Question

"Jill buys a house for $100,000 with no mortgage. Jill s buying costs were 5% of the house price. Jill lives there for exactly 30 years and sells it. Suppose Jill s annual cost of ownership net of tax savings 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 4.5% per year (compounded annually). Suppose selling expenses are 8% of the sale price. What is Jill s annual IRR from owning net of renting?"

Answer 1

Cost of the House = Purchase Cost of the House + Buying cost of the house

= 100,000 + 100,000*5%

= $105,000

.

Annual cost of ownership net of tax savings = Annual rent she would have paid to live in the same house

So inflow outflow from the house.

.

Sale price of the house after 30 years with growth rate of 4.5% per year in the price of the house

= 100,000*(1.045^30)

= 100,000*3.745318

= $374,531.81

.

Selling cost of the house = 8% of Sale Price of the House

= 374,531.81*8%

= $29,962.55

.

Net sale proceeds from sale of House = 374,531.81 - 29,962.55

=$344,569.27

.

.

At IRR ,

Present Value of Cash Outflow = Present Value of Cash Inflows

105,000 = 344,569.27/(1+IRR)^30

(1+IRR)^30 = 344,569.27/105,000

(1+IRR)^30 = 3.281612

1+IRR = 3.281612^(1/30)

1+IRR =1.040406

IRR = 0.040406

IRR = 4.041%

.

.

Jill's annual IRR from owning net of renting is 4.04%