LECTURE 6
Quiz #6
If you are going to finance the purchase of a car,
would you want the interest on your loan be
compounded daily, monthly, quarterly, annually or
continuously?
FV For The Compound Interest Case
with unequal sums
FV = (PV)1(1+ie)t-1 + (PV)2(1+ie)t-2+…(PV)n(1+ie)t-n
A landowner receives annual royalty payments of $2,000, $2,200,
$1,900, $2,500, $1,500 over the next five years. What is FV of
these payments at an interest rate of 8%.
FV = $2,000(1+.08)4+$2,200(1+.08)3+$1,900(1+.08)2+
$2,500(1+.08)1+$1,500(1+.08)0
FV = $11,908.50
Annuity
Annuity – a series of equal periodic payments at regular
intervals over a period of time while the interest is
compounding.
Examples: auto loans, mortgage payments, insurance
premiums, installment loans, etc.
PV = AV[((1+ie)t – 1)) / ie(1+ie)t]
where AV = amount of each equal future payment
Annuity Example #1
An oil company has to pay $10,000 per year, starting
one year from today, on a five year loan at 8% interest.
Calculate the PV of these five yearly payments.
PV = $10,000 [ ((1+0.08)5 – 1) / .08(1+0.08)5]
= $10,000 (3.9927)
PV = $39,927
Annuity Example #2
Calculate the Future Value of the annuity given in the
previous example.
FV = AV[((1+ie)t – 1)) / ie(1+ie)t] (1+ie)t
or; FV = AV((1+ie)t – 1)) / ie
FV = $10,000 [ ((1+.08)5 –1) / 0.08]
FV = $58,666 = $39,927(1+ie)t
Annuity Example #3
You borrow $20,000 from the bank at 8% and agree to
pay off the loan through a series of five equal year-end
payments beginning one year from today. What will
your yearly payments be?
AV = PV [ (ie(1+ie)t) /( (1+ie)t – 1))]
AV = $20,000 [ (0.08(1+0.08)5) / ((1+0.08)5 – 1)]
AV = $20,000 ( 0.2505) = $5,010 per year
Loan Amortization
Loan Amortization = Paying off a debt
Example: an oil company borrows $100,000 at 8% for 3
years. Payments will be quarterly with the first 3 months
from today. Calculate the quarterly payment amount.
AV = $100,000 [ (in/4(1+ in/4)t x 4) / ((1+ in/4)t x 4 – 1)]
= $100,000 (0.09456) = $9,456 per quarter
borrowed
Period, yrs
Pmts/yr
Nom. Int.
Qtr. Pmt.
Qtr. End
1
2
3
4
5
6
7
8
9
10
11
12
100,000
3
4
0.08
($9,455.96)
Interest
Principal
($2,000.00)
($7,455.96)
($1,850.88)
($7,605.08)
($1,698.78)
($7,757.18)
($1,543.64)
($7,912.32)
($1,385.39)
($8,070.57)
($1,223.98)
($8,231.98)
($1,059.34)
($8,396.62)
($891.41)
($8,564.55)
($720.11)
($8,735.85)
($545.40)
($8,910.56)
($367.19)
($9,088.77)
($185.41)
($9,270.55)
Balance
$92,544.04
$84,938.96
$77,181.78
$69,269.46
$61,198.89
$52,966.90
$44,570.28
$36,005.73
$27,269.88
$18,359.32
$9,270.55
($0.00)
Homework #2
Using annual yearend discounting, calculate the Present
Value [PV] for the following future cashflow stream for
5%, 10%, 15% and 50% discount interest rates. Show
the resulting Cumulative discounted value for each rate.
Year
FV
1
$2,500,000
2
$2,250,000
3
$2,025,000
4
$1,822,500
5
$1,640,250
6
$1,476,225
7
$1,328,603
8
$1,195,742
9
$1,076,168
10
$968,551
Cumulative
$16,283,039
PV(5)
PV(10)
PV(15)
PV(50)
FORECASTING
Tings we must know or estimate when evaluating a producing
property are:
- Present producing rate - Future producing rate
- Ultimate recovery
- Product prices
- Operating costs
- Capital costs
- Ownership Interests
- Taxes
The development of forecasts of future oil and gas production
form wells is an engineering responsibility. It is an essential part
of any economic evaluation.
IT IS FROUGHT WITH UNCERTAINTY AND RISK, WHILE
HUGE SUMS OF MONEY ARE INVESTED BASED ON
FORECAST RESULTS