Question

Lucy bought a house for $100,000. Lucy’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. The house price grows 4.5% annually (compounded annually).

Suppose buying costs are 5% (of the purchase price of the house) and selling costs are 8% (of the selling price of the house). Lucy owns the house for 30 years. Lucy buys the home with an 80% LTV IO mortgage. The interest rate is irrelevant because the cost of ownership net tax shield is equal to rent. What is Lucy’s annualized IRR?

Answer 1

Net cash flows at the end of year 1

Net cash outflow (1,00,000$ *80%) 80,000 $ morgage and remaining 20% i.e 20,000 $ is deposited to the bank , as per LTV IO Morgage plan.Accordingly

Net cash inflow (100000*104.5%) = 104500$

Net cash outlow of the cost attached to it =

Net buying cost of purchase price (100,000)* 5%= 5000$ and selling cost is (104500*8%) = 8360 $.

Annualised cash flow = Net cash inflow -Net cash outflow

= 104500$ - (80000$+5000$+8360$)

= 11140 $ Net Cash Inflow at the end of year 1.

Hence IRR = Net cash Inflow/ Net cash Outflow

=(104500/93360)$

IRR for first year= 1.12% .