In: Finance
Please show details of solving. Thank you.
Ann buys a property that costs $1,000,000.
She finances the purchase with a 80% LTV mortgage.
She gets a 20 year interest only fixed rate mortgage at an annual interest rate of 5%, with annual compounding and annual payments.
Ann must pay 1.5 points upfront in mortgage closing costs (as a % of the loan amount).
The loan has a 5/4/3/2/1 prepayment penalty structure (she must pay a 5% penalty if she prepays at any time in the first year, 4% penalty in the second year etc).
Suppose Ann will sell the property in 3 years, after her 3rd year’s mortgage payment and pay off the balance when she sells.
What is Ann’s annualized IRR for the loan?
Cost of the property = $1,000,000
LTV = 80%
Therefore, loan value = $800,000
Cash flow in year 0 =
Inflow in form of loan = $800,000
Outflow in the form of mortgage closing cost = 1.5% of loan amount
= ($12,000)
Inflow - Outflow = $788,000
Cash flow in years 1 and 2 = Annual loan payment =
Therefore,
Year 1 cash outflow = ($64,194.07)
Year 2 cash outflow = ($64,194.07)
Cash flow in year 3 = Annual payment on loan + repayment
of outstanding loan + penalty of 3% on outstanding
loan
--> Annual payment on loan = $64,194.07 (calculated above)
--> Outstanding loan amount = $723,728.20 (calculated below in
the amortization table)
--> Penalty of 3% on outstanding loan = $21,711.85
Therefore, total outflow in year 3 =
($809,634.11)
==> Annualized IRR for the loan =
Therefore, the Annualized IRR for the loan is 6.46%
--> Amortization table: