Consider an income producing property that according to your assumptions and estimations is currently worth $4M...

Consider an income producing property that according to your assumptions and estimations is currently worth $4M on an unlevered basis when a 7.5% required rate of return is applied. One of the assumptions that you have made when arriving at that estimate is that you will sell the property in 6 years for a CAP of 8%, which translates to $4.4M at that future point in time.

a. At what price will you sell the property in 6 years if all your assumptions materialized except that you will sell the property for a CAP of 7% instead of 8%? Show your calculations.

b. All other things equal, by how much the situation described in part a affects the current value of the property. Show your calculations.

Solutions

Expert Solution

The property value will be composed of two parts, namely the present values of the property's annual NOI (Net Operating Income) denoted as PV(NOI) and the present value of the property's sale proceeds after 6 years, all discounted at the required return rate of 7,5 %.

NOTE: One important point to note is that NOls are beng used to calculated property value because the valuation is being done on an unlevered basis, which means that the property is entirely equity financed and hence has no portion of NOI going towards servicing of debt, thereby accruing to the property's equity owner completely

Property Sale Price $4.4 million and Initial Cap Rate = 8%

Therefore, NO16 (NOI at the end of Year 6) = Property Sale Price X Cap Rate = 4.4 x 0.08 = $ 0.352 million

Further, Current Property Value = PV(NOI) PV(Sale Proceeds) = $ 4 million

4 = PV(NOI) + 4.4 / (1.075)^(6)

PV(NOI) = (4 - 2.851) - $ 1.15 million

If the CAP Rate changes from 8% to 7%, the NO16 value remaining constant, we get new property

value as shown below:

New Sale Price = Property Value (at end of Year 6)

= NO16 / New Cap Rate = 0.352 / 0.07 = $5.02857 million - 5.029 million

PV(Sale Proceeds) = PV(Property Value at the end of Year 6)

= 5.029 / (1.075)^(6) = $ 3.258 million

New Current Value of Property = PV(NOI) + PV(PV of Sale Proceeds)

= 1.15 + 3.258 = $ 4.408 million - $ 4.41 million

therefore, change in current value owing to change in sale Cap Rate = (4.41 - 4) = $0.41 million

jeff jeffy answered 1 year ago

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