FUTURE VALUE
ie What is the future value of $100 if you put it in the bank today with interest compounded annually @ 10% for three years: FV = PV(1+r)
(FV=Future Value; PV=Present Value; r=annual interest rate)
|--------------------------------|-------------------------------|--------------------------------|
1 2 3
$100
(1 + .1)* 100 =
$110 (1 + .1) * 110 =
$121 (1 + .1) * 121 =
$133.10
The future value of $100 compounded annually @ 10% for 3 years is $133.10. or Look in the Future Value tables for the future value of $1. Find 10% in the columns and the number 3 in the rows. The future value of $1 for 3 periods @ 10% is 1.33100. To calculate the future value of a single amount from time zero:
FV = PV (FVIFr,n)
133.10 = 100 (1.33100)
(FVIF=Future Value Interest Factor; n=number of periods)
PRESENT VALUE
ie What is the present value of $100 to be received 1 year from today with interest compounded annually @ 11%? PV = FV (1+r)
|-------------------------------------------------|
0 1
<------------------------------$90.09 or Look in the Present Value tables for the present value of $1. Find 11% in the columns and the number 1 in the rows. The present value of $1 for 1 period @ 11% is .90090 To calculate the present value of a single amount from time zero:
100/(1 + .11)
$100
PV = FV (PVIFr,n)
(PVIF=Present Value Interest Factor)
90.09 = 100 * .90090
ie What would be the present value of $1000 received 2 years from now if interest is compounded annually @ 12%?
|-------------------------------------------------|--------------------------------------------| 0 <------------------------------1 <------------------------------- 2 $797.20 $892.86 /(1 + .12) $892.86 $1000 /(1 + .12) $1000 or
PV = FV (PVIFr,n)
$797.20 = $1000 * .79719
(.79719 is the PVIF of $1 for 2 periods at 12%)
ie What is the PV of $1000 received 4 years from now with if interest is compounded annually @ 9%?
PV = FV (PVIFr,n)
[$708.43 = $1000 * .70843]
(.70843 is the PVIF of $1 for 4 periods @ 9%)
----------------------------------If interest is compounded semiannually, half the interest and double the periods. ie What is the present value of $500 @10% compounded semiannually for 5 years.
PV = FV (PVIF1/2r,2n) [ $306.96 = $500 * .61391 ] (where .61391 is the PVIF of $1 for 10 periods @5%)
ANNUITIES
PRESENT VALUE
An annuity is a series of equal consecutive amounts. An ordinary annuity begins at the end of each period. An annuity due begins at the beginning of each period. ie What is the present value of $100 received every year for 3 years @10% compounded annually? You can use the PV of $1 formula for each year as follows:
PV = FV (PVIFr,n)
|--------------------------------|-------------------------------|--------------------------------|
1 2 3
$90.91 <------------------- $100
100(.90909)
82.65 <-------------------------------------------------- $100
100(.82645)
75.31 <----------------------------------------------------------------------------------------$100 $248.70 100(.75131) or the quicker way is to use the annuity tables
PVA = A(PVIFAr,n)
$248.69 = $100(2.48685) (where PVA=Present Value of Annuity; A=Annuity; PVIFA=Present Value Interest Factor of an Annuity)
FUTURE VALUE
ie What is the future value of $100 received every year for three years @10% compounded annually? (ordinary annuity)
|--------------------------------|-------------------------------|--------------------------------|
1 2 3
$100 (100 * .1) + 100 = $110 (110 * .1) + 110 = $121.00 + $100 (100 * .1) + 100 = 110.00 100.00 $331.00 or
FVA = A(FVIFAr,n)
$331.00 = $100(3.31000) (where FVA=Future Value of an Annuity; A=annuity; FVIFA=Future Value Interest Factor of an annuity)
A bond is set up so the:
PV of the bond’s maturity value + PV of the bond’s consecutive equal interest payments = Face value of the bond
ie If a company issues $400,000 face value of 10%, 15 year bonds, dated June 30, calling for semi annual interest payments, determine the present value of the bond. Step 1:
Calculate the contractual interest. I = interest P = principle CR = contract rate T = time
I = P x CR x T
$20,000 = $400,000 x .10 x 6/12
Step 2:
Calculate the present value of the principle PVP= present value of principle mr= market rate
PVP = P x PVIF2n, 1/2mr
$92,552 = $400,000 x .23138
Step 3:
Calculate the present value of the interest PVI= present value of the interest
PVI = I x PVIFA2n,1/2mr
$307,449 = $20,000 x 15.37245
Step 4:
Calculate the present value of the bond PVB= present value of the bond
PVB = PVP + PVI
$400,000 = $92,552 + $307,449
When the market rate equals the contract rate, the present value of the bond equals the face amount of the bond.
If the market rate is different than the contract rate, the bond will sell at a premium or a discount.
CR = MR FACE VALUE CR > MR PREMIUM CR < MR DISCOUNT
If you sell $400,000 face value of 10%, 15 year bonds dated Jun 30, on Jun 30, calling for semiannual interest payments when the yield is 8%, compute the bond issue price. Step 1:
I = P x CR x T
$20,000 = $400,000 x .10 x 6/12
Step 2: Step 3: Step 4:
PVP = P x PVIF2n, 1/2mr
$123,328 = $400,000 x .30832
(PV of $1 @4% for 30 periods)
PVI = I x PVIFA2n, 1/2mr
$345,841 = $20,000 x 17.29203
(PV of annuity @4% for 30 periods)
PVB = PVP + PVI
$469,169 = $123,328 + $345,841
NOTE: The interest is always calculated using the contract rate, and the present value is calculated using the yield rate. Journal entry to record sale: Cash B/P Premium on B/P 469,169 400,000 69,169
TO AMORTIZE THE PREMIUM USING THE EFFECTIVE INTEREST METHOD: You amortize premiums and discounts against bond interest expense.
Step 5: Step 6:
Calculate the bond interest expense. BIE= Bond Interest Expense
CV = B/P + Premium
$469,169 = $400,000 + $69,169
BIE = CV x MR x T
$18,767 = $469,169 x .08 x 6/12
Journal entry: Bond Interest Expense Premium [plug] Cash [contract amount] 18,767 1,233 20,000
Step 7: Post to the ledger and go back to Step 5
next period: CV = B/P + Premium $467,936 = $400,000 + $67,936 BIE = CV x MR x T $18,717.44 = $467,936 x .08 x 6/12
Journal entry: Bond Interest Expense Premium [plug] Cash [contract amount] 18,717.44 1,282.56 20,000
The effective amortization method amortizes bond premiums and discounts at a constant rate, NOT a constant amount. As you amortize the premium, CV decreases, BIE decreases, premium amortization increases, and the premium account decreases. On maturity, the CV of the bond should be equal to the face value.
Entries to issue a bond:
Drew Corportation issued $100,000 of 12% bonds on the date of bonds, Jan 1. Prepare the entry for the issuance if they were sold at : a) Face value b) @ 96 (a discount of $4000) c) @104 (a premium of $4000)
a) Jan 1 Cash Bonds Payable b) Jan 1 Cash Discount on B/P B/P c) Jan 1 Cash Premium on B/P B/P
100,000 100,000 96,000 4,000 100,000 104,000 4,000 100,000
Note: Bonds Payable are always recorded at their face value The carrying value (CV) of a bond: CV = B/P + Premium or CV = B/P - Discount
PV & Amortization of Premium
Step 1: Step 2:
I = P x CR x T PVP = P x PVIF2n, 1/2mr
Step 3:
PVI = I x PVIFA2n, 1/2mr
Step 4: Step 5:
PVB = PVP + PVI CV = B/P + Premium
Step 6:
Journal Entry:
BIE = CV x MR x T
Step 7: Post to the ledger and go back to Step 5
Bonds Payable | | | | | | | | Premium | | | | | | | |
PV & Amortization of Discount
Step 1: Step 2:
I = P x CR x T PVP = P x PVIF2n, 1/2mr
Step 3:
PVI = I x PVIFA2n, 1/2mr
Step 4: Step 5:
PVB = PVP + PVI CV = B/P - Discount
Step 6:
Journal Entry:
BIE = CV x MR x T
Step 7: Post to the ledger and go back to Step 5
Bonds Payable | | | | | | | | Discount | | | | | | | |