Question

Explain and summarise each calculatin and result which already calculated below.

1) Coversion to bond from commercial paper

•idy=(Pf-Po)/Pf × 360/h

•4%?0.04= ($1M-Po)/$1M=360/80 days

•0.04 =($1M-Po)/$1M ×4.5

•0.00889 = ($1M-Po)/$1M

•8889=$1M-Po

•Po = $1M-8889

•   =$991,111

•ibey=(Pf-Po)/Po × 365/h

•=($1M-$991,111)/$991,111 × 365/80

•=8,889/$991,111 ×365/80

•=3,244,485/79,288,8880

•=0.0040919794 = 4.0920%

•The Commercial paper equivalent yield to bond is 4.0920%

2) Conversion to CD

•CD has 5 % single payment yield

•ibey=ispy(365/360)

•ibey=0.05 × (365/360)

•=0.050694

•=5.07%

•The bond equivalent yield for the CD is 5.07%

3) EAR

•EAR=[1+ibey/(365/h)]365/h -1

•=[1+0.04092/(365/80)]365/80-1

•=1.04157874784-1

•=0.04157874784

•=4.158%

Answer 1

1) Coversion to bond from commercial paper -

The below portion is calculating the current price of the bond equivalent to a 80-day commercial paper with face value $1 million and commercial paper follows a 360 day year convention.

Commerical Papers are stated in face value terms with a fixed maturity. There is no explicit coupon interest payment and the difference between the face value at maturity (Pf =1 mn) and the current price (Po) is the implied interest payment. The amount of the discount (Pf - P0) is stated as a percentage of the face value (Pf), which is annualized over a 360-day year for 80 days.

•idy=(Pf-Po)/Pf × 360/h

•4%?0.04= ($1M-Po)/$1M=360/80 days

•0.04 =($1M-Po)/$1M ×4.5

•0.00889 = ($1M-Po)/$1M

•8889=$1M-Po

•Po = $1M-8889

•   =$991,111

This below portion does the same thing, but annualizes over a 365 day period as bonds follow a 365 day convention. This is to calculate the bond equivalent yield of the aforementioned commercial paper.

•ibey=(Pf-Po)/Po × 365/h

•=($1M-$991,111)/$991,111 × 365/80

•=8,889/$991,111 ×365/80

•=3,244,485/79,288,8880

•=0.0040919794 = 4.0920%

•The Commercial paper equivalent yield to bond is 4.0920%

2. Conversion to CD

Certificate of Deposit are also quoted on a 360-day convention and has a single payment at the end of the term. Thus, to convert it into a bond equivalent which are quoted on 365 day convention, it simply multiplies by (365/360)

•CD has 5 % single payment yield

•ibey=ispy(365/360)

•ibey=0.05 × (365/360)

•=0.050694

•=5.07%

•The bond equivalent yield for the CD is 5.07%

3) EAR

This is the effective annual rate taking into account the compounding effect on the interest received during 80 days using the bond equivalent yield using a 365-day bond convention.

•EAR=[1+ibey/(365/h)]365/h -1

•=[1+0.04092/(365/80)]365/80-1

•=1.04157874784-1

•=0.04157874784

•=4.158%

Do reach out in case of any clarifications. Thanks