Interest Rate Factor in Financing Objectives

1
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

2
Compound Interest

• PV present value
• iinterest rate, discount rate, rate of return
• Idollar amount of interest earned
• FV future values
• Other terms
• Compounding
• Discounting

3
Compound Interest

• FVPV (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.

4
The Financial Calculator

• n number of periods
• iinterest 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

5
Future Value of a Lump Sum

• FVPV(1i)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.

6
Present Value of a Future Sum

• PVFV 1/(1i)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

7
Future Value of an Annuity

• FVAP(1i)n-1 P(1i)n-2 .. P
• Ordinary annuity (end of period)
• Annuity due (begin of period)

8
Present Value of an Annuity

• PVA R 1/(1i)1 R 1/(1i)2..
• R 1/(1i)n

9
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

10
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

11
Annuities

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

12
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

13
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

14
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

15

Yield IRR

• 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

16
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

17
Conventional MortgageObjectives

• 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

18
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 rf
• Nominal rate real rate plus a premium for
  inflation

19
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
• ir f P

20
Exhibit 4-1 to be inserted by McGraw-Hill
21
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

22
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

23
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

24
Loan Closing Costs and Effective Borrowing Costs

• Statutory costs
• Third party charges
• Additional finance charges i.e. loan discount
  fees, points

25
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

26
Effective Interest Cost Examples Continued

• Calculator solution
• n360
• PMT -617.17
• PV 58,200
• FV 0
• i1.034324 (12.41 annualized)

27
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)

28
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

29
Reverse Annuity Mortgage Example Continued

• Calculator solution
• FV-250,000
• i10/ 12
• PMT ?
• n120
• Solve for payment 1220.44