Bonds Bought at Par: Understanding Price Determination
Explore an example scenario of buying a bond at par value, calculate the bond price to yield a specified annual effective rate, and learn about the implications of buying at par. Beware that buying at par does not equate to the price being equal to the face value. Dive into the intricacies of bond pricing with actionable insights.
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SOA Exam FM Module 3 Section 6 (Part 3) Bond Bought at Par Example
Example You buy a 4-year 1000 face value bond, redeemable at 1200, with 3% annual coupons. Determine the price of the bond to yield 2.5% annual effective.
Example You buy a 4-year 1000 face value bond, redeemable at 1200, with 3% annual coupons. Determine the price of the bond to yield 2.5% annual effective. 1200 30 30 30 30 3 4 1 2 ?
Example You buy a 4-year 1000 face value bond, redeemable at 1200, with 3% annual coupons. Determine the price of the bond to yield 2.5% annual effective. 1200 30 30 30 30 3 4 1 2 4 = 30? 4|0.025+ 1200?0.025 ?
Example You buy a 4-year 1000 face value bond, redeemable at 1200, with 3% annual coupons. Determine the price of the bond to yield 2.5% annual effective. 1200 30 30 30 30 3 4 1 2 4 = 30? 4|0.025+ 1200?0.025 ? = 1200.00
Example You buy a 4-year 1000 face value bond, redeemable at 1200, with 3% annual coupons. Determine the price of the bond to yield 2.5% annual effective. 1200 30 30 30 30 3 4 1 2 4 = 30? 4|0.025+ 1200?0.025 ? = 1200.00 Note: ? = ?
Example You buy a 4-year 1000 face value bond, redeemable at 1200, with 3% annual coupons. Determine the price of the bond to yield 2.5% annual effective. 1200 30 30 30 30 3 4 1 2 4 = 30? 4|0.025+ 1200?0.025 ? = 1200.00 Note: ? = ? When ? = ?,the bond is said to be ???? ? ?? ??? .
Example You buy a 4-year 1000 face value bond, redeemable at 1200, with 3% annual coupons. Determine the price of the bond to yield 2.5% annual effective. 1200 30 30 30 30 3 4 1 2 4 = 30? 4|0.025+ 1200?0.025 ? = 1200.00 Note: ? = ? When ? = ?,the bond is said to be ???? ? ?? ??? . BEWARE:Bought at Par means ? = ?.
Example You buy a 4-year 1000 face value bond, redeemable at 1200, with 3% annual coupons. Determine the price of the bond to yield 2.5% annual effective. 1200 30 30 30 30 3 4 1 2 4 = 30? 4|0.025+ 1200?0.025 ? = 1200.00 Note: ? = ? When ? = ?,the bond is said to be ???? ? ?? ??? . BEWARE:Bought at Par means ? = ?. (Confusing:It does NOT mean P = F)
Example You buy a 4-year 1000 face value bond, redeemable at 1200, with 3% annual coupons. Determine the price of the bond to yield 2.5% annual effective. 1200 30 30 30 30 3 4 1 2 4 = 30? 4|0.025+ 1200?0.025 ? = 1200.00 Note: ? = ? When ? = ?,the bond is said to be ???? ? ?? ??? . BEWARE:Bought at Par means ? = ?. Redeemable at Par means ? = ?. (Confusing:It does NOT mean P = F)
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? 0 1 30 2 30 3 30 ?4= ? = 1200 4 30
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? 0 1 30 2 30 3 30 ?4= ? = 1200 4 30 4 = 1200.00 = 30? 4|0.025+ 1200?0.025 ?
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 0 1 30 2 30 3 30 ?4= ? = 1200 4 30
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 0 1 30 30 2 30 3 30 ?4= ? = 1200 4 30 ?1= 0.025 1200 = 30
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 0 1 30 30 0 2 30 3 30 ?4= ? = 1200 4 30 ?1= 0.025 1200 = 30 ?1= 30 30 = 0
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 0 1 30 30 0 2 30 3 30 ?4= ? = 1200 4 30 ?1= 0.025 1200 = 30 ?1= 30 30 = 0 ?1= 1200 0 = 1200
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 0 1 30 30 0 2 30 30 0 3 30 ?4= ? = 1200 4 30
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 ?3= 1200 ?4= ? = 1200 0 1 30 30 0 2 30 30 0 3 30 30 0 4 30
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 ?3= 1200 ?4= ? = 1200 0 1 30 30 0 2 30 30 0 3 30 30 0 4 30 30 0
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 ?3= 1200 ?4= ? = 1200 0 1 30 30 0 2 30 30 0 3 30 30 0 4 30 30 0 General Remarks: 1. ?1,?2, ,?? is a geometric sequence with common ratio ? = 1 + ? 2. ??= ?1+ ?2+ + ??= ?11 + (1 + ?) + + (1 + ?)? 1= ?1 ? ?|= ? ? 3. ??= ? ?? ?|+ ?? ?? ? ? < ? one step TVM calculation
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 ?3= 1200 ?4= ? = 1200 0 1 30 30 0 2 30 30 0 3 30 30 0 4 30 30 0 Question:Determine a condition required in order for a bond to be bought at par.
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 ?3= 1200 ?4= ? = 1200 0 1 30 30 0 2 30 30 0 3 30 30 0 4 30 30 0 Question:Determine a condition required in order for a bond to be bought at par. At purchase,we know the values of ?,?,?,and ?.
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 ?3= 1200 ?4= ? = 1200 0 1 30 30 0 2 30 30 0 3 30 30 0 4 30 30 0 Question:Determine a condition required in order for a bond to be bought at par. At purchase,we know the values of ?,?,?,and ?. We need the payment coupon and the interest earned each installment to be equal.
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 ?3= 1200 ?4= ? = 1200 0 1 30 30 0 2 30 30 0 3 30 30 0 4 30 30 0 Question:Determine a condition required in order for a bond to be bought at par. At purchase,we know the values of ?,?,?,and ?. We need the payment coupon and the interest earned each installment to be equal. ? = ? ? and ?1= ? ?0
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 ?3= 1200 ?4= ? = 1200 0 1 30 30 0 2 30 30 0 3 30 30 0 4 30 30 0 Question:Determine a condition required in order for a bond to be bought at par. At purchase,we know the values of ?,?,?,and ?. We need the payment coupon and the interest earned each installment to be equal. ? = ? ? and ?1= ? ?0 ?0= ? = ? if bought at par
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 ?3= 1200 ?4= ? = 1200 0 1 30 30 0 2 30 30 0 3 30 30 0 4 30 30 0 Question:Determine a condition required in order for a bond to be bought at par. At purchase,we know the values of ?,?,?,and ?. We need the payment coupon and the interest earned each installment to be equal. ? = ? ? and ?1= ? ? ?0= ? = ? if bought at par
???????????? ????? ? = 0.025 Interest Earned ?? Principal Adjustment ?? Time ? Payment ? Book Value ?? ?0= ? = 1200 ?1= 1200 ?2= 1200 ?3= 1200 ?4= ? = 1200 0 1 30 30 0 2 30 30 0 3 30 30 0 4 30 30 0 Question:Determine a condition required in order for a bond to be bought at par. At purchase,we know the values of ?,?,?,and ?. We need the payment coupon and the interest earned each installment to be equal. ? = ? ? and ?1= ? ? ?0= ? = ? if bought at par Answer: ? ? = ? ? in order for a bond to be bought at par.
Another Bond Pricing Formula ? ? ? ? ?= Price
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ??
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ? ? ?|+ ? ??
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ?? ? ?|+ ? ??
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ?? ? ?|+ ? ? + ? ??
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ?? ? ?|+ ? ?(1 ??)
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? ? = ?? ? ?|+ ? ?(1 ??) ?
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ?? ? ?|+ ? ?? ? ?|
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ? + ?? ? ?| ?? ? ?|
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ? + (?? ??) ? ?|
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ? + (?? ??) ? ?| Sometimes referred to as the Premium/Discount Formula
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ? + (?? ??) ? ?| Sometimes referred to as the Premium/Discount Formula If ?? > ?? then the bond is bought at a premium of (?? ??) ? ?|
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ? + (?? ??) ? ?| Sometimes referred to as the Premium/Discount Formula If ?? > ?? then the bond is bought at a premium of (?? ??) ? ?| If ?? < ?? then the bond is bought at a discount of |(?? ??)| ? ?|
Another Bond Pricing Formula ? ? ? ? ?= Price Coupon Payment = ? = ?? ? = ? + (?? ??) ? ?| Sometimes referred to as the Premium/Discount Formula If ?? > ?? then the bond is bought at a premium of (?? ??) ? ?| If ?? < ?? then the bond is bought at a discount of |(?? ??)| ? ?| If ?? = ?? then the bond is bought at par
