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Loan Valuation and Analysis
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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.
If a T-bill promises to repay $10,000 in 1 year and the market interest rate is 7 percent, how much will the bill sell for in the market?– PV = 10,000 / 1.07 = 9345.79
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Interest Only Loan
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.
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Amortized Loan with Fixed Payment
Amortized loan is the most common consumer loans, including mortgages, car loans, etc.
Since periodic payment is a fixed amount, an amortized loan is an annuity
Each payment covers the interest expense plus reduces the principal
Consider a 4 year loan with annual payments. The interest rate is 8% and the principal amount is $5000.– What is the annual payment?
• 5000 = C[1 – 1 / 1.084] / .08• C = 1509.60
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Amortization Schedule
Beginning Principal Balance = previous beginning principal balance – previous principal component of payment
Periodic Payment: fixed, computed as an annuity Interest component = Periodic interest rate x
current beginning principal balancePrincipal Component = Periodic Payment –
Interest component
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Amortization Table Example
Year Beg. Balance
Total Payment
Interest Paid
Principal Paid
End. Balance
1 5,000.00 1509.60 400.00 1109.60 3890.40
2 3890.40 1509.60 311.23 1198.37 2692.03
3 2692.03 1509.60 215.36 1294.24 1397.79
4 1397.79 1509.60 111.82 1397.78 .01
Totals 6038.40 1038.41 4999.99
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Payment Frequencies
Remember to convert interest rate and terms to the appropriate frequency
Example: 30 year fixed rate mortgage at 6% per year with monthly payments
Number of payments = 30 x 12 = 360Interest per month = 6% / 12 = 0.5% per
month
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New Choices in Mortgages
My, What an exotic mortgage you have– By Stacey L. Bradford