Intermediate Chapter 6
PV of annuity due
-amount that must be deposited now at a specified rate of interest to permit withdrawals of $1 at begin of regular periodic intervals for the specified number of periods -find PVF-AD that correlates with your n and i -find PV-AD= CF x PVF-AD -if waiting a period your FV will be less than if you need your money now- today -PV calc: determined on the day of the first cash flow in the series -effect on the PV: it will be higher because cash flow doesn't have time to accrue interest
PV of ordinary annuity
-amounts that must be deposited now at a specified rate of interest to permit withdrawals of $1 at the end of regular periodic intervals for the specified number of periods -find PVF-OA that correlates with your n and i -PV-OA= CF x PVF-OA -PV calc: determined one period prior to first CF occurring -if cash flow doesn't occur until 1 period later
FV of an annuity due
-amounts to which periodic payments/receipts of $1 will accumulate if the payments/receipts are invested at the begin of each period at a specified rate of interest for a specified number of periods -multiply OA factors (1+interest rate) to find the AD factors *multiply FVF-OA by (1+i) to obtain FVF-AD -each deposit gets to accrue interest for an extra period so FV will be higher -FV calc: determined one period after the last CF in the series is made
FV of an ordinary annuity
-amounts to which periodic payments/receipts of $1 will accumulate if the payments/receipts are invested at the end of each period at a specified rate of interest for a specific number of periods -find FVF-OA that correlates with n and i -FV-OA= CF * FVF-OA -if occurring on the date that you calc the FV -n always equal to number of cash flows -fv calc: determined on the day the last cash flow in the series occurs
deferred annuities
-an annuity in which the payments/receipts begin after a specified number of periods -FV of a deferred annuity is the same as the FV for an annuity that is not deferred -no payments are made during the deferral period, therefore interest cannot accrue during this period- interest can only begin accruing once the payments begin to be made -FV of deferred annuity= FV of annuity not deferred - not true for PV of deferred
bond issued at premium amortization table
-begin bal -cash payment: FV x coupon rate -interest expense: CV x market rate -amortization: cash payment - interest expense -end bal: begin bal - amortization
amortization: period 1
-begin bal: PV -cash payment: FV x coupon % *does not change -interest expense: CV at begin of 1st period x market % -amortization: cash payment and interest expense dif -end bal: CV begin +/- amortization
amortization: period 2
-begin bal: previous ending bal -cash payment: same as before -interest expense: CV at begin of 2nd period x market % -amortization: dif between cash payment and interest expense -end bal: CV at begin +/- amortization
annuity due
-beginning- begin of month -assumes that periodic payments/receipts occur at the begin of each period- so interest is accumulated during the first period, as opposed to an ordinary annuity -FV of an annuity due is determined 1 period after the last cash flow in the series -PV of an annuity due is determined on the day of the first cash flow in the series -n will always be number of cash flows- factor in the table accounts for appropriate number of compounding periods
determining bond issue price
-bond issue price= PV of all future cash payments (including interest payments and final principal payment) discounted at the market rate on the date of issuance- historical market rate, what bond worth on day it is used in marketplace -for discounting purposes: n= number of interest payments, i= market rate per period -always use an ordinary annuity to calculate the present value of the interest as interest payments are not made until the end of each bond period -bonds usually semiannually -don't pay interest on day 1- pay after 1st 6 months
effective interest amortization of discount/premium: amortization, bond interest expense, amortization of premium/discount, total interest expense
-calculates interest expense based on CV -amortizing= allocates interest expense over the life of the bond regardless of the amount of physical cash payments -bond interest expense= computed by multiplying carrying value (PV) of the bonds at the begin of each period by effective (market) interest rate -amortization of premium/discount= difference between bond interest expense and the bond interest cash payment (cash payment is coupon rate x face value) -total interest expense over time= total cash paid - total cash received
long term bonds: effect of financial statements- balance sheet
-carrying value (CV) (also called BV) of bonds is always equal to the PV of all future cash payments, discounted at the market rate of interest in effect of the date of issuance -on date of issuance, CV is equal to bond's issue price -for the remainder of bonds life, CV will be equal to: *if bond was issued at premium: face value + unamortized bon premium *if bond was issued at discount: face value - unamortized bond discount -CV can also be calculated via an amortization table -CV is value reported on bal sheet -unamortized is what remains on premium bal
bond issued at premium 2
-cash interest payments is not the interest expense -premium (extra cash received over the face value) helps to fund our interest payments and reduce interest expense on the income statement -effective cost of borrowing is less than stated rate -interest expense= cash paid - premium
long term bonds: effect of financial statements- income statement: interest expense over the life of the bond
-cash received: bond issue price- cash received at issuance -cash you paid: interest payment- based on coupon rate and principal payment at maturity
long term bonds
-comps borrow cash from multiple lenders (investors) by issuing bonds -comp promises to pay the lender: 1. principal amount (face value of the bond) at maturity 2. periodic interest payments over the life of the bond
bond issued at discount 2
-comps cost of borrowing is higher because less cash is received upon the bond's issuance even though the face value will be due at maturity and the interest payments are based on the face value, not the lesser amount received
compound interest
-computed on principal + accrued interest -ex. 1000 12 month note pays interest 12% annual *120 year 1, 134 year 2, 150 year 3 *total compound interest= 404 -advantage if saving money -disadvantage if borrowing money
simple interest
-computed on principal only -principal x rate x time -ex. 1000 12 month note that pays interest at 12% annually *1000 x .12 x 12/12= 120 *total simple interest over 3 years= 360 (earn 120 every year)
coupon v market rate
-coupon: for cash interest payments -market: everything else -can't change coupon rate but can change what you invest so will invest less because of market rate
bond issuance: journal entries- issuance of bonds payable
-debtor issues the bonds in exchange for cash now -cash is always debited at PV and bonds payable is always credited at FV -difference- premium or discount
CV: discount v premium
-discount: CV will be amortized up to FV -premium: CV will be amortized down to FV
effective interest amortization of discount/premium: discount and premium
-discount= you end up incurring higher amount of interest expense compared to interest payment -premium: you end up incurring lower amount of interest expense compared to interest payment
long term bonds 2
-ex. Disney bond prospectus- can call if interest low- may call all of them and refinance/recall their bonds -why comp issues bonds: spreads out the risk -investors in bonds will get interest payments
long term bonds: effect of financial statements- income statement: bond issued at premium
-extra cash received on the issue date will be used to fund interest payments thereby reducing interest expense through amortization of premium -premium amount used to help fund the interest expense to reduce it -reduces interest expense over life of bond -interest expense will be less than cash paid -lower cost of borrowing
long term bonds: effect of financial statements- income statement
-for the bond issues at face value, the yearly interest expense will be equal to the cash interest payment -for the bond issued at premium or discount, the interest expense recorded in the income statement will not be equal to the periodic interest payments made over the bonds life as interest expense is affected by premium/discount -reports interest expense -at par: D interest expense and C cash/interest payable
interest rate and bond price relationship
-increase interest rate and decrease bond price
time value of money
-interest or the cost of using money over time -difference between FV and PV -take 1000 today v 1000 in 10 years because you can invest it and end up with more- you can earn interest -ex. equip 1000/month for 60 months: D equip 60000 and c n/p for 6000- can't do this entry- you need to account for PV -car payment: interest + principal
long term bonds: effect of financial statements- income statement: bond issued at discount
-less cash was received on the issue date than the face value of the bond -in addition to the periodic interest payments, the company will also have to pay the full face value of the bond to investors at maturity (more cash than they received up front) -extra cash needs to be associated with each and every interest period in the life of the bond -creates higher interest expense on income statement compared to the cash payment -amortization of the discount, increases the interest expense -interest expense greater than cash payment
effect of compounding interest
-more often interest is compounded, the higher the result -effective yield is whatever % results from compounding more than once a year -requires adjustment of interest rate and number of periods -more interest compounded= higher effective yield -effective yield= actual rate of return
full amortization table
-premium: CV decreases over time, at end the CV is equal to amount that the issuer has to pay to the purchasers of the bonds -discount: CV increases over time, at end CV is equal to amount that issuer has to pay to the purchasers of bonds -CV of the bonds is always equal to the PV of all future cash payments, discounted at the market rate of interest in effect on date of issuance -no change cash paid -premium: interest expense decreases -discount: interest expense increases look at consider this
coupon/stated rate
-rate on the face of the bond instrument -only used to determine the amount of periodic cash interest payment (it's never actually used for discounting) -this rate is determined on the date of original issuance -compare the coupon rate with the market rate to determine whether the bond is issued at a discount or premium -what you will receive in cash, stated on prospectus doc -determine cash going out the door
bond issued at discount 3
-recording interest payments: D interest expense C discount on b/p C cash
bond issued at premium 3
-recording interest payments: D interest expense D premium on b/p C cash -if payments due 1/1 and 7/1 rather than 6/30 and 12/31, you would have to credit interest payable
interest expense
-straight line method -GAAP requires effective interest method as it results in better matching of interest expense with its related liability balance -can't use straight line
ordinary annuity
-the end- end of the month -payments are made at the end of each period- so interest can only be earned for subsequent periods (after the first deposit occurring at the end of the period) -FV of an ordinary annuity is determined on the day that the last cash flow in the series is made -PV of an ordinary annuity is determined 1 period before the first cash flow in the series is made -n will always be number of cash flows- factor in the table accounts for appropriate number of compounding periods
PVF v FVF
-they are inverses -if you only have FVF: divide by 1 to find PVF -divide 1 by PVF to find FVF
market/effective yield
-this rate is used for discounting (in determine the bond issue price) and for determining interest expense on the income statement in the effective interest amortization method -this is the rate of return that investors demand for this particular bond and is the rate that is actually earned by bondholders -also the firm's cost of borrowing- not the coupon rate -rate that makes the PV of all future cash flows= to the bond issue price -how much the bond gives in cash when bond purchased -rate of return investor earns
if not given PVF-AD
-you could take PVF-OA x (1+i) and calculate it -relationship exists because each cash flow is being discounted one less period under an annuity due scenario (therefore each cash flow will be greater by (1+i) -PVFOA * (1+i)= PVFAD
2 parts of bond issue price
1. PV of the principal 2. PV of the interest payments (PMT)
long term bonds: 2 interest rates
1. coupon/stated rate 2. market/effective yield
finding PV of deferred annuity: 2 steps
1. find PV of annuity for just the periods in which the payments/receipts occur 2. take the value from step 1 and discount it back to today (time=0)- discount it over n periods, where n=number of compounding periods between the value calculated in step 1 and t=0 -can calc value in step 1 using either PVOA or PVAD- need to use same for step 1 and step 2
issuance of bonds payable: 3 journal entries
1. par: PV=FV D cash at PV C b/p at FV -interest expense= cash paid for interest 2. discount: PV < FV D cash at PV D discount on b/p at FV - PV C b/p at FV -market rate > coupon rate, contra liability- reduces value on b/p account 3. premium: PV > FV D cash at PV C premium on b/p at PV - FV C b/p at FV -normal credit bal- adjunct- increases value on b/p
interest (3)
1. payment for the use of money: the amount of money paid/received in excess of the amount of money borrowed/lent *ex. buy car for 20,000: after 60 months paid 25,000---> means 5,000 interest 2. expressed as a percent: assume annual rate of interest unless stated otherwise, pay attention to dates 3. determined based on credit risk: risk of nonpayment, the higher the credit risk, the higher the rate
annuities
1. periodic payment or receipts (cash flows) of the same amount- called rents 2. same length interval between such cash flows 3. interest compounding once each interval -combo of single sum calculations
5 examples where PV and FV can be used
1. purchase price of assets under long term agreements 2. n/r and n/p 3. bonds payable and investments in bonds 4. long term leases 5. pension obligations
premium: interest expense journal entry
D interest exp D premium on b/p C cash
discount: interest expense journal entry
D interest expense C discount on b/p C cash
bond issued at discount amortization table
look at premium table -end bal: begin CV + amortization -ending bal of carrying value will increase over time -discount will decrease
bond issue price
-a function of the market rate: *coupon rate = market rate: bond issue price= face value *coupon rate < market rate: bond issue price < face value ----discount on b/p- contra liability *coupon rate > market rate: bond issue price > face value ----premium on b/p- adjunct liability account -discount and premium have an effect on interest expense -if coupon is 5% and market 6%: bond issue price < face value
bond issued at discount
-amortization of discount increases interest expense -bond issuance: D cash D discount on b/p C b/p -cash paid= total interest payments + principal payment -total interest over the life of the bond= total cash paid - total cash received (from D cash)
bond issued at premium
-amortization of premium decreases interest expense (goes down over the life of the bond) -bond issuance: D cash C b/p C premium on b/p -cash paid= interest payment (payment x number of periods) + principal payment -total interest over the life of the bond= cash paid - cash received (debit in journal entry)
single sum problems: FV
-FV of $1: the amounts to which $1 will accumulate if deposited now at a specific rate and left for a specific number of periods -FVF correlates with n (compounding periods) and i (interest rate / period) -FV of single sum: FV= PV x FVF -accumulating interest to get to FV
single sum problems: PV
-PV of $1: amounts that must be deposited now at a specified rate of interest equal to $1 at the end of specified number of periods -PVF correlates with n (compounding periods) and i (interest rate / period) -PV of single sum: PV= FV x PVF -discounting interest to get to PV
sum today
-a certain sum today is not equal to the same sum at a future point in time
