# Interest Rate Factor in Financing Objectives Present value of a single sum Future value of a single sum Present value of an annuity Future value of an.

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Interest Rate Factor in Financing Objectives Present value of a single sum Future value of a single sum Present value of an annuity Future value of an annuity Calculate the effective annual yield for a series of cash flows Define what is meant by the internal rate of return

Compound Interest PV= present value i=interest rate, discount rate, rate of return I=dollar amount of interest earned FV= future values Other terms: Compounding Discounting

Compound Interest FV=PV (1 + i) n When using a financial calculator: n= number of periods i= interest rate PV= present value or deposit PMT= payment FV= future value n, i, and PMT must correspond to the same period: Monthly, quarterly, semi annual or yearly.

The Financial Calculator n= number of periods i=interest rate PV= present value, deposit, or mortgage amount PMT= payment FV= future value When using the financial calculator three variables must be present in order to compute the fourth unknown. PV or PMT must be entered as a negative

Future Value of a Lump Sum FV=PV(1+i) n This formula demonstrates the principle of compounding, or interest on interest if we know: 1. An initial deposit 2. An interest rate 3. Time period We can compute the values at some specified time period.

Present Value of a Future Sum PV=FV 1/(1+i) n The discounting process is the opposite of compounding The same rules must be applied when discounting n, i and PMT must correspond to the same period Monthly, quarterly, semi-annually, and annually

Future Value of an Annuity FVA=P(1+i) n-1 +P(1+i) n-2 ….. + P Ordinary annuity (end of period) Annuity due (begin of period)

Present Value of an Annuity PVA= R 1/(1+i) 1 + R 1/(1+i) 2 ….. R 1/(1+i) n

Future Value of a Single Lump Sum Example: assume Astute investor invests \$1,000 today which pays 10 percent, compounded annually. What is the expected future value of that deposit in five years? Solution= \$1,610.51

Future Value of an Annuity Example: assume Astute investor invests \$1,000 at the end of each year in an investment which pays 10 percent, compounded annually. What is the expected future value of that investment in five years? Solution= \$6,105.10

Annuities Ordinary Annuity - (e.g., mortgage payment) Annuity Due - (e.g., a monthly rental payment)

Sinking Fund Payment Example: assume Astute investor wants to accumulate \$6,105.10 in five years. Assume Ms. Investor can earn 10 percent, compounded annually. How much must be invested each year to obtain the goal? Solution= \$1,000.00

Present Value of a Single Lump Sum Example: assume Astute investor has an opportunity that provides \$1,610.51 at the end of five years. If Ms. Investor requires a 10 percent annual return, how much can astute pay today for this future sum? Solution = \$1,000

Payment to Amortize Mortgage Loan Example: assume Astute investor would like a mortgage loan of \$100,000 at 10 percent annual interest, paid monthly, amortized over 30 years. What is the required monthly payment of principal and interest? Solution= \$877.57

IRR (Internal Rate of Return) is the most Important alternative to NPV. The IRR is closely related to NPV. With the IRR, we try to find a single rate of return that summarizes the merits of a project. Furthermore we want this rate to be an "internal" rate in the sense that it depends only on the cash flows of a particular investment, not on rates offered elsewhere. If future value and present value are known then you can play a guessing game. For example if you have a \$5,639 investment that will be worth \$15,000 after 7 years. If you guess that the IRR will be 10% you get a PV of \$7,697. Is our next guess greater than 10% or less? Why? Solve on calculator Yield & IRR

Remaining Loan Balance Calculation Example: determine the remaining balance of a mortgage loan of \$100,000 at 10 percent annual interest, paid monthly, amortized over 30 years at the end of year four. The balance is the PV of the remaining payments discounted at the contract interest rate. Solution= \$97,402.31

Conventional Mortgage Objectives Characteristics of constant payment (CPM), constant amortization (CAM), and graduated payment mortgages (GPM) Effective cost of borrowing v.s. lenders effective yield Calculate discount points or loan origination fees

Determinants of Mortgage Interest Rates Real rate of interest- the required rate at which economic units save rather than consume Rate of inflation Nominal rate or constant rate i= r+f Nominal rate= real rate plus a premium for inflation

Determinants of Mortgage Interest Rates Default risk- creditworthiness of borrowers Interest rate risk- rate change due to market conditions and economic conditions Prepayment risk- falling interest rates Liquidity risk i=r+ f+ P…

Exhibit 4-1 to be inserted by McGraw-Hill

Development of Mortgage Payment Patterns Constant amortization mortgage (CAM) Constant payment Interest computed on the monthly loan balance Constant amortization amount Total payment= constant amortization amount plus monthly interest

Development of Mortgage Payment Patterns Constant payment mortgage (CPM) Constant monthly payment on original loan Fixed rate of interest for a given term Amount of amortization varies each month Completely repaid over the term of the loan

Development of Mortgage Payment Patterns Graduated payment mortgage (GPM) Mortgage payments are lower in the initial years of the loan GPM payments are gradually increased at predetermined rates

Loan Closing Costs and Effective Borrowing Costs Statutory costs Third party charges Additional finance charges i.e. loan discount fees, points

Effective Interest Cost Examples Contractual loan amount \$60,000 Less origination fee(3%) \$ 1,800 Net cash disbursed by lender \$58,200 Interest rate= 12% Term 30 years

Effective Interest Cost Examples Continued Calculator solution – n=360 – PMT= -617.17 – PV= 58,200 – FV= 0 – i=1.034324 (12.41% annualized)

Other Fixed Rate Mortgages Characteristics and Requirements: Regulation Z- truth in lending (APR) RESPA- Real Estate Settlement Procedures Act Prepayment penalties and other fees Reverse annuity mortgages (RAMs)

Reverse Annuity Mortgage Example Residential property value \$500,000 Loan amount \$250,000 (to be disbursed in monthly installments) Term 10 years 120 months Interest Rate 10%

Reverse Annuity Mortgage Example Continued Calculator solution: – FV=-250,000 – i=10%/ 12 – PMT= ? – n=120 – Solve for payment \$1220.44

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