Question

In: Finance

Please show details of solving. Thank you. Ann buys a property that costs $1,000,000. She finances...

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?

Expert Solution

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:

jeff jeffy answered 1 year ago

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