Question

Steve has a house and lot for sale for $70, 000. It is estimated that $10,000 is the value of the land and $60 000 is the value of the house. Annthea is purchasing the house on January 1 to rent and plans to own the house for 5 years. After 5 years, it is expected that the house and land can be sold on December 31 for $80,000 ($20,000 for the land and $60,000 for the house). Total annual expenses (maintenance, property taxes, insurance, etc.) are expected to be $3000 a year. The house would be depreciated using a CCA rate of 10%. Annthea wants a 15% after-tax rate of return on her investment. You may assume that Annthea has an incremental income tax rate of 27% in each of the 5 years. Capital gains are taxed at 13.5%. Determine the following:
(a) The annual depreciation.
(b) The capital gain (loss) resulting from the sale of the house.
(c) The annual rent Annthea must charge to produce an after-tax rate of return of 15%.

Answer 1

Greetings,

1) Annual depreciation is as under on reducing balance basis -

Usually land is not depreciable as land has infinite life. Therefore depreciation is to be applied only on 60000.

Year 1 = 60000*0.10 = 6000

Year 2 = (60000-6000)*0.1 = 5400

Year 3 = (54000-5400)*0.10 = 4860

Year 4 = (48600-4860)*0.10 = 4374

Year 5 = (43740-4374)*0.10= 3937

2) WDV at the end if 5 years = (70000 - 6000 -5400 -4860 - 4374 - 3937) = 45429

Sale price = 80000

Therefore capital gain = 80000 - 45429 = 34571

Tax on capital gain = 34571 * 0.135 = 4667

3) Annual depreciation tax shield (DTS) is as under -

Y 1 = 6000 * 0.27 = 1620

Y 2 = 5400 * 0.27 = 1458

Y 3 = 4860 * 0.27 = 1312

Y 4 = 4374 * 0.27 = 1181

Y 5 = 3937 * 0.27 = 1063

PV of DTS @15% = 4578

Annual after tax expenses = 3000*(1-0.27) = 2190

PV of expenses @15% = 7341

Annuity factor for 5 years @15% on after tax basis = 7341/2190 = 3.352

Initial Outlay = 70000

Post tax salvage value = 80000 -4667 = 75333

PV of SV = 75333/(1.15)^5 = 37454

Let after annual rental being = x

So PV of rental = 3.352x

At 15% rate of return, annual rental can be calculated as under -

Initial Outflow = Annual Rental + DTS + Post tax SV - Annual after tax expenses

70000 = 3.352x + 4578 + 37454 - 7341

x = 1053

This is on after tax basis. But before tax rental is given by

10534/(1-0.27) = 14430