Financial Management  Test 2 – Leah
Chapter 5 –Discounted Cash Flow Value
Finding the FV of an OA
Deposit(d)= 4000, Rate(r)=8%, number of years(t)=3
or 4, account balance at beginning= 7000
Formula
: today
FV=7000(1+r)^3
Year 1: FV= d(1+r)^2, Year 2: FV=d(1+r), Year 3:
value=4000.
Answer= today + year 1 + year 2 + year 3
You invest $500 today and $600 in 1 yr.
Pays 9%
annually, how much will you have in 5 yrs?
FV = 500(1.09)
5
+ 600(1.09)
4
= $1616.26
You deposit $100 in 1 yr & $300 in 3 yrs. Pays 8%
annually, how much will be in the acct in 5 yrs?
FV = 100(1.08)
4
+ 300(1.08)
2
= 136.05 + 349.92 =
$485.97
Time Line:
A
n investment that will pay you 200 in 1 yr, 400 in 2
yrs, 600 in 3 yrs, & 800 in 4yrs.
If you want to earn
10% per yr, how much would you be willing to pay?
Year 1 CF: 200 / (1.12)1 = 178.57,
Year 2 CF: 400 /
(1.12)2 = 318.88
,
Year 3 CF: 600 / (1.12)3 =
427.07
, Year 4 CF: 800 / (1.12)4 = 508.41
Total PV
= 178.57 + 318.88 + 427.07 + 508.41=$1432.93
PV=FV(1+r)^t
Time Line:
Year 1 CF = $100; Years 2 and 3 CFs = $200;
Years 4 and 5 CFs = $300. The required discount
rate is 7%. What is the value of the cash flows at yr
5?
FV
5
= 100x1.07
4
+ 200x1.07
3
+ 200x1.07
2
+ 300x1.07
+ 300= $1226.07
What is the value of the cash flows today?
PV=100/1.07 + 200/1.07
2
+ 200/1.07
3
+ 300/1.07
4
+
300/1.07
5
= $874.17
Annuity
– finite series of equal payments that occur
at regular intervals
If the first payment occurs at the end of the period,
it is called an
ordinary annuity
If the first payment occurs at the beginning of the
period, it is called an
annuity due
Perpetuity
– infinite series of equal payments
Perpetuity:
PV = C / r
Borrow money TODAY & you can afford a
632.00/month payment which you would like to
extend 4 years. What can you borrow at 12%
annualized interest?
Loan or PV= C(11/(1+r)
t
)
/r
$632(1 – 1/(1+.01)
48
) / .01 = $23999.54
Annual salary of $36,000 & the bank is willing to
allow your monthly mortgage payment to = 28% of
your monthly income.
max month pmt or C= ($36000/12) x.28= $840.00

interest rate on the loan is 6% per year with for a
30year fixed rate loan.
Loan amount= 840(1 – 1/1.005
360
)/ .005
≈
$140,105
You know the payment amount for a loan and you
want to know how much was borrowed.
Do you
compute PV or FV?
Answer= PV
Receive 5,000 per month for 25 years.
you can
earn .75% per month following retirement. What is
the needed PV?
PV = C(1 – 1/(1+r)t)/r
$5000(1 – 1/(1.0075)300)/.0075 =$595,808
To compute payment amount:
C = PV/[(1 – (1/(1+r)t))/r]
put $1,000 on credit card. make the minimum pmt of
$20 per mon. interest rate =1.5% How long will you
need to pay off the $1,000.
T = [ln(C)ln(Cr(PV))]/ln(1+r)=
[ln(20)ln(20.015(1000))]/ln(1.015)= 93.11
Finding the Rate w/o a Financial Calculator
(trial and error process) Get starting point by
calculating table value from
PV/C
Choose appropriate interest ratebased on that
calculation and compute PV of the payments based
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 Fall '10
 dr.lee
 Accounting, Interest Rates

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