©2015, College for Financial Planning, all rights reserved.

Session 13Bond Calculations – TEY, CY, YTC, YTM, PV, and Conversion Value

CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMInvestment Planning

Session Details

Module 7

Chapter(s)

1

LOs 7-1 Explain factors that affect the price and yield of fixed income securities.

7-2 Calculate the price, compound return, yield-to-maturity, yield-to-call, and taxable equivalent yield, of fixed income securities.

7-7 Calculate the conversion value, investment value, investment premium, conversion premium, and downside risk of convertible securities.

13-2

Current Value

The current value of a bond• the present value of

the cash flows • discounted back to

the present • at the going rate of

interest on comparable debt

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Bond at Par Value

$1,000 7%

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Bond at Discount

$950

8%

13-5

Bond at Premium

$1,050

6%

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Calculations

Brad Feathers is in the 33% marginal income

tax bracket and is considering investing in

a municipal bond with a yield of 4.2%.

He is also considering Treasury bonds with the same maturity that have a yield of 5.5%. Which should he purchase?

Tax-free yieldTEY

1 Marginal tax bracket

6.27%.331

4.2TEY

Taxable-Equivalent Yield

13-7

TEY

Both Federal and State Income Tax and Taxpayer Itemizes If a municipal bond is free from both federal and state income taxation, and the taxpayer itemizes deductions, then the formula is:

FMTB)-SMTB)(1-(1

yieldfree-TaxTEY

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Double Tax-Exempt Calculation

Brad Feathers, who itemizes deductions, is in the 33% federal MTB, and the 10% state MTB and is considering a bond issued by his state with a yield of 4.2%. What is the TEY?

Answer: 6.97%

.33)-.10)(1-(14.2%

TEY

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Bond Calculations

For bond calculations, make the following assumptions unless the problem specifically

states otherwise: Face value of $1,000 Semiannual compounding (even zeros) Coupon interest needs to be converted into a semi-

annual payment, and entered as a payment Number of compounding periods: 2 per year End mode Always reserve the I/YR function (“i” on 12C) for

current interest rates (YTM) PV is a negative number, FV is a positive number,

coupon payments (PMT) are a positive number13-10

Calculations: Current Yield

Current Yield is simply:

Example: Bond A has a coupon rate of 7%, and is currently trading at 980, what is the current yield?

70/980 = .0714 = 7.14%

BondofPrice

PaymentInterestAnnual

13-11

Calculations: YTM and YTCJames has just purchased a bond for $950. The coupon rate is 7.5%, and the bond

matures in 20 years. It is callable at $1,020 in 8

years.

What is the YTM and YTC of James’ bond?

Set calculator for 2 P/YR YTM YTCPMT 37.50 37.50 PV (950) (950)FV 1000 1020

N 20, SHIFT, N (40) 8, SHIFT, N (16)

i = 8.01% i = 8.56%13-12

Yield-to-Call

13-13

Calculations: Present Value

Jenny Vegas owns a AAA-rated bond with a

face value of $1,000 and a coupon rate of 7%, and interest is paid semiannually. The bond matures in nine years. Similar bonds have a YTM of 12%.

What is the current price of the bond?Set calculator for 2 P/YR (2, SHIFT, P/YR)

FV = 1000PMT = 35I = 12N = 9 (SHIFT, n) PV = 729.31

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Calculations: Present Value

Beth Reno owns a AAA-rated, zero coupon municipal

bond with a face value of $1,000. The bond matures

in 23 years. Comparable bonds with the same maturity are yielding 9.5%.

What is the current price of the bond?

Set calculator for 2 P/YR (2, SHIFT, P/YR)

FV = 1000

i = 9.5

N = 23 (SHIFT, n)

PV = 118.28

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Fluctuations in Bond Prices

Prices of bonds

• with lower coupons fluctuate more (higher duration)

• with higher coupons fluctuate less (lower duration)

• with longer terms to maturity fluctuate more (higher duration)

• with shorter terms to maturity fluctuate less (lower duration)

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Yield “Seesaw”

CY YTM YTC

CY = current yieldYTM = yield-to-maturityYTC = yield-to-call

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Yield “Seesaw” Premium Bond

CY YTM YTC

CY = current yieldYTM = yield-to-maturityYTC = yield-to-call

13-18

Yield “Seesaw” Discount Bond

CY = current yieldYTM = yield-to-maturityYTC = yield-to-call

CY YTM YTC

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Convertible Bond

ParCV Ps

CP

Conversion Value

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Conversion Value Calculation

Example: Convertible bond is currently trading for $925, and has a conversion price of $40 per share.

The current price of the underlying stock is $35, what is the conversion value?

Conversion ratio:

1,000/$40 = 25 shares

25 shares x $35 = $875 conversion value

Bond Investment Value: Values the convertible bond as a straight bond based on current interest rates

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Convertible Bond Sample Calculations

Kathleen Sullivan purchased a convertible bond of GetGo Corporation a few years ago. The bond has an 8½% coupon rate and the bond matures in 6 years.

Comparable debt currently yields 9½%, and the bond is convertible at $29 per share. The current price of GetGo common stock is $32, and the current price of the convertible bond is $1,226.

1. Solve for the conversion value of the bond2. Solve for the investment value of the bond3. Solve for the downside risk of the bond

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Conversion Value Solution

Conversion formula

sPCP

ParCV

$1,103.45$32 34.4828

shares 34.4828$29

1000Cs

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Investment Value Calculation

Calculate value as a bond, based on current interest rates

Set for 2 P/YRN = 6, SHIFT N (12 periods)I = 9.5 PMT = 42.50FV = 1000 PV = $955.05

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Downside Risk

• The downside risk is the difference between the current market price of the convertible bond and the investment value of the bond.

• $1,226 current market price – $955.05 investment value = $270.95

• Note that you do not use the conversion value, even when it is higher than the investment value, which it is in this case ($1,103.45).

• Investment value will change (and so will downside risk) as interest rates change.

13-25

Convertible Bond Relationships

Market price

Conversion value line

Investment value of bond

Stock Price ($)

Bond Price ($)

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Question 1

Which of the following relationships are true for a bond selling at a premium or a discount?

I. When selling at a premium, yield-to-call is higher than yield-to-maturity.

II. When selling at a premium, current yield is higher than yield-to-call.

III. When selling at a discount, yield-to-call is higher than yield-to-maturity.

IV. When selling at a discount, current yield is higher than yield-to-call.a. I and II onlyb. I and IV onlyc. II and III onlyd. II and IV onlye. III and IV only

13-27

Question 2

Rex owns a corporate bond that currently sells for $1,090. The coupon rate is 9%, and the bond matures in 23 years. The bond is callable in 8 years at $1,020. What is the yield-to-call of this bond?a. 6.84%b. 7.66%c. 7.93%d. 8.13%

13-28

Question 3

Regina owns a zero coupon bond with face value of $1,000. It has a yield-to-maturity of 7.5%, and 13 years until maturity. What is the intrinsic value of this bond?a. $383.98b. $387.66c. $390.56d. $393.72

13-29

Question 4

Ken Kline is in the 33% marginal income tax bracket. He owns a corporate bond that pays $35 in interest semiannually. What yield on municipal bonds would be comparable to the after-tax yield Ken is currently receiving?a. 2.35%b. 4.69%c. 4.97%d. 5.22%

13-30

Question 5

What is the intrinsic value of a 19-year, 7% coupon bond selling in a market that has a required return of 8%?a. $567.84b. $877.42c. $898.12d. $903.16

13-31

Question 6

Dawn has just purchased a bond for $960. It matures in 20 years, has a coupon rate of 9.5%, and pays interest semiannually. What is the internal rate of return (yield-to-maturity) of the bond?a. 9.97%b. 10.15%c. 10.48%d. 10.67%

13-32

Question 7

James owns V-Corp bonds (A-rated) that mature in 9 years, pay semiannual interest, and have a coupon of 9%. Similar bonds (A-rated with 9 years to maturity) yield 8%. The V-Corp bonds are convertible into common stock at $18 per share, and the current market price of V-Corp is $17. What is the conversion value of the V-Corp bond?a. $944.44b. $977.62c. $1,000.00d. $1,063.30

13-33

Question 8

John owns a convertible bond that has a conversion price of $25 per share and a coupon of 6%. Interest is paid semiannually. The current market price of the stock is $26 per share. The investment value of the bond is $970, and the bond is currently trading at $1,150. What is the downside risk of the bond?a. $110b. $140c. $160d. $180

13-34

©2015, College for Financial Planning, all rights reserved.

Session 13End of Slides

CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMInvestment Planning