V: Debt Markets 12: Prices and Yields. Chapter 12: Prices and Yields Time Value of Money © Oltheten & Waspi 2012

V: Debt Markets

12: Prices and Yields

Chapter 12: Prices and Yields © Oltheten & Waspi 2012

Time Value of Money


$100 £100¥100

M 300

Time Value of Money


$100 £100¥100100 1.61

Time Value of Money


Time Value of Money

$1002016$1002017$1002015

3% 4%


Time Line

$100 $200 -$100 $300 $100

3% 4% 5% 4% 5% 3%

Cash flows Positive and negative at or between compounding lines

Compounding lines Interest rates between compounding lines


Time Line

$100 $200 -$100 $300 $100

3% 4% 5% 4% 5% 3%

Chapter 12: Prices and Yields

Bonds

© Oltheten & Waspi 2012


Bonds

DocumentaryEvidence of Debt

Specifies Principal Coupon Maturity


Principal: $1,000,000 Coupon: 6% Maturity:

Discovery Café Bond

February 17, 2019


Contract specifies payments over time

$30,000

Discovery Café BondS

tart at the M

aturity D

ate

$30,000$1,000,000

Go back six months at a time2/17/15

$30,000$30,000$30,000 $30,000 $30,000 $30,000

8/17/15 8/17/16 8/17/17 8/17/182/17/16 2/17/17 2/17/18 2/17/19


Yield versus Coupon

$30,000$1,000,000

$30,000$30,000

$30,000 $30,000

$30,000$30,000

$30,000

6% Coupon

$40,000$1,000,000

$40,000$40,000

$40,000 $40,000

$40,000$40,000

$40,0008% Coupon

-$1,000,000 (PV @ 8%)Market Yield:

Yield on alternative investments


Yield versus Coupon

$30,000$1,000,000

$30,000$30,000

$30,000 $30,000

$30,000$30,000

$30,000

6% Coupon

$20,000$1,000,000

$20,000$20,000

$20,000 $20,000

$20,000$20,000

$20,0004% Coupon

-$1,000,000 (PV @ 4%)

Market Yield:Yield on alternative investments


Price Yield Curve

40

60

80

100

120

140

0% 3% 6% 9% 12% 15% 18% 21%

n

n

tt 2

2

1

t

2Yd

1

P

2Yd

1

CPrice

Prices expressed as % of face value;100. not $100.


Calculator Techniques

SDT = CPN = 6 (%) RDT = RV = 100 (%)

360 (Days in a Year) 2/Y (2 coupons per year)

YLD = 7 (%) PRI = [CPT] (%) AI = 0.000 (%)

Coupon Rate(Annual)

2.17 15

2.17 19

Chapter 12: Prices and Yields

Yields

© Oltheten & Waspi 2012


Nominal Yield

Coupon Rate

Discovery Café$1,000,000. @ 6%

.Discovery Café Inc, incorporated in the State of Illinois (herein called the Company) for value received hereby promises to pay to the registered owner hereof on February 20, 2013 the sum of one million dollars and to pay interest semi-annually on August and February 20 of each year the sum of one half the annual interest thereon calculated at a semi-annual rate of half the stated annual interest of 6%.

due February 17, 2019


Income Yield

Current or Income Yield

Price

CouponYield Income


Promised Yield to Maturity

n

n

tt 2

2

1

t

2Yd

1

P

2Yd

1

CPrice


Promised Yield to Maturity

22.630,965$

207

1

0000001$

207

1

00030$8

8

1

.

,,

.

,

tt

YTM=7%

Yield Income=6.214%Capital Gain=0.876%


YTM = 7.00%

$30,000$1,000,000

$30,000$30,000

$30,000 $30,000

$30,000$30,000

$30,000

6% Coupon

Priced to yield 7%

Matures @ 100

SDT =YLD =PRI =

RDT =RV =

CPN = 6.3602/Y


$30,000$1,000,000

6% Coupon

$30,000 $30,000

$30,000$30,000

$30,000

YTM = 5.00% (Buyer)

Priced to yield 5%

Matures @ 100

SDT =YLD =

RDT =RV =

CPN = 6.3602/Y


Realized Yield = 12.432% (Seller)

$30,000

6% Coupon

Buy @ 96.563022YTM=7%

Sell @ 102.754063YTM=5%

SDT =PRI = 96.563022

RDT =RV = 102.754063

CPN = 6.3602/Y

2.17 16

2.17 15


Realized Yield

hp

hp

tt 2

2

1

t

2Yd

1

Price Selling

2Yd

1

CPrice

22.630,965$

2124317

1

63.540,027,1$

2124317

1

00030$2

2

1

..

,

tt

12.4317%


Effective Annual Rate

Including compounding

2

2

0.121 :annuallySemi

12

12

0.121 :monthly

365

365

0.121 :daily

12. :lycontinuous


Bond Equivalent Yield

Twice the semi-annual rate

12% .1211.12362

annually 12.360%


Yields

12 – 8:

V: Debt Markets I

Documents

V: Debt Markets 12: Prices and Yields. Chapter 12: Prices and Yields Time Value of Money © Oltheten & Waspi 2012