Discounted Cash Flow Valuation Some Extensions

APR vs. EAR APR (Annual Percentage Rate) EAR (Effective Annual Rates) It serves as a common representation of cost (return). It is an annualized figure. It does not provide a complete picture of these costs (Why) EAR (Effective Annual Rates) It takes into account the effects of compound interest, and is useful for evaluating loans that compound interest at regular intervals, such as monthly or daily. Implications of the differences: Differences between APR and EAR are most significant for loans that carry high closing costs and/or annual fees, such as mortgage loans. In this case, EAR will be much more useful in budgeting for the cost of borrowing the money. In investing, EARs are more important for investments in which interest cannot be withdrawn midway through the term of the loan. EAR will be more pertinent to an individual retirement account, for instance, than for an income investment in which money is paid to the investor rather than reinvested. Discounted Cash Flow Valuation

Example – APR to EAR =1.1956-1=0.1956 or 19.56% Find the Effective Annual Rate (EAR) of an 18% APR loan that is compounded monthly. =1.1956-1=0.1956 or 19.56% Discounted Cash Flow Valuation

Loan Types Pure Discount Loans Interest-Only Loans Amortized Loans Discounted Cash Flow Valuation

Pure Discount Loans They are the simplest form of loan. The borrower receives money today and repays a single lump sum (principal and interest) at a future time. Treasury bills are excellent examples of pure discount loans. The principal amount is repaid at some future date, without any periodic interest payments. If a T-bill promises to repay $10,000 in 12 months and the market interest rate is 7 percent, how much will the bill sell for in the market? PV = 10,000 / 1.07 = 9,345.79 Discounted Cash Flow Valuation

Interest-Only Loans They require an interest payment each period, with full principal due at maturity. 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. Discounted Cash Flow Valuation

Amortized Loans They require repayment of principal over time, in addition to required interest. Two Forms: Amortized Loan with Fixed Principal Payment Amortized Loan with Fixed Payment Discounted Cash Flow Valuation

Example – Excel Loan Amount $50,000 Annual Interest: 8% Loan Period=10 years Amortized Loan with Fixed Principal Payment Amortized Loan with Fixed Payment Discounted Cash Flow Valuation

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