Question

Lett's commercial paper is presently selling at a discount. It sells for 98.19 of par and matures in 100 days. (Use 365 days o year. Do not round intermediate calculations. Round the final answers to 2 decimal places.) a. Calculate its yield as quoted in the market Yield 6.73 % b. Calculate its effective annual yield Effective annual yield %

Answer 1

Solution:

a. Calculation of quoted yield of a commercial paper in the market :

The formula for calculating the quoted yield of a commercial paper in the market is

= [ (Par value – Quoted price ) / Quoted Price ] * ( 365 / Days to maturity )

Let us assume the Par value of the commercial paper = $ 100

As per the Information given in the question we have

Quoted value = 98.19 % of par value

= 98.19 % * $ 100

= $ 98.19

The No. of days to maturity = 100

Applying the above information in the formula we have

= [ ( 100 – 98.19 ) / 98.19 ] * ( 365 / 100 )

= [ 1.81 / 98.19 ] * ( 365 / 100 )

= 0.018434 * 3.65

= 0.067283

= 6.7283 %

= 6.73 % ( when rounded off to two decimal places )

Thus the quoted yield of the commercial paper in the market is = 6.73 %

b.Calculation of Effective annual yield of a commercial paper :

The formula for calculating the Effective annual yield of a commercial paper is

= [ [ 1 + [ (Par value – Quoted price ) / Quoted Price ] * ^{( 365 / Days to maturity )} ] – 1

Let us assume the Par value = $ 100

As per the Information given in the question we have

Quoted value = 98.19 % of par value

= 98.19 % * $ 100

= $ 98.19

The No. of days to maturity = 100

Applying the above information in the formula we have

= [ [ 1 + [ ( 100 – 98.19 ) / 98.19 ] ^{( 365 / 100 )} ] – 1

= [ [ 1 + [ 1.81 / 98.19 ] ^{( 3.65 )} ] – 1

= [ [ 1 + 0.018434 ] ^{( 3.65 )} ] – 1

= [ [ 1.018434 ] ^{( 3.65 )} ] – 1

= 1.068943 – 1

= 0.068943

= 6.8943 %

= 6.89 % ( when rounded off to two decimal places )

Thus the Effective annual yield of the commercial paper is = 6.89 %

Note : The value of ( 1.018434 ) ^3.65   has been calculated using the excel function =POWER(Number,Power). Thus =POWER(1.018434,3.65) = 1.068943