AAA AA A and BBB are deemed investment grade Ratings below BBB are more

# Aaa aa a and bbb are deemed investment grade ratings

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AAA, AA, A, and BBB are deemed “investment grade” Ratings below BBB are more “speculative” FIN 300 - Bonds Pt. 1 9 Bond Math Now to the mathematics of bonds Just re-use the previous time-value of money formulas: PV of the ordinary annuity & lump- sum For exams There will be some qualitative, conceptual questions – but, they will be focused less on definitions/vocabulary and more on the intuition of what causes the change in prices and rates of return, or yields FIN 300 - Bonds Pt. 1 10 Bond Math In this class, we will keep it pretty simple and focus on 2 basic types of bonds Coupon-paying (or, “coupon”) bonds Zero-coupon bonds In our calculations, we will not be so concerned as to whether the bond is a treasury, corporate, muni, etc. Our basic bond math applies across many segments of the bond market and covers the majority of bonds Of course, there are many bonds that involve quite complicated rules & math – we’ll leave that alone FIN 300 - Bonds Pt. 1 11 Coupon (Paying) Bond A coupon bond pays both: A series of repeated, identical coupon payments (think of this as a series of interest payments) Plus a large lump-sum payment made at the end of the bond’s life – this is known as the face-value (or par value) of the bond You might think of this as a “balloon” payment due at maturity, or the end of the life of the bond FIN 300 - Bonds Pt. 1 12 Coupon Rate vs. YTM Coupon Rate Stated in the bond contract Determines the size of the coupon payment relative to the size of the par (or, face) value It does not change – nor, is it determined by the market Yield - aka. Yield-to-Maturity (YTM) This is determined by the market and may fluctuate from moment-to-moment This is, in effect, the discount rate used by investors in the market – to determine a fair market value (or, price) FIN 300 - Bonds Pt. 1 13 Price a Coupon Bond We will determine the price given: Maturity – length of time remaining on the bond’s life Par (or, Face) value – paid at maturity Coupon Rate – is the yearly sum of the coupon payments stated as a percentage of par value Yield-to-Maturity (YTM) – market discount rate that constantly changes and effects market price of the bond Frequency of coupon payment Generally coupons are paid semi-annually or annually There are some exceptions, though We will focus on semi-annual coupons in this class You will have only semi-annual on exams! FIN 300 - Bonds Pt. 1 14 Coupon Bond Diagram (Semi-Annual) FIN 300 - Bonds Pt. 1 15 PV = Bond Price (at T=0, or today) 0.5 yr. 1.0 yr. 1.5yr. 6mths. before maturity C C + Face Value maturity C C C We will calculate an (ordinary annuity) PV of just the coupons Separately we will calculate the PV of the Face Value as a lump-sum Price = sum of these 2 PV’s Semi-Annual Coupon Price From previous slide C = coupon pmt. = (coupon rate x face)/2 Face Value = FV = face value is given (not necessarily the same as bond price) Price (of bond) is the PV of the cash flows PV of the coupon ordinary annuity + PV of the face- value lump-sum Also, you would be given the YTM & Maturity (in years) Treat YTM as an APR with semi-annual compounding Discount rate/coupon period = YTM/2 N = maturity in years x 2 FIN 300 - Bonds Pt. 1 16 Divide by 2, since “semi” annual - if annual, don’t div. by 2 Mult. by 2, since “semi” annual - if annual, don’t mult. by 2  #### You've reached the end of your free preview.

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