Question

Jill buys a house for $800k, lives there for exactly 10 years and sells it.

Suppose Jill’s annual cost of ownership is exactly equal to the annual rent she would have paid to live in the same house.

Suppose the price of Jill’s house grows 3.4% annually.

Buying expenses are 5% of purchase price and selling expenses are 8% of sale price.

Compute Jill’s annual IRR from owning net of renting.

(hint: look at the buy vs rent slides, assume no mortgage.)

Answer 1

Cash flow for owning

Purchase Price of house = $800k = $800000

Buying expenses = 5% x purchase price of house = 5% x 800000 = $40000

Initial Cash flow in year 0 = - Purchase price - Buying expenses = -800000 - 40000 = -$840000

Operating cash flow for year 1 to year 10 = - Annual cost of ownership from year 1 to year 10

Selling price of price of house in year 10 = Purchase price x (1+growth rate)ⁿ = 800000 x (1+3.4%)¹⁰ = 800000 x 1.397028 = $1117622.40

Selling expenses = 8% x selling price = 8% x 1117622.40 = 89409.792

Terminal cash flow in year 10 = Selling price - selling expenses = $1028212.608

Cash flow for Renting

Operating cash flow for year 1 to year 10 = - Annual rent

Calculating IRR owning net renting

IRR owning net renting is the discount rate such that

Present value of cash flows for owning = Present value of cash flows for renting

Initial cash flow in year 0 + Present value of operating cash flow for buying + Present value of Terminal cash flow = Present value of Operating cash flow renting

-$840000 - Present value of Annual costs of ownership from year 1 to year 10 + 1028212.608 / (1+IRR)¹⁰ = - Present value of Annual Rents from year 1 to year 10                             (equation 1)

As it Annual cost of ownership = Annual rent, so Present value of Annual Costs of ownership from year 1 to year 10 = Present value of Annual rents from year 1 to year 10

So Equation 1 becomes

-840000 + 1028212.608 / (1+IRR)¹⁰ = 0

IRR = (1028212.608/ 840000)^1/10 - 1 = (1.224062)^1/10 - 1 = 1.020423 - 1 = 0.020423 = 2.0423% = 2.04%

Hence Annual IRR of owning net renting = 2.04%