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CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning

CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning. Session 13 Bond Calculations – TEY, CY, YTC, YTM, PV, and Conversion Value. Session Details. Current Value. The current value of a bond the present value of the cash flows

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CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning

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  1. CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMInvestment Planning Session 13Bond Calculations – TEY, CY, YTC, YTM, PV, and Conversion Value

  2. Session Details

  3. 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

  4. Bond at Par Value $1,000 7%

  5. Bond at Discount 8% $950

  6. Bond at Premium $1,050 6%

  7. Calculations Taxable-Equivalent Yield 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?

  8. 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:

  9. 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%

  10. 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 number

  11. 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%

  12. Calculations: YTM and YTC James 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 YTC PMT 37.5037.50 PV (950)(950) FV 1000 1020 N 20, gold, N (40) 8, gold, N (16) i = 8.01% i = 8.56%

  13. Yield-to-Call

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

  15. 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 FV = 1000 i = 9.5 N = 23 (SHIFT, n) PV = 118.28

  16. 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)

  17. Yield “Seesaw” CY YTM YTC CY = current yield YTM = yield-to-maturity YTC = yield-to-call

  18. Yield “Seesaw” Premium Bond CY YTM YTC CY = current yield YTM = yield-to-maturity YTC = yield-to-call

  19. Yield “Seesaw” Discount Bond CY = current yield YTM = yield-to-maturity YTC = yield-to-call YTC YTM CY

  20. Convertible Bond Conversion Value

  21. 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

  22. 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. • Solve for the conversion value of the bond • Solve for the investment value of the bond • Solve for the downside risk of the bond

  23. Conversion Value Solution Conversion formula

  24. Investment Value Calculation Calculate value as a bond, based on current interest rates Set for 2 P/YR N = 6, SHIFT N (12 periods) I = 9.5 PMT = 42.50 FV = 1000 PV = $955.05

  25. 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.

  26. Convertible Bond Relationships Bond Price ($) Market price Conversion value line Investment value of bond Stock Price ($)

  27. Question 1 Which of the following relationships are true for a bond selling at a premium or a discount? • When selling at a premium, yield-to-call is higher than yield-to-maturity. • When selling at a premium, current yield is higher than yield-to-call. • When selling at a discount, yield-to-call is higher than yield-to-maturity. • When selling at a discount, current yield is higher than yield-to-call. • I and II only • I and IV only • II and III only • II and IV only • III and IV only

  28. 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? • 6.84% • 7.66% • 7.93% • 8.13%

  29. 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? • $383.98 • $387.66 • $390.56 • $393.72

  30. 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? • 2.35% • 4.69% • 4.97% • 5.22%

  31. 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%? • $567.84 • $877.42 • $898.12 • $903.16

  32. 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? • 9.97% • 10.15% • 10.48% • 10.67%

  33. 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? • $944.44 • $977.62 • $1,000.00 • $1,063.30

  34. 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? • $110 • $140 • $160 • $180

  35. CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMInvestment Planning Session 13End of Slides

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