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Chapter. 5. Discounted Cash Flow Valuation. 5.4 Loan Types and Loan Amortization. Loan Types and Loan Amortization. Three basic types of loans: Pure Discount Loans Interest–Only Loans Amortized Loans. Pure Discount Loans. The pure discount loan is the simplest form of loan

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  1. Chapter 5 Discounted Cash Flow Valuation

  2. 5.4 Loan Types and Loan Amortization

  3. Loan Types and Loan Amortization • Three basic types of loans: • Pure Discount Loans • Interest–Only Loans • Amortized Loans

  4. 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. 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. 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 / 1.125 • PV = $25,000 / 1.7623 • PV = $14,186 • Or simply enter into your financial calculator and solve for the PV – next slide

  7. 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. 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. 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. 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 amortizingthe loan.

  11. 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. Amortized Loan with Fixed PaymentExample: (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. Amortization Table:

  14. 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. 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)

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