Download Bond Pricing on a BAII Plus

Bond Pricing on a BAII Plus
Initial date
Current date
B0 = ?
Coupon payment dates
C …… C ….. C ….. C ….. C
Maturity date
M+C
Bond specifications (indenture)
semi-annual coupon payments
time to next coupon = 6-months  Current date is a coupon payment date
c = coupon rate = 4.5%
M = face value = $5,000
time-to-maturity = 7.5 years
semi-annual compounding
required return = 6.0%
Set P/Y = 2
C = 0.5* c * M = $112.50
B0 =
B0 =
N = number of payment dates = 15
I/Y = required return
PMT = C = 112.50
FV = M = 5,000
CPT  PV = B0
Required return (r)
6.5%
6.0%
5.5%
4.5%
Bond value (B0)
$4,413.76
$4,552.33
$4,696.08
$5,000.00
What risks need to be considered to determine the required rate of return?
Bond pricing relationship is convex.
1
When the next coupon is not one full period from current date.
Initial date
…C …C - (1-v) -
0-vB0 = ?
-Coupon payment dates
C …… C ….. C ….. C
Maturity date
M+C
semi-annual coupon payments
time to next coupon = 2-months  v = 2/6 = 1/3
c = coupon rate = 4.5%
M = face value = $5,000
time-to-maturity = 7.17 years
semi-annual compounding
required return = 6.0%
Finding B0 when v  1.0 requires three steps on a BAII Plus



Find present value on next coupon payment date of remaining cash flows.
Add next coupon to this value.
Discount this sum to the current date.
B0 =
B0 = present value of remaining cashflows
P = clean (flat) price
AI = accrued interest
B0 = P + AI
Required return (r)
6.5%
6.0%
5.5%
4.5%
Bond value (B0)
$4,508.88
$4,642.92
$4,781.79
$5,074.72
AI
2/3 * $112.5 = $75
$75
$75
$75
2
Clean price (P)
$4,433.88
$4,567.92
$4,706.79
$4,999.72
3