Lecture 10-Bonds Flashcards
What are bonds
2 features
Bonds are debt instruemnts whereby the issues (borrower) agreez to pay the bondholer at the maturity sate
A dingle amount at a specified future date (a lump sum of money paid)
+
Plus a series of “coupon” or interest payments (an annuity)
What is the par value (also known as face value and principal)
, maturity date, and
market (also known as effeective or discount or yield rate)
Par value: the amount payable at the maturity of the bond
*Equal to Future value in out lump sum calculations. FV
Maturity date: The date at which the par value will be paid
Used to calculate n
Copoun rate: The interest rate stated on the bond contract
* Used to calculate payments in out annunity calculations
Market = Effective = Discount = Yield Rate:
The interest rate the market charges (the rate investors demand for loaning money)
*Determines i in our calculations
Remeber formula for bonds
FV=PC+(1+i)^n
How to value bonds
and what interest do we use?
Bonds are determined by the market not by the company , and they are going to determine that by the time vlaue of oney
PV of principla + PV of interest =issue price of bonds
Present value of the face value (a single payment)
+ present value of the interest payments (an annuity) = issue price of the bond
Also the interest rate used to compute the present value is the market itnerest rate,
while the interest rate used to compute the payments is the coupon rate.
Periodic cash itnerest payments =
Periodic cash itnerest payments = copun rate * face value
3 bonds issuance scenarios:
Par, premium and discount
Par- if copun rate = market rate, bond Price will be equalt of ace value
(this means marke interest = bond itnerest)
Premimum = if cooun ate> market rate, bond price will be higher than the face value
Inestors will pay MORE for a bond that pays higher than market interest
Ex. 1m bond was issues for 1.022M
“the bond was isued at 102.2%
Discount - if couponr ate < market rate, bond price will be lower than face value
ex: 1m bond issued for 978,000
“the bond was isued at 97.8%
Inestors will pay MlessRE for a bond that pays lower than market interest
Example question,
company A issued 100,000$ of bonds that mature in 3 years and pay 6% copoun interest annually. The market interest rate at the time was 7%
what is the bond valued at?
First step is find the PV of the principal
1) Principal - PV of a lump sum of 100,000. n=3 and i=7
PV = FV*0.8163= 81,630$
which means that the only ebneift the invesor is going to recevie was this future face vlue if we werent going to pay them any copoun payments , this is the amount they’d be willing to give us in exhange to get 100,000 in 3 years
but they’re also getting series of copoun interest payment , so were going to value these interest payments in todays dollars. Becuase those are goignt om eb apar tof the bonds value
2) Interest - PV of annunity of 6,000 $, n=3. I=7
the reason its 6,000$ is becauese:
Interest payments = copoun * bond face value
so were going to look a the table of PV annunity where n=3, and I=7
pVA= 15,756
So combining these two the value of today would be 97,376
this means the issuance price is lower than face value, which means itw as disoutned because the bond pays 6% which is lower than market itnerest rate of 7%
Jounrnal entry on issuance:
Cash (+a) 97,376
Bonds payable (+L) 97,376
The 97,376 is the carrying value of the bond
What is i= to?
the market rate, for both the principal and interest
Carrying vlaue of the bond
Is the amount of bonds payable
is the true value of the bond after valauting it with princiapla dn itnerest
A bond discont and what is efective interest method
A bond disocunt is essential a form of additonal itnerest expense
- we intieally record a bond payable smaller than the face value, but we still have to pay the face value at the maturity date
the additnl amound we have to pay is the additoal interest expense
a bond preimum is a form of interest saving
- we intially recorded a bond payable larger than th face value, but we only have to pay the face value at the maturity date
Differences between the bonds payable and the face value are amortiized over time using the Effective Interest Method:
- Calculate Bond itnerest expense =
Bond carrying value at the beginning of period * Market itnerest rate - Calculate bond interest paid =
Face value ofm bond * coupn interest rate - Calculate amortization
Bond interest expense - bond interest paid
Ex. Use Effective interest method every time a copoun interest payment is made
Year 1- First interest payments
For out example: bod issued at a discount for 97,373; CR=6% and MR=7%
and what is te carrying value now?
and on the maturity date what is the final copun payment and face value
Interst expense 6816
Bonds payable 816
Cash (-a) 6,000
which means the carrying value of the bod is now higher (97,376+816) = 98,192
Calcualt444ed:
Interst expens 6935
Bonds apyable 935
cash paid 6,000
Bonds payable -L(100,000)
Cash (-A) 100,000
Actual coupon payment:
Interest expense;
Discount depreiation
Discount Balance
Bonds payable
Actual coupon payment: Face value ( coupon rate
Interest expense; Beginning bonds payable * market itnerest rate
Discount depreiation = (2)-(1). Interest expense 0 cash copoun PMT (Cash pad)
Discount Balance= Face value - bonds payable
Bonds payable = Beginning year of bonds payable - current year amortization
