?

but isnt book value 450 because it was 500 - 50? so i think that 50 for depreciation was accounted for…

but since sales price was higher than purchase price, depreciation should be recaptured and taxed. Niblita, we need your help.

ERAT = 650,000 - 50,000 - 450,000 - 50,000 = 100,000 —>A probably a typo: it is Taxable Gains and not ERAT. ERAT is as Niblita correctly calculated ERAT = 650,000 - 50,000 - 385,000 - 20,000 - 14,000 = 181,000 ---->B The second 50000 in A above is recaptured depreciation. maratikus is correct, with sales price > cost, depcn has to be recaptured and taxed.