# Fixed income concept

Doubt regarding Fixed income concept.

PV or price of a discount bond with in periodicity coupons from annual to semi annual to quarterly.

PV or price of a premium bond with in periodicity of coupons from annual to semi annual to quarterly.

Kindly guide me the logic with which the above concept.

This has been bugging me for a few days, so I tried out an example on my BAII:

\$1,000 face, 5 years, 4% coupon with discount rate =8% EAR

Case 1 annual coupon

P/Y=C/Y=1, N=5, I=8, PMT=40, FV= 1000 CPT PV 840.2915

Case 2 quarterly coupon of \$10, everything else the same

P/Y=4, C/Y=1 (fixed!),
N=20, I=8, PMT=10, FV=1000 CPT PV 845.006

The \$40 annual coupon will be discounted by a full year’s interest, whereas if I spread it out as \$10/quarter, then the PV should increase, regardless of whether it’s a discount or premium bond.

If I have misinterpreted your question, please let me know!

i think the I for quarterly bond would be 2%.

So the PV for quarterly bond will be 836.457.

If you set I=2, you are implicitly using an EAR of 8.243%. In both my calcs, the only thing I am changing is the timing of the coupon payments.

actually i was not able to convey my doubt clearly.

For discount bonds :
Annual coupon bonds - ytm 8% and pv 840.2915
Semi ann coup bonds - ytm 8.160% and pv 837.782
quarterly coup bonds - ytm 8.243 and pv 836.457

hence i conculde that for achieving a higher ytm in bonds with more coupon frequency price or pv is less…

But if we apply the same thing in premium bonds even if the ytm increases from annual to semi annual to quarterly the pv keeps on increasing rather than decreasing…
why such anomaly in premium bonds.

Your YTMs for the non-annual cases are not correct: they should be 7.846 and 7.771 for semi-annual and quarterly, respectively. They will then match the EAR of 8%. You will then see that as you increase the coupon frequency, the PV will rise for both premium and discount bonds.