1. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.0 Chapter 5 Discounte d Cash Flow Valuation

2. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.1 5.4 Loan Types and Loan Amortization

3. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.2 Loan Types and Loan Amortization Three basic types of loans: Pure Discount Loans Interest–Only Loans Amortized Loans

4. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.3 Pure Discount Loans The pure discount loan is the simplest form of loan The borrower receives money today (a discounted PV amount) and repays a single lump sum at some time in the future A one year, 10% pure discount loan would require the borrower to repay $1.10 in one year for every dollar borrowed today i.e. borrow $1.00 today and repay $1.10 in one year

5. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.4 Pure Discount Loans Treasury bills are excellent examples of pure discount loans. The principal amount is repaid at some future date, without any periodic interest payments. Example Page 131: If a T-bill promises to repay $10,000 in 12 months (1 year) and the market interest rate is 7 percent, how much will the bill sell for in the market? PV = FV/(1+r) t PV = 10,000 / (1.07) 1 = 9345.79 Using the Financial Calculator: Fv = 10,000 N = 1 I = 7 PV = 9,345.79

6. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.5 Pure Discount Loans Example: Bottom Pg 130 Suppose a borrower was able to repay $25,000 in five years. If we, acting as the lender, wanted a 12 percent interest rate on the loan, how much would we be willing to lend? Put another way, what value would we assign today (the present value) to that $25,000 to be repaid in five years? Just compute the PV of $25,000 at 12% for 5 yrs. Using the Formula: PV = FV/(1+r) t PV = $25,000 / 1.12 5 PV = $25,000 / 1.7623 PV = $14,186 Or simply enter into your financial calculator and solve for the PV – next slide

7. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.6 Pure Discount Loans (Financial Calculator) Example: Bottom Pg 130 Suppose a borrower was able to repay $25,000 in five years. If we, acting as the lender, wanted a 12 percent interest rate on the loan, how much would we be willing to lend? Put another way, what value would we assign today to that $25,000 to be repaid in five years? Just compute the PV of $25,000 at 12% for 5 yrs. Using the Financial Calculator: n = 5 i = 12 FV = 25,000 PV = 14,186

8. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.7 Interest-Only Loans A loan that has a repayment plan that calls for the borrower to pay interest each period and to repay the entire principal (the original loan amount) at some point in the future. For example: With a three-year, 10%, interest-only loan of $1000: The borrower would pay $100 in interest ($1,000 x.10) at the end of the first and second years. At the end of the third year, the borrower would return the $1,000 along with another $100 in interest for that year.

9. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.8 Interest Only Loan - Example Consider a 5-year, interest only loan with a 7% interest rate. The principal amount is $10,000. Interest is paid annually. What would the stream of cash flows be? Years 1 – 4: Interest payments of.07(10,000) = 700 Year 5: Interest + principal = 10,700 This cash flow stream is similar to the cash flows on corporate bonds and we will talk about them in greater detail later.

10. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.9 Amortized Loans With a pure discount or interest-only loan, the principal is repaid all at once. An alternative is an amortized loan. The lender requires the borrower to repay parts of the loan amount (principal) over time. (i.e. a home mortgage) The process of paying off a loan by making regular principal reductions is called amortizing the loan.

11. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.10 Amortized Loans The most common way of amortizing a loan is to have the borrower make a single, fixed payment every period. Consumer Loans (such as car loans) Mortgages Each payment covers the interest expense plus reduces principal

12. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.11 Amortized Loan with Fixed Payment Example: (Using the Financial Calculator) Consider a 4 year loan with annual payments (ordinary annuity). The interest rate is 8% and the principal amount is $5000. What is the annual payment? Using the Financial Calculator n = 4 i = 8 PV = - 5,000 PMT = $1,509.60

13. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.12 Amortization Table: YearBeg. Balance Total Fixed Payment Interest Paid (8%) Principal Paid End. Balance 15,000.001509.60400.001109.603890.40 2 1509.60311.231198.372692.03 3 1509.60215.361294.241397.79 4 1509.60111.821397.78.01 Totals6038.401038.414999.99

14. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.13 Quick Quiz What is a pure discount loan? What is a good example of a pure discount loan? The borrower receives money today and repays a single lump sum at some time in the future Treasury Bills What is an interest only loan? What is a good example of an interest only loan? A loan that has a repayment plan that calls for the borrower to pay interest each period and to repay the entire principal (the original loan amount) at some point in the future. Corporate Bonds

15. McGraw-Hill/Irwin ©2001 The McGraw-Hill Companies All Rights Reserved 5.14 Quick Quiz What is an amortized loan? What is a good example of an amortized loan? The lender requires the borrower to repay parts of the loan amount over time. Mortgages and Consumer Loans (i.e.Car Loans)