# CFA Official Mock AM #49 Scott

All,

Question 49 - Fixed Income - Scott

Can someone explain me how they reached the FV of 141.87 on the solutions for this question? They will invest the coupons with the Forward rate which will produce an higher return comparing with the YTM 6.72% but I don’t know how they reach to that value.

Much appreciated!

Bond Price and YTM can be found (if not given) using the Spot rates. How:

Use the Bootstrapping equation (i.e., relationship between Par rates and Spot Rates) and substitute the Par Rates with Cash flows of the Bond (i.e., coupons) and substitute the “1” unit notional principal with the Face Value of the Bond. Then discount each Cash Flow (coupons) and the Principal (Face Value) with its respective Spot rates. The value thus found is the PV of the bond. Now key in all the values that you have into the TVM func on the calculator and solve for YTM.

(7*1.0501*1.0703*1.0906*1.111 + 7*1.0703*1.0906*1.111 + 7*1.0906*1.111 + 7*1.111)+107 = 141.87

Then you annualize: 141.87/101.15 ^ 1/5 -1 = 7% which is greater than 6.72%

@Croky: That calculation I placed above is what I learnt directly from the CFAI official texts. You can read more there. Schweser doesn’t expound on it like the official curriculum book does.

where in the text is the 6.72%

“Bird is analyzing a newly issued US Treasury bond with a five-year maturity and a 7.00% coupon. For long-term investors that buy this US Treasury bond and hold it to maturity, Bird is assessing whether the realized return will match its current 7.00% yield to maturity…”

i am so confused…

@Claudz6: 3rd paragraph, 2nd line of vignette - “The bond was issued at a price of 101.15. The bond’s YTM at issuance was 6.72%. Bird is evaluating this bond for long term investors…”

Oh looks like it is mentioned in the question… so yeah, that…

Olympria, that can be done as well, but takes up time because the 6.72% is already directly given in the vignette.

yeah if its given, then that makes it much easier…

hey all

thanks kyrsbev, but has the vignette been updated - here is my direct quote:

Bird is analyzing a newly issued US Treasury bond with a five-year maturity and a 7.00% coupon. For long-term investors that buy this US Treasury bond and hold it to maturity, Bird is assessing whether the realized return will match its current 7.00% yield to maturity. Her analysis is based on an expectation that the forward path of interest rates will follow the current spot rate curve. Current spot rates and extrapolated one-year forward rates are provided in Exhibit 1.

i dont see that 6% anywhere Thanks for the explanation kyrsbev and olympria!