©2015, college for financial planning, all rights reserved. session 13 bond calculations – tey,...
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©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
13-3
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
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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
13-8
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
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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
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
13-14
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” Premium Bond
CY YTM YTC
CY = current yieldYTM = yield-to-maturityYTC = yield-to-call
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Yield “Seesaw” Discount Bond
CY = current yieldYTM = yield-to-maturityYTC = yield-to-call
CY YTM YTC
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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
13-21
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
13-23
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 ($)
13-26
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
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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