Question

Consider the following bond issued by Walmart:

coupon rate: 6.541% face value: $1,000

maturity date: July 15, 2040 semi-annual coupons

settlement date: March 8, 2020 yield

(YTM): 5.654%

most recent coupon payment date: January 15, 2020

What is the value of the bond? (Equivalently, we are calculating the “dirty price”.) Express your answer as the dollar and cents price for a bond with $1,000 face value.

Answer 1

Solution:

Given Data in the example is

Face Value:   1000
Coupon rate:   6.541%
Maturity Date:   15 July 2040
Settlement Date:   08 March 2020
Yield:   5.654%
Most Recent Coupon Date:   15 January 2020

We will be using 30/360 days convention to solve this example. I will share some excel formula i have used. You may use business calculators to solve this as well.

Semi Annual Coupon Payment: 32.705 [face value * Coupon rate /2]

Next Coupon Date:   15 July 2020 [ 6 months from last coupon]

Maturity (years from last coupon):   20.50 years [=DAYS360(15 January 2020,15 July 2040)/360

Therefore, Price of the bond at the last coupon date = $1106.86 [=-PV(5.654%/2,20.50*2,32.705,1000)]

Days from Last Coupon   53 [=DAYS360(15 January 2020,08 March 2020) ] MOst recent coupon to settlement
Days to Next Coupon   127 ----settlement to next coupon
Days in coupon period   180

Dirty Price = Clean Price + Accrued Interest

We know the price of the bond on last coupon date, it is $1106.86, 53 days have passed till the settlement date.

Price on the settlement date ..Dirty Price = $1106.86 *( 1+ yield%/2)^(53/180) =  1,115.98

Accrued Interest = Coupon * 127/180 =  23.08

Clean price of the bond =  1,115.98 - 23.08 = $1092.90 quoted as 109 2/8.

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