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

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%

Explanation / Answer

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

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