03_INTERESTE RATES
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Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-7
Present Value Introduction
• Different debt instruments have very different streams of cash payments to the holder (known as cash flows), with very different timing. • All else being equal, debt instruments are evaluated against one another based on the amount of each cash flow and the timing of each cash flow. • This evaluation, where the analysis of the amount and timing of a debt instrument’s cash flows lead to its yield to maturity or interest rate, is called present value analysis.
Chapter Preview
• Interest rates are among the most closely watched variables in the economy. • yield to maturity (YTM) is the most accurate measure of interest rates.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
3-4
Chapter Preview
• So, in this chapter, we will develop a better understanding of interest rates. We examine the terminology and calculation of various rates, and we show the importance of these rates in our lives and the general economy. Topics include:
Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-15
Yield to Maturity: Bonds
4. One-Year Discount Bond (P = $900, F = $1000)
$1000 $900 = ⇒ (1 + i)
3-8
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
Present Value
• The concept of present value (or present discounted value) is based on the commonsense notion that a dollar of cash flow paid to you one year from now is less valuable to you than a dollar paid to you today. This notion is true because you could invest the dollar in a savings account that earns interest and have more than a dollar in one year. • The term present value (PV) can be extended to mean the PV of a single cash flow or the sum of a sequence or group of cash flows.
Four Types of Credit Instruments
1. Simple Loan • principal + interest, maturity • Commercial loan 2. Fixed Payment Loan • Same payment every month • Mortgages, installment loans 3. Coupon Bond • Coupon payment • Face value or par value • Issuer, maturity, coupon rate • Treasury bonds, corporate bonds 4. Discount Bond • Price below face value • Repaid face value • No interest payment
Fixed coupon payments of $C forever，perpetuity bond
C P= i
C i= P
3-14
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
Relationship Between Price and Yield to Maturity
3. Coupon Bond (Coupon rate = 10% = C/F)
$100 $100 $100 $100 $1000 P= + 2 + 3 + ... + 10 + (1+ i ) (1 + i) (1+ i ) (1+ i ) (1 + i )10 C C C C F P= + 2 + 3 + ... + n + (1+ i ) (1 + i) (1+ i ) (1+ i ) (1 + i )n
• Three interesting facts in Table 3-1
1. When bond is at par, yield equals coupon rate 2. Price and yield are negatively related 3. Yield greater than coupon rate when bond price is below par value
3-9
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
Present Value Concept: Simple Loan
Simple loan of $100 Year: 0 1 $100 $110
2 $121
3 $133
n 100×(1+i)n
$1000 − $900 i= = .111 = 11.1% $900
F−P i= P
Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-16
Global perspective
– Measuring Interest Rates – The Distinction Between Real and Nominal Interest Rates – The Distinction Between Interest Rates and Returns
Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-5
• Yield to maturity = interest rate that equates today's value with present value of all future payments 1. Simple Loan
$100 = $110 (1 + i ) ⇒
$110 − $100 $10 i= = = .10 = 10% $100 $100
Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-12
Yield to Maturity: Loans
2. Fixed Payment Loan (i = 12%)
$126 $126 $126 $126 $1000 = + 2 + 3 + ... + 25 (1+ i ) (1 + i) (1+ i ) (1+ i )
批注本地保存成功开通会员云端永久保存去开通
Part Two
Fundamentals of Financial Markets
Chapter 3
Understanding Interest Rates
Outlines
• Measuring Interest Rates – Present Value – Yield to Maturity • Other Measures of Interest Rates • The Distinction Between Real and Nominal Interest Rates • The Distinction Between Interest Rates and Returns – Maturity and the Volatility of Bond Returns: Interest-Rate Risk • The Practicing Financial Institution Manager: Calculating Duration to Measure Interest-Rate Risk – Calculating Duration – Duration and Interest-Rate Risk
periodically
Only at maturity dates
Present Value Concept: Simple Loan Terms
• Loan Principal: the amount of funds the lender provides to the borrower. • Maturity Date: the date the loan must be repaid; the Loan Term is from initiation to maturity date. • Interest Payment: the cash amount that the borrower must pay the lender for the use of the loan principal. • Simple Interest Rate: the interest payment divided by the loan principal; the percentage of principal that must be paid as interest to the lender. Convention is to express on an annual basis, irrespective of the loan term.
FP FP FP FP LV = + 2 + 3 + ... + n (1 + i ) (1 + i ) (1+ i ) (1+ i )
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
3-13
Yield to Maturity: Bonds
$1 PV of future $1 = (1+ i )n
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
3-10
Present Value of Cash Flows: Example
Yield to Maturity: Loans
Present Value Introduction
• Different debt instruments have very different streams of cash payments to the holder (known as cash flows), with very different timing. • All else being equal, debt instruments are evaluated against one another based on the amount of each cash flow and the timing of each cash flow. • This evaluation, where the analysis of the amount and timing of a debt instrument’s cash flows lead to its yield to maturity or interest rate, is called present value analysis.
Chapter Preview
• Interest rates are among the most closely watched variables in the economy. • yield to maturity (YTM) is the most accurate measure of interest rates.
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
3-4
Chapter Preview
• So, in this chapter, we will develop a better understanding of interest rates. We examine the terminology and calculation of various rates, and we show the importance of these rates in our lives and the general economy. Topics include:
Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-15
Yield to Maturity: Bonds
4. One-Year Discount Bond (P = $900, F = $1000)
$1000 $900 = ⇒ (1 + i)
3-8
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
Present Value
• The concept of present value (or present discounted value) is based on the commonsense notion that a dollar of cash flow paid to you one year from now is less valuable to you than a dollar paid to you today. This notion is true because you could invest the dollar in a savings account that earns interest and have more than a dollar in one year. • The term present value (PV) can be extended to mean the PV of a single cash flow or the sum of a sequence or group of cash flows.
Four Types of Credit Instruments
1. Simple Loan • principal + interest, maturity • Commercial loan 2. Fixed Payment Loan • Same payment every month • Mortgages, installment loans 3. Coupon Bond • Coupon payment • Face value or par value • Issuer, maturity, coupon rate • Treasury bonds, corporate bonds 4. Discount Bond • Price below face value • Repaid face value • No interest payment
Fixed coupon payments of $C forever，perpetuity bond
C P= i
C i= P
3-14
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
Relationship Between Price and Yield to Maturity
3. Coupon Bond (Coupon rate = 10% = C/F)
$100 $100 $100 $100 $1000 P= + 2 + 3 + ... + 10 + (1+ i ) (1 + i) (1+ i ) (1+ i ) (1 + i )10 C C C C F P= + 2 + 3 + ... + n + (1+ i ) (1 + i) (1+ i ) (1+ i ) (1 + i )n
• Three interesting facts in Table 3-1
1. When bond is at par, yield equals coupon rate 2. Price and yield are negatively related 3. Yield greater than coupon rate when bond price is below par value
3-9
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
Present Value Concept: Simple Loan
Simple loan of $100 Year: 0 1 $100 $110
2 $121
3 $133
n 100×(1+i)n
$1000 − $900 i= = .111 = 11.1% $900
F−P i= P
Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-16
Global perspective
– Measuring Interest Rates – The Distinction Between Real and Nominal Interest Rates – The Distinction Between Interest Rates and Returns
Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-5
• Yield to maturity = interest rate that equates today's value with present value of all future payments 1. Simple Loan
$100 = $110 (1 + i ) ⇒
$110 − $100 $10 i= = = .10 = 10% $100 $100
Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-12
Yield to Maturity: Loans
2. Fixed Payment Loan (i = 12%)
$126 $126 $126 $126 $1000 = + 2 + 3 + ... + 25 (1+ i ) (1 + i) (1+ i ) (1+ i )
批注本地保存成功开通会员云端永久保存去开通
Part Two
Fundamentals of Financial Markets
Chapter 3
Understanding Interest Rates
Outlines
• Measuring Interest Rates – Present Value – Yield to Maturity • Other Measures of Interest Rates • The Distinction Between Real and Nominal Interest Rates • The Distinction Between Interest Rates and Returns – Maturity and the Volatility of Bond Returns: Interest-Rate Risk • The Practicing Financial Institution Manager: Calculating Duration to Measure Interest-Rate Risk – Calculating Duration – Duration and Interest-Rate Risk
periodically
Only at maturity dates
Present Value Concept: Simple Loan Terms
• Loan Principal: the amount of funds the lender provides to the borrower. • Maturity Date: the date the loan must be repaid; the Loan Term is from initiation to maturity date. • Interest Payment: the cash amount that the borrower must pay the lender for the use of the loan principal. • Simple Interest Rate: the interest payment divided by the loan principal; the percentage of principal that must be paid as interest to the lender. Convention is to express on an annual basis, irrespective of the loan term.
FP FP FP FP LV = + 2 + 3 + ... + n (1 + i ) (1 + i ) (1+ i ) (1+ i )
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
3-13
Yield to Maturity: Bonds
$1 PV of future $1 = (1+ i )n
Copyright © 2009 Pearson Prentice Hall. All rights reserved.
3-10
Present Value of Cash Flows: Example
Yield to Maturity: Loans