Chapter 5

Question 1

time value of money

Answer 1

money can be invested today to earn interest and grow to a larger dollar amt in the future

has nothing to do with the worth or buying power of the dollars

ex:
invested in bank $100

annual yield is 6%

FV is $106

Question 2

time value of money is useful for

Answer 2

valuing a variety of assets/liabilities and rev/exp

Question 3

interest

Answer 3

amount of money paid/received in excess of the amt of money borrowed or lent

Question 4

simple interest

Answer 4

initial investment x annual interest rate x period of time

can also do: [ I x R x T ]/100

Question 5

compound interest

Answer 5

includes interest not only on the initial investment, but also on the accumulated interest in previous periods

when money remains invested for multiple periods

Question 6

how else can you calculate compound interest

Answer 6

future value of a single amount

Question 7

effective rate

Answer 7

actual rate at which money grows per year

Question 8

interest rate per compounding period for effective rate (what must be done to %)

Answer 8

semiannually –>
12% / 2 = 6%

quarterly –>
12% / 4 = 3%

monthly –>
12% / 12 = 1%

Question 9

future value (of a single amount)

Answer 9

is the amt of money that a dollar will grow to at some point in the future

also principle + interest

Question 10

formula for future value (of a single amount)

Answer 10

FV = I (1+i)^n

FV = FV of invested amt
I = amt invested at the beginning period
i = interest rate per compounding period
n = number of compounding periods

Question 11

what must change to the FV formula when interest is compounded semiannually

Answer 11

if its 1,000 @ 10%, for three years

semi annual is 2 times a year

must multiply n x 2

divide r / 2

so:

1000 [1+ (.01/2)] ^ 3 x 2

NOTE: if using table, your table amount would be multiplied by 1,000

Question 12

BUT what is the formula for future value of a single amt when using the table

Answer 12

FV = I x FV Factor

example: assume invested $1,000 in an investment account for three years paying 10% interest compounded annually

FV = $1,000 x FV Factor
FV = $1,000 x 1.331
FV = $1,331

Question 13

present value (of a single amount)

Answer 13

PV = [FV]/[(1 + i)^n]

example: present value of $1,331 received at the end of three years when the interest rate is 10%

PV = FV x PV Factor
PV = $1,331 x .75131
PV = $1,000

Question 14

What is a result of PV

Answer 14

requires the removal of compound interest

higher the interest rate –> lower the present value

further into the future –> lower the present value

Question 15

determining an unknown interest rate

Answer 15

PV = 500
FV = 605
n = 2

FV/PV = 605/500 = 1.21 (in table)

look under n=2

so i = 10%

Question 16

Determining an unknown number of periods

Answer 16

PV = 10,000
FV = 16,000
i = 10%
n =?

10,000/16,000 = .625
under 10% –> .625 –> n = 5

Question 17

valuing a note: one payment, explicit interest

Answer 17

company sold shoes to Sporting Goods Inc. for $50,000.

Shoe Company agrees to accept a note in payment for the shoes requiring payment for $50,000 in one year plus interest at 10%

FV is 55,000
because 50,000 –> then 10% of 50,000

what is PV today?

55,000 x .90909 = 50,000

.90909 comes from table (n=1, i = 10)

Question 18

valuing a note: one payment, no interest stated

Answer 18

Shoe Co sells shoes to Sporting Goods Inc.
Terms of sale require Sporting Goods Inc to sign a non-interest bearing note of 60,500 with payment due in 2yrs

know that the FV is 60,500
n = 2
i = 10%
what is PV?

to find PV (price of shoes) have to know either the cash price of the shoes? or the interest rate? (we were given interest rate)

60,500 (fv) x .82645 = 50,000 (pv)

.82645 comes from table ( n= 2, i = 10%)

Question 19

annuity

Answer 19

series of cash flows of the same amount received or paid each period

Question 20

examples of when need annuities

Answer 20

loan where periodic interest is paid in equal amounts

a lease paid in equal installments during a specified period

Question 21

ordinary annuity

Answer 21

cash payments occur at the END of each period

if have to make payments “due at the end of each year” –>
today (NO)
1: end of year one
2: end of year two
3: end of year three

Question 22

annuity due

Answer 22

cash payments occur at the beginning of each period

so if have to make three payments “immediately” –> 1: today,
2: end of year 1,
3: end of year two

Question 23

future value of ordinary annuity

Answer 23

“accumulate” ,
rather than investing single amount today,
investing 10,000 over the next three years,
10% interest compounded annually,
first payment is made one year from today,

how much will accumulate in the acct by the end of year 3?

SOLVE:
- formula
- PMT x table value

Question 24

Future value of annuity due

Answer 24

not investing single amount today,
growing to future value, decide to invest 10,000 a year over the next three years, 10% interest compounded annually,
making the first payment immediately

how much will you have in acct at end of three years?

SOLVE:
- formula
- PMT x table

Question 25

present value of ordinary annuity

Answer 25

want to determine the cost today, of a three yr graduate program, program cost is 10,00 each year, payments made at end of each year 10% SOLVE: - formula - PMT x table

Question 26

NOTE!!!!!!!!!

Answer 26

for example, when looking at FVAD: you know how to solve for the first payment (what was done above) we take n = 3 and i = 10% and find our corresponding table value to multiply by 10,000 but this can be broken down into each payment so for first payment, 10,000 x table value of (n = 1 and i = 10%) = FV at end of year 1 this can be done for payment n =1, payment n = 2, payment n =3 add up payment table values and the corresponding PV from each year

Question 27

present value or ordinary annuity

Answer 27

want to determine the cost today of three year grad program, cost is 10,000 each year, payments are made at the end of year, 10% SOLVE: - formula - 10,000 x table value

Question 28

present value of an annuity due

Answer 28

want to determine the cost today, three year grad program, 10,000 each year, payments made at beginning of year, 10% interest rate what is the cost today of the program? SOLVE: - formula - table

Question 29

NOTE: when breaking up annuity due

Answer 29

because making payment on first day for three years: n = 0, n = 1, n = 2

Question 30

deferred annuity

Answer 30

when the first cash flow occurs more than one period after the date the agreement begins

Question 31

present value of a deferred annuity

Answer 31

buying investment, provide three equal payments of 10,000, received at the end of three consecutive years, the first payment is not expected until three years from now, 10% how much would you be willing to invest? n = 0 (today) n = 1 (end of year one) n = 2 (end of year two) n = 3 (end of year three) n = 4 (end of year four) n = 5 (end of year five) BREAK DOWN

Question 32

BREAK DOWN: PV of deferred annuity

Answer 32

step one: calculate the PV of the annuity as the beginning of the annuity period (using PV of ordinary annuity) step two: reduce the single amount calculated in (1) to its present value as of today (using PV of $1) Step 1: PVA = 10,000 x table value (10%, n = 3) --> 24,869 Step 2: PV = 24,869 x (10%, n =2) 24,869 is a FV that need to be converted to PV

Question 33

determining the annuity amount when other variables are known (PMT)

Answer 33

assume borrow $700 from friend, intend to repay in 4 equal annual installments beginning one year from today, friend wants to be reimbursed for time value of money at 8% annual rate, what is the required annual payment that must be made, to repay the loan in four years?? basically, what is the pv of ordinary annuity amount?? 700 is PV n =4 i = 8% solving for PMT

Question 34

determining the annuity amount when other variables are known (years)

Answer 34

PV of ordinary annuity 700 is pv, 100 is PMT (annuity amount) i = 7% Divide 700/100 so n = 10yrs (when looking at table value

Question 35

determining interest rate when other variables are known

Answer 35

a friend asked to borrow 331 from you (331 is PV), promised to repay you 100 (annuity amt) at the end of each of the next four years. What is the annual interest rate? Looking at PV of ordinary annuity divide 331/100 n = 4 i = ? (this interest rate is known as the effective interest rate)

Question 36

Determining interest when other variables are known - unequal cash flows

Answer 36

borrowed $400 from a friend and promised to repay the loan, three annual payments of $100 at the end of each of the next three years, plus a final payment of $200 at the end of year four? What is the interest rate implicit in this agreement? $100 single annuity, n = 3, i = ? $200 single payment has n = 4, i = ?

Question 37

valuation of long term bonds

Answer 37

from previous semester

Question 38

valuation of long term bonds - calculating interest expense

Answer 38

(what sold for or calculated price of bond) x 12% x 1/2 the 12% is the MR Debit: Interest expense Credit: Interest Payable

Question 39

valuation of long-term leases

Answer 39

25yr lease 10,000 PMT beginning of each year (which means PV of ordinary annuity) i = 10% trying to solve for the face value of the note so... PVAD = 10,000 x table value = x PVAD represents face value of note 10,000 is PMT

Question 40

journal entry for long term lease

Answer 40

debit: right of use asset credit: lease payable

Question 41

valuation of installment notes

Answer 41

35,000 machine, 5,000 down payment, 5yr installment note, remaining 30,000 payed on a note note calls for annual installment payments, 1st payment is Jan 1 2024 i = 4% paying loan over 5yrs we are solving for PMT have to use PV of annuity due table because given PVAD of 30,000 PVAD = PMT x table value 30,000 = PMT x table value PMT = 6,480

Question 42

journal entry for valuation of installment notes for acquisition of machinery

Answer 42

Debit: machine 35,000 Credit: cash 5,000 Credit: NP 30,000

Question 43

journal entry for first installment payment on machinery

Answer 43

Notes Payable 6,480 Cash 6,480

Question 44

when valuing installment notes is there a need for first installment payment on interest?

Answer 44

no because no interest has accrued on the 2nd payment will need to pay interest and there will be a reduction on the loan Debit: Interest Expense 941 Debit: Notes Payable 5539 Credit: cash 6,480

Question 45

how is interest expense calculated for valuation of installment notes?

Answer 45

Interest expense: 4% x (30,000 - 6480) = 941 interest x (face value of note - cash payed to reduce note on first payment)

Question 46

valuation of pension obligation

Answer 46

Jan 1, 2024 hired new manager, manger must work 25yrs before retirement on Dec 31, 2048 annual retirement payments will be paid at the end of each year during his retirement period (expected to be 20yrs) first payment will be on Dec 31, 2049 during 2024, manager earned annual retirement benefit estimated to be 2,000 per year company plans to contribute cash to pension fund that will accumulate amount sufficient to pay this benefit 6% on all funds in pension plan How much would the company have to contribute at the end of 2024 to pay for the pension benefits earned in 2024?

Question 47

BREAK DOWN of valuation of pension obligation

Answer 47

Deferred annuity must begin with PV of ordinary annuity and convert to PV of $1 PVA = 2,000 x table value PVA = 2,000 (PMT) x 11.46992 = $22,940 Table value uses n = 20 and i = 6% then convert PVA, which is FV to PV PV = 22,940 (future amount) x .24698 = 5,666 (n = 24 and i = 6%) 2,000 is annual payments for 20 yrs but for PV of $1, n = 24 because 2048-2024 = 24yrs