This document defines key terminology used in financial appraisal tools. It discusses fundamental concepts like alternatives, cash flows, time value of money, and evaluation criteria. It also defines interest rate, rate of return, simple interest, and compound interest. Various symbols used in financial analysis are introduced, like principal (P), future value (F), interest rate (i), and number of periods (n). Cash flow diagrams and the distinctions between rate of return, cost of capital, and minimum attractive rate of return are covered at a high level. Finally, common spreadsheet and financial calculator functions for present value, future value, payments, number of periods, interest rate, and internal rate of return are listed.

1. EGN 3203 Engineering Economics
LO 2 – a
Financial Appraisal Tools
Key Terminologies

2. Financial Appraisal Tools – Key Terminology:

3. Financial Appraisal Tools – Key Terminology:
 Fundamental terminology:
 Alternative -- stand-alone solution
 Cash flows -- estimated inflows (revenues, savings) and outflows
(costs, expenses) for an alternative
 Evaluation criteria -- basis used to select ‘best’ alternative;
usually money (currency of the country)
 Time value of money -- change in amount of money over time
(Most important concept in Engineering Economy)
Interest Rate, ROR, MARR:
 Interest is a manifestation of time value of money
 Calculated as difference between an ending amount and a
beginning amount of money
 Interest = end amount – original amount ……
(1.1)

4. Financial Appraisal Tools – Key Terminology:
Equivalence:Different sums of money at different times may be equal in
economic value
Interpretation: $94.34 last year, $100 now, and $106 one year from
now are equivalent only at an interest rate of 6% per year

5. Financial Appraisal Tools – Key Terminology:
Interest Rate, ROR, MARR:
 Interest rate is interest over specified time period based on original
amount
 Interest rate (%) =
 Interest rate and rate of return (ROR) have same numeric value, but
different interpretations

6. Financial Appraisal Tools – Key Terminology:
Interest Rate and ROR Interpretations:
Borrower’s perspective
(money paid to lender)
Take loan of $5,000 for
one year; repay
$5,350
Interest paid = $350
Interest rate =
350/5,000
= 7%
INTEREST RATE
Investor’s perspective
(money earned by lender)
Invest (or lend)
$5,000 for one year;
receive $5,350
Interest earned = $350
Rate of return =
350/5,000
= 7%
RATE OF RETURN
(ROI has same numeric

7. Financial Appraisal Tools – Key Terminology:
Example 1: An employee at LaserKinetics.com borrows $10,000 on May 1
and must repay a total of $10,700 exactly 1 year later. Determine the
interest amount and the
interest rate paid.

8. Financial Appraisal Tools – Key Terminology:

9. Financial Appraisal Tools – Key Terminology:

10. Financial Appraisal Tools – Key Terminology:

11. Financial Appraisal Tools – Key Terminology:
Simple and Compound Interest:
Simple interest is always based on the original amount,
which is also called the principal
Interest per period = (principal)(interest rate)
Total interest = (principal)(number of
periods)(interest rate)
Example: Invest $250,000 in a 3-year bond at 5% per year
simple
Interest each year = 250,000(0.05) = $12,500
Interest over 3 years = 250,000(3)(0.05) =
$37,500

12. Financial Appraisal Tools – Key Terminology:

13. Financial Appraisal Tools – Key Terminology:

14. Financial Appraisal Tools – Key Terminology:
Simple and Compound Interest:
Compound interest is based on the principal plus all accrued
interest
Interest per period = (principal + accrued interest)(interest
rate)
Total interest = (principal)(1+interest rate)n periods
– principal
Total due = principal(1+interet rate)n periods
Example: Invest $250,000 for 3 years at 5% per year compounded
Interest, year 1 = 250,000(0.05) = $12,500
Interest, year 2 = 262,500(0.05) = $13,125
Interest, year 3 = 275,625(0.05) = $13,781
Interest over 3 years = 250,000(1.05)3
– 250,000 = $39,406
Total due after 3 years = 250,000(1.05)3 = $289,406

15. Financial Appraisal Tools – Key Terminology:

16. Financial Appraisal Tools – Key Terminology:

17. Financial Appraisal Tools – Key Terminology:
Terminology and Symbols:
 t = time index in periods; years, months, etc.
 P = present sum of money at time t = 0; $
 F = sum of money at a future time; $
 A = series of equal, end-of-period cash flows;
currency per period, $ per year
 n = total number of periods; years, months
 i = compound interest rate or rate of return; % per
year

18. Financial Appraisal Tools – Key Terminology:
Terminology and Symbols:
Example: Borrow $5,000 today and repay annually for
10 years starting next year at 5% per year
compounded. Identify all symbols.
Given: P = $5,000 Find: A = ? per year
i = 5% per year
n = 10 years
t = year 1, 2, …, 10
(F not used here)

19. Financial Appraisal Tools – Key Terminology:
Cash Flow Estimates:
Cash inflows – receipts, revenue, income, savings
Cash outflows – cost, expenses, disbursements,
losses
Net cash flow (NCF) = inflows –
outflows
End-of-period convention: all cash flows and NCF occur
at the end of an interest period

20. Financial Appraisal Tools – Key Terminology:
Cash Flow Diagrams:

21. Financial Appraisal Tools – Key Terminology:
ROR and MARR:
Example: Find an amount to deposit 2 years from now
so that $4,000 per year can be available for 5 years
starting 3 years from now. Assume i = 15.5% per year

22. Financial Appraisal Tools – Key Terminology:
ROR and MARR:
Cost of capital (COC) –
interest rate paid for funds
to finance projects
Minimum Attractive Rate of
Return MARR (hurdle rate)
– Minimum ROR needed for
an alternative to be justified
and economically
acceptable. MARR ≥ COC.
If COC = 5% and 6% must
be realized, MARR = 11%
Always, for acceptable
projects
ROR ≥ MARR > COC

23. Financial Appraisal Tools – Key Terminology:
 Introduction to Spreadsheet and Financial Calculator
FunctionsTo display Spreadsheet Function Calculator
Function
Present value, P = PV(i%,n,A,F) PV(i,n,A,F)
Future value, F = FV(i%,n,A,P) FV(i,n,A,P)
Annual amount, A = PMT(i%,n,P,F)
PMT(i,n,P,F)
# of periods, n = NPER(i%,A,P,F)
n(i,A,P,F)
Compound rate, i = RATE(n,A,P,F) i(n,A,P,F)
i for input series = IRR(first_cell:last_cell)
P for input series = NPV(i%,second_cell:last_cell) +
first_cell
Items to remember
Spreadsheets: Omitted parameters are assumed to be zero
Interior parameters omitted require entry of comma
Calculators: Procedures and notation varying between
manufacturers

24. Notes