Question

1. Bond A sells at a premium, so the YTM must be less than the coupon rate. Assume the required rate of return remains constant when we're trying to determine the likelihood of a call being made. If the YTM stays less than the 9% coupon rate, then 5 years from now when the call protection ends, the bond issuer will call the bond, pay the call premium, and refinance with new bonds at lower market rates. Thus, the market yield today is a YTC and not the YTM: PMT = $45, N = 10, FV = $1,100, PV = $1,170 →i = 3.332%; YTC = 2 x 3.332 = 6.66% The term used here is "yield to call" because the yield return is being calculated using a maturity horizon stopping at the bond's first call date, and not all the way out to its maturity date. In the marketplace, when callable bonds are priced at a premium to par value, it is market practice to report the YTC. For Bond B, it sells at a discount to par, so by the same reasoning as above, it's not expected to be called; its market yield is the normal YTM: PMT = $25, N = 24, FV = $1,000, PV = $746 => i = 4.200%; YTM = 2 x 4.200 = 8.40%

Answer 1

YTM=Yield to maturity is the total return anticipated on a bond if the bond is held until it matures.

To calculate YTM there is two formula one is trial and error and another is short cut here we use short cut.

For Bond A has has protection of 5 year so we calculate YTC (Yield to call) means N (No. of year)=5

Face Vaue= 1000+100(Premium)= 1100

Market Price = 117% of FV (1000 Because 100 is premium which is paid for getting protection) so MP= 1170 now here market price>face value it means YTM<Coupon rate because there is inverse relationship between YTM and Market value.

Coupon Rate = 9% P.a.

solution- Interest Payment is 9% of 1000 is 90

YTC = MP = (I*PVIFA_5year&Rate) + (fv*PVIF_5year&Rate)Note. PVIFA = Present value interest factor annuity for multiple payments.

   PVIF = Present value Interest Factor for single payment

Formula= (I +( FV-MP)/N)/(FV+MP)/2

(90+(1100-1170)/5)/(1100+1170)/2

(76/1135)*100 = 6.69%.

For B bond- Coupon rate= 5% P.a.

MP= 746 (discount)

FV = 1000 because it has no premium for the protection there here we calculate the YTM rather than YTC

N= 10 year so, the interest is 50

Formula= (I +( FV-MP)/N)/(FV+MP)/2

(50+(1000-746)/10)/(1000+746)/2

(75.4/873)*100 = 8.63% YTM.

Note: Here we can use the excel for formula to calculate the Yield called RATE.