Chapter 7 — Bond Pricing

FIN301 • Coupon bonds, zero-coupon bonds, YTM, current yield, price sensitivity, ratings, and homework.
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Learning Goals

  • Understand coupon, par value, maturity, price, and yield.
  • See why bond prices and yields move in opposite directions.
  • Compute bond price, current yield, and yield to maturity.
  • Use Excel-style formulas and interactive tools to check answers.

Chapter 7 Slides (PPT)

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Bond Basics

A bond is a loan you make to a company or government. In return, you usually receive periodic coupon payments and the par value at maturity.

TermMeaning
CouponPeriodic interest payment in dollars
Coupon rateAnnual coupon divided by par value
Par valueFace value repaid at maturity, often $1,000
Market priceWhat the bond sells for today
Current yieldAnnual coupon / bond price
Yield to maturity (YTM)Discount rate that makes PV of cash flows equal the bond price
MaturityTime until principal repayment

Intro Video

Open on YouTube

Adjustable Bond Cash-Flow Timeline

Change the bond inputs and redraw the timeline. The tool computes price directly from the YTM you enter.

Purchase price (outflow)
Coupons and final par (inflows)

Cash-Flow Breakdown

Price–Yield Curve

Annual coupon bond first. Semi-annual coupon bond is below in a collapsed section.

Annual Coupon Bond

Open JU Bond Calculator

This graph assumes 1 payment per year.

Semi-Annual Coupon Bond (click to open)

Semi-Annual Coupon Bond

Open JU Bond Calculator

This graph assumes 2 payments per year.

Excel Recipes

Key formulas

  • Annual coupon bond price: =ABS(PV(yield, maturity, coupon, 1000))
  • Semi-annual coupon bond price: =ABS(PV(yield/2, maturity*2, coupon/2, 1000))
  • Annual coupon YTM: =RATE(maturity, coupon, -price, 1000)
  • Semi-annual coupon YTM: =RATE(maturity*2, coupon/2, -price, 1000)*2
  • Current yield: =annual coupon / bond price

Examples

  • Annual coupon: If a bond sells for $1,200, solve YTM with RATE(n, coupon, -1200, 1000).
  • Semi-annual coupon: If a bond sells for $1,200, solve YTM with RATE(n*2, coupon/2, -1200, 1000)*2.
  • Zero-coupon price: =ABS(PV(y/2, years*2, 0, 1000))

Bond Calculators

Use these tools to compute bond price, YTM, and current yield. Each one also shows the Excel formula and the math setup.

Calculator A: Price from YTM

Price Result

Bond price
—
Annual coupon ($)
—
Current yield
—

Price is the present value of all future cash flows discounted at the YTM.

Excel Formula

—

Math Setup

—

—

Calculator B: YTM from Price

YTM Result

YTM (annual %)
—
Current yield
—

Excel Formula

—

Math Setup

—

—

Calculator C: Current Yield

Current Yield Result

Annual coupon ($)
—
Current yield
—

Excel Formula

—

Math Setup

—

—

Yield Curve (FYI)

Yield curves summarize market yields across maturities. Watch how the shape changes over time.

Yield Curve (FINRA / Morningstar) Yield Curve (GuruFocus) U.S. Treasury Rates

Chapter 7 Study Guide

1) Use FINRA to find corporate bond information

Search a company such as Walmart on FINRA fixed income data.

FINRA Fixed Income Bond Center
Example bond: Walmart (WMT5571329 / CUSIP 931142FE8)

Symbol: WMT5571329 | CUSIP: 931142FE8 | Type: CORP

Open Walmart bond on FINRA
2) Key terms to know
  • Coupon: periodic interest payment.
  • Coupon rate: coupon / par value.
  • Par value: amount repaid at maturity.
  • Market price: current trading price.
  • Yield: general return measure.
  • YTM: discount rate that matches PV to market price.
  • Current yield: annual coupon / price.
  • Maturity: time until principal repayment.
3) Pricing a bond (PV)

Annual coupon bond: Bond price = ABS(PV(yield, maturity, coupon, 1000))

Semi-annual coupon bond: Bond price = ABS(PV(yield/2, maturity*2, coupon/2, 1000))

Key idea: bond price and yield move inversely.

4) Calculating bond return (YTM)

Annual coupon: YTM = RATE(maturity, coupon, -price, 1000)

Semi-annual coupon: YTM = RATE(maturity*2, coupon/2, -price, 1000) * 2

5) Current yield

Current yield = annual coupon / bond price

6) Zero-coupon bond
  • 10-year zero sells for $400 → find YTM.
  • 10-year zero has YTM = 10% → find price.
7) Bond ratings and Z-score discussion
  1. Who are Moody’s, S&P, and Fitch?
  2. What is IBM’s rating?
  3. Is IBM’s rating the highest?
  4. Who earns the highest rating?
8) Bond cash flows (investor view)

Example: 5-year annual coupon bond, coupon rate = 5%, par = $1,000.

YearCash flow
1$50
2$50
3$50
4$50
5$1,050 (coupon + par)

Practice

Try each question first on your own. Then open the help box to see the Excel inputs and solution method.

1) Price a 10-year zero-coupon bond with YTM = 10%
Zero coupon • PV
Show Excel inputs and detailed solution
Given
Par = 1000, Years = 10, YTM = 10%
Assumption
Use semi-annual convention unless told otherwise
rate
10%/2 = 5% per half-year
nper
10*2 = 20 periods
pmt
0 because it is a zero-coupon bond
fv
1000
Excel
=ABS(PV(10%/2,10*2,0,1000))copy
Excel steps
1. In Excel, type the rate per period: 10%/2
2. Type the number of periods: 10*2
3. Payment is 0
4. Future value is 1000
5. Wrap with ABS() so the price shows as positive
Math idea
Price = 1000 / (1 + 10%/2)^(10*2)
2) Find current yield for a coupon bond selling below par
Current yield
Show Excel inputs and detailed solution
Example inputs
Coupon rate = 6%, Par = 1000, Price = 950
Annual coupon
6%*1000 = 60
Current yield
Annual coupon / Price
Excel
=(6%*1000)/950copy
Excel steps
1. Compute annual coupon using coupon rate × par
2. Divide that annual coupon by the market price
3. Format the result as a percentage
Math idea
Current yield = 60 / 950
Teaching note
Because the bond sells below par, current yield is usually higher than the coupon rate.
3) Solve YTM for a 5-year annual coupon bond selling at $950
Annual coupon • RATE
Show Excel inputs and detailed solution
Example inputs
Years = 5, Coupon rate = 2%, Par = 1000, Price = 950
Function
RATE
nper
5
pmt
2%*1000 = 20
pv
-950
fv
1000
type
0
Excel
=RATE(5,2%*1000,-950,1000)copy
Excel steps
1. Since it is annual coupon, use nper = 5
2. Coupon payment each year is 2% × 1000 = 20
3. Use -950 for price because Excel needs opposite cash-flow signs
4. Use 1000 for face value at maturity
Math idea
950 = 20/(1+r)^1 + 20/(1+r)^2 + 20/(1+r)^3 + 20/(1+r)^4 + 1020/(1+r)^5
4) Draw a price–yield graph
Price–yield relationship
Show Excel inputs and detailed solution
Suggested bond
Par = 1000, Coupon rate = 5%, Years = 10, Semi-annual
Goal
Create prices for many YTM values, then graph them
YTM column
Enter yields such as 1%, 2%, 3%, ... 12%
Price formula
=ABS(PV(A2/2,10*2,5%*1000/2,1000))copy
Excel steps
1. In column A, list YTM values from low to high
2. In column B, compute bond price using the PV formula
3. Fill the formula down for all YTM values
4. Highlight both columns
5. Insert a scatter chart or line chart

Chapter 7 Homework (due with the second mid-term)

Show steps. Open each problem to see the Excel function and the input setup. Answers are intentionally hidden so students solve them on their own.

1) IBM 5-year, 2% annual coupon, price $950 → YTM?
IBM 5-year, 2% annual coupon bond is selling for $950. How much is this IBM bond’s YTM?
Annual coupon • RATE
Show Excel setup
Function
RATE
rate
(solve)
nper
5
pmt
2%*1000 = 20
pv
-950
fv
1000
type
0
Excel
=RATE(5,2%*1000,-950,1000)copy
2) IBM 10-year, 4% semi-annual coupon, price $950 → YTM?
IBM 10-year, 4% semi-annual coupon bond is selling for $950. How much is this IBM bond’s YTM?
Semi-annual coupon • RATE
Show Excel setup
Function
RATE
rate
(solve per half-year)
nper
10*2 = 20
pmt
4%*1000/2 = 20
pv
-950
fv
1000
type
0
Excel
=RATE(10*2,4%*1000/2,-950,1000)*2copy
3) IBM 10-year, 5% annual coupon, YTM 8% → price?
IBM 10-year, 5% annual coupon bond offers 8% return. How much is the price of this bond?
Annual coupon • PV
Show Excel setup
Function
PV
rate
8%
nper
10
pmt
5%*1000 = 50
pv
(solve)
fv
1000
type
0
Excel
=ABS(PV(8%,10,5%*1000,1000))copy
4) IBM 5-year, 5% semi-annual coupon, YTM 8% → price?
IBM 5-year, 5% semi-annual coupon bond offers 8% return. How much is the price of this bond?
Semi-annual coupon • PV
Show Excel setup
Function
PV
rate
8%/2
nper
5*2 = 10
pmt
5%*1000/2 = 25
pv
(solve)
fv
1000
type
0
Excel
=ABS(PV(8%/2,5*2,5%*1000/2,1000))copy
5) IBM 20-year zero coupon, YTM 8% → price?
IBM 20-year zero coupon bond offers 8% return. How much is the price of this bond?
Zero coupon • PV
Show Excel setup
Function
PV
rate
8%/2
nper
20*2 = 40
pmt
0
pv
(solve)
fv
1000
type
0
Excel
=ABS(PV(8%/2,20*2,0,1000))copy
6) Collingwood Homes: 8.5% coupon, 18.5 years, price 964.20, semiannual → YTM?
Collingwood Homes has a bond issue outstanding that pays an 8.5% coupon and matures in 18.5 years. The bonds have par value $1,000 and market price $964.20. Interest is paid semiannually. What is the YTM?
Semi-annual coupon • RATE
Show Excel setup
Function
RATE
rate
(solve per half-year)
nper
18.5*2 = 37
pmt
8.5%*1000/2 = 42.5
pv
-964.20
fv
1000
type
0
Excel
=RATE(18.5*2,8.5%*1000/2,-964.20,1000)*2copy
7) Grand Adventure Properties: 9.5% annual coupon, YTM 11.2%, 11 years → price?
Grand Adventure Properties offers a 9.5% annual coupon bond. The YTM is 11.2% and the maturity date is 11 years from today. Face value is $1,000. What is the market price?
Annual coupon • PV
Show Excel setup
Function
PV
rate
11.2%
nper
11
pmt
9.5%*1000 = 95
pv
(solve)
fv
1000
type
0
Excel
=ABS(PV(11.2%,11,9.5%*1000,1000))copy
8) D&L Movers zero: price 319.24, FV 1,000, YTM 9.17% → years to maturity?
The zero coupon bonds of D&L Movers have market price $319.24, face value $1,000, and YTM 9.17%. How many years until these bonds mature?
Zero coupon • NPER
Show Excel setup
Function
NPER
rate
9.17%/2
nper
(solve half-year periods)
pmt
0
pv
-319.24
fv
1000
type
0
Excel
=NPER(9.17%/2,0,-319.24,1000)/2copy
9) Zero coupon: FV 1,000, price 212.56, maturity 25 years → YTM?
A zero coupon bond with face value $1,000 is issued with initial price $212.56. The bond matures in 25 years. What is the yield to maturity?
Zero coupon • RATE
Show Excel setup
Function
RATE
rate
(solve per half-year)
nper
25*2 = 50
pmt
0
pv
-212.56
fv
1000
type
0
Excel
=RATE(25*2,0,-212.56,1000)*2copy
10) Stainless Tubs: 6% coupon, semiannual, 11 years, price 989 → YTM?
The bonds issued by Stainless Tubs bear a 6% coupon, payable semiannually. The bonds mature in 11 years and have face value $1,000. Currently, the bonds sell for $989. What is the yield to maturity?
Semi-annual coupon • RATE
Show Excel setup
Function
RATE
rate
(solve per half-year)
nper
11*2 = 22
pmt
6%*1000/2 = 30
pv
-989
fv
1000
type
0
Excel
=RATE(11*2,6%*1000/2,-989,1000)*2copy

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