Question

Use the following property data: cash flow from operations: year 1 1 2 3 4 5 noi $150,000 $150,000 $150,000 $150,000 $150,000 debt service $125,000 $125,000 $125,000 $125,000 $125,000 cash flow at sale: sale price: $2,000,000 cost of sale: selling expense $125,000 mortgage balance: principle $1,500,000

a. assuming the going-in capitalization rate is 8 percent, com- pute a value for the property using direct capitalization.
b. assuming the required return on unlevered cash flows is 10 percent, and that the property will be held by a buyer for five years, compute the value of the property based on discount- ing unlevered cash flows.
c. assuming the relevant required return on levered cash flows is 15 percent, and that the property will be held by a buyer for five years, what is the present value of the levered cash flows?

Answer 1

a. The value of the property using direct capitalization is $1,875,000. b. The value of the property based on discounting unlevered cash flows is $1,710,063. c. The present value of the levered cash flows is $1,362,662.

Step-by-step explanation:

a. To compute the value of the property using direct capitalization, we need to divide the Net Operating Income (NOI) by the going-in capitalization rate. In this case, the NOI is $150,000 for each year, and the capitalization rate is 8%. Therefore, the value of the property is:

V = NOI / cap rate = $150,000 / 0.08 = $1,875,000

b. To compute the value of the property based on discounting unlevered cash flows, we need to discount the cash flow from operations and cash flow at sale to present value using the required return rate. The calculations for each year would be:

Year 1: PV = $150,000 / (1 + 0.10) = $136,364

Year 2: PV = $150,000 / (1 + 0.10)^2 = $123,967

Year 3: PV = $150,000 / (1 + 0.10)^3 = $112,697

Year 4: PV = $150,000 / (1 + 0.10)^4 = $102,452

Year 5: PV = $150,000 / (1 + 0.10)^5 = $93,138

The present value of the cash flow at sale would be:

PV = ($2,000,000 - $125,000) / (1 + 0.10)^5 = $1,142,445

Therefore, the value of the property based on discounting unlevered cash flows is:

V = PV of cash flows from operations + PV of cash flow at sale = $136,364 + $123,967 + $112,697 + $102,452 + $93,138 + $1,142,445 = $1,710,063

c. To compute the present value of the levered cash flows, we need to discount the cash flow from operations and cash flow at sale using the required return rate on levered cash flows. The calculations are the same as in part (b), but with a required return rate of 15%:

Year 1: PV = $150,000 / (1 + 0.15) = $130,435

Year 2: PV = $150,000 / (1 + 0.15)^2 = $113,232

Year 3: PV = $150,000 / (1 + 0.15)^3 = $98,467

Year 4: PV = $150,000 / (1 + 0.15)^4 = $85,811

Year 5: PV = $150,000 / (1 + 0.15)^5 = $74,619

The present value of the cash flow at sale would be:

PV = ($2,000,000 - $125,000) / (1 + 0.15)^5 = $860,098

Therefore, the present value of the levered cash flows is:

PV = PV of cash flows from operations + PV of cash flow at sale = $130,435 + $113,232 + $98,467 + $85,811 + $74,619 + $860,098 = $1,362,662