CHAPTER 17: Mechanics: How to calculate the first payment in a GPM...For example,A potential problem with GPMs:Design your own custom loan . . .Section 17.2.1: Computing Mortgage Yields. . .Example:17.2.2 Why do points & fees exist?. . .17.2.3 Using Yields to Value Mortgages. . .Example:If you know:“Bond-Equivalent” & “Mortgage-Equivalent” Rates…“Bond-Equivalent” & “Mortgage-Equivalent” RatesExample:Answer: Example:Answer:CHAPTER 17: CHAPTER 17: MORTGAGE BASICS II:Payments, Yields, & ValuesThe “Four Rules” of Loan Payment & Balance Computation. . . • Rule 1: The interest owed in each payment equals the applicable interest rate times the outstanding principal balance (aka: “outstanding loan balance”, or “OLB” for short) at the end of the previous period: INTt = (OLBt-1)rt. • Rule 2: The principal amortized (paid down) in each payment equals the total payment (net of expenses and penalties) minus the interest owed: AMORTt = PMTt - INTt. • Rule 3: The outstanding principal balance after each payment equals the previous outstanding principal balance minus the principal paid down in the payment: OLBt = OLBt-1 - AMORTt. • Rule 4: The initial outstanding principal balance equals the initial contract principal specified in the loan agreement: OLB0 = L. Where: L = Initial contract principal amount (the “loan amount”); rt = Contract simple interest rate applicable for payment in Period "t"; INTt = Interest owed in Period "t"; AMORTt = Principal paid down in the Period "t" payment; OLBt = Outstanding principal balance after the Period "t" payment has been made; PMTt = Amount of the loan payment in Period "t". Know how to apply these rules in a Computer Spreadsheet!Interest-only loan: PMTt=INTt (or equivalently: OLBt=L), for all t. Exhibit 17-1a: Interest-only Mortgage Payments & Interest Component: $1,000,000, 12%, 30-yr, monthly pmts. Rules 3&4: Rule 1: Rule 2: Rules 3&4:Month#: OLB(Beg): PMT: INT: AMORT: OLB(End):0 $1,000,000.00 1 $1,000,000.00 $10,000.00 $10,000.00 $0.00 $1,000,000.00 2 $1,000,000.00 $10,000.00 $10,000.00 $0.00 $1,000,000.00 3 $1,000,000.00 $10,000.00 $10,000.00 $0.00 $1,000,000.00 ... ... ... ... ... ...358 $1,000,000.00 $10,000.00 $10,000.00 $0.00 $1,000,000.00 359 $1,000,000.00 $10,000.00 $10,000.00 $0.00 $1,000,000.00 360 $1,000,000.00 $1,010,000.00 $10,000.00 $1,000,000.00 $0.00 Interest Only Mortgage020004000600080001000012000140001336597129161193225257289321353PMT Number$PMTINT$1000000How do you construct the pmt & balance schedule in How do you construct the pmt & balance schedule in ExcelExcel?...?...Four columns are necessary:Four columns are necessary:••OLB, PMT, INT, AMORT.OLB, PMT, INT, AMORT.••(OLB may be repeated at Beg & End of each pmt period to add a 5(OLB may be repeated at Beg & End of each pmt period to add a 5ththcol.;)col.;)••First, First, ““Rule 4Rule 4””is applied to the 1st row of the OLB column to set initial OLBis applied to the 1st row of the OLB column to set initial OLB00= L = L = Initial principal owed;= Initial principal owed;••Then, the remaining rows and columns are filled in by copy/pastThen, the remaining rows and columns are filled in by copy/pasting formulas ing formulas representing representing ““Rule 1Rule 1””, Rule 2, Rule 2””, and , and ““Rule 3Rule 3””, , ••Applying one of these rules to each of three of the four necessApplying one of these rules to each of three of the four necessary columns.ary columns.••““CircularityCircularity””in the Excel formulas is avoided by placing in the remaining coin the Excel formulas is avoided by placing in the remaining column lumn (the 4(the 4ththcolumn) a formula which reflects the definition of the type of column) a formula which reflects the definition of the type of loan:loan:••e.g., For the intereste.g., For the interest--only loan we could use the only loan we could use the PMTPMTtt==INTINTttcharacteristic of characteristic of the interestthe interest--only mortgage to define the PMT column.only mortgage to define the PMT column.••Then:Then:••““Rule 1Rule 1””is employed in the INT column to derive the interest from the is employed in the INT column to derive the interest from the beginning OLB as: beginning OLB as: INTINTtt= OLB= OLBtt--11* * rrtt;;••““Rule 2Rule 2””in the AMORT column to derive in the AMORT column to derive AMORTAMORTtt= = PMTPMTtt--INTINTtt; ; ••““Rule 3Rule 3””in the remainder of the OLB column (t > 0) to derive in the remainder of the OLB column (t > 0) to derive OLBOLBtt=OLB=OLBtt--11––AMORTAMORTtt;;••(Alternatively, we could have used the (Alternatively, we could have used the AMORTAMORTtt=0 loan characteristic to =0 loan characteristic to define the AMORT column and then applied define the AMORT column and then applied ““Rule 2Rule 2””to derive the PMT to derive the PMT column instead of the AMORT column.)column instead of the AMORT column.)What are some What are some advantagesadvantagesof the of the interestinterest--only loanonly loan?...?...••Low payments.Low payments.••Payments entirely taxPayments entirely tax--deductible deductible (only marginally valuable for high tax-bracket borrowers)..••If FRM, payments always the same (easy budgeting).If FRM, payments always the same (easy budgeting).••Payments invariant with maturity.Payments invariant with maturity.••Very simple, easy to understand loan.Very simple, easy to understand loan.What are some What are some disadvantagesdisadvantagesof the of the interestinterest--only loanonly loan?...?...••Big Big ““balloonballoon””payment due at end payment due at end (maximizes refinancing stress)(maximizes refinancing stress)..••Maximizes total interest payments Maximizes total interest payments (but this is not really a cost or (but this is not really a cost or disadvantage from an NPV or OCC perspective)disadvantage from an NPV or OCC perspective)..••Has slightly higher Has slightly higher ““durationduration””than amortizing loan of same maturity than amortizing loan of same maturity ((ÎÎgreater interest rate risk for lender, possibly slightly highergreater interest rate risk for lender, possibly slightly higherinterest interest rate when yield curve has normal positive slope)rate when yield curve has normal positive slope)..••Lack of Lack of paydownpaydownof principle may