工程经济学第四-1章(英文版)
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– interest rate, – amount of money involved, and – timing of monetary receipts or expenses.
• Using these elements we can “move” cash flows so that we can compare them at particular points in time.
• Interest and profit pay the providers of capital for forgoing its use during the time the capital is being used.
• Interest and profit are payments for the risk the investor takes in letting another use his or her capital. • Any project or venture must provide a sufficient return to be financially attractive to the suppliers of money or property.
5
Compound Interest
Compound Interest – occurs when the interest earned is added to the principal, so that from that point on the interest and principal both earn interest.
A dollar today is worth more than a dollar one or more years from now
2
Capital Return
• Return of capital in the form of interest and profit is an essential ingredient of engineering economy studies.
years years
SOLUTION Draw the cash flow diagram Year Positive Negative 0 $0 -$10,000 1 $5,310 -$3,000 2 $5,310 -$3,000 3 $5,310 -$3,000 4 $5,310 -$3,000 5 $7,310 -$3,000
Period 1
2 3
$1,100 $1,210
$110 $121
$1,210 $1,331
7
Compound Interest Example
8
Economic Equivalence
• Allows us to compare alternatives on a common basis.
• Each alternative can be reduced to an equivalent basis dependent on
Net -$10,000 $2,310 $2,310 $2,310 $2,310 $4,310
15
16
Cash-Flow Diagrams in Excel
Cash flow tables and column charts may be used to model engineering cash flow problems in Excel.
13
14
Cash-Flow Diagram in Excel
Cash flow diagrams may be represented in Excel with column charts corresponding to the cash flow tables.
EX 4-1 Before evaluating the merits of a proposed investment XYZ insists that they develop a cash flow diagram for the proposal. Initial Investment Annual Revenue Annual Revenue Period Market Recovery Value Market Recovery Point Annual Expense $10,000 $5,310 5 $2,000 5 $3,000
– Downward arrows represent disbursements or negative cash flows (cash outflows) – Upward arrows represent receipts or positive cash flows (cash inflows)
• For the following example, assume $1,000 is invested at 10% compound interest
6ຫໍສະໝຸດ Baidu
Compound Interest Example
(1) Amount owed at beginning of period $1,000 (2)=(1)x10% Interest amount for period $100 (3)=(1)+(2) Amount owed at end of period $1,100
17
Compound Interest Formula
18
Compound Interest Formulas
Using the standard notation, we find that a present amount, P, can grow into a future amount, F, in N time periods at interest rate i according to the formula below.
4
Simple Interest Example
If $5,000 were loaned for five years at a simple interest rate of 7% per year, the interest earned would be
So, the total amount repaid at the end of five years would be the original amount ($5,000) plus the interest ($1,750), or $6,750.
• F = future sum of money; equivalent value of one or more cash flows at a reference point in time; the future
• A = end-of-period cash flows in a uniform series continuing for a certain number of periods, starting at the end of the first period and continuing through the last
• Rule 2. To move a cash flow forward in time by one time unit, multiply the magnitude of the cash flow by ( 1 + i), where i is the interest rate that reflects the time value of money. • Rule 3. To move a cash flow backward in time by one time unit, divide the magnitude of the cash flow by ( 1 + i).
F P (1 i)
N
In a similar way we can find P given F by
P F (1 i)
-N
F N (1 i)
19
Basic Cash Flow Rules
• Rule 1. Cash flows cannot be added or subtracted unless they occur at the same point in time.
9
Cash Flow Notation
• i = effective interest rate per interest period
• N = number of compounding (interest) periods • P = present sum of money; equivalent value of one or more cash flows at a reference point in time; the present
10
Cash-Flow Diagram
Cash Flow Diagram – a tool used by accountants and engineers to represent the transactions which will take place over the time scale of a given project which may include initial investments, maintenance costs, projected earnings or cost savings resulting from the project, as well salvage and resale value of equipment at the end of the project. • Horizontal Line: time scale • Arrows: cash flows
• Compound interest reflects both the remaining principal and any accumulated interest.
• Compound interest is commonly used in personal and professional financial transactions.
Time Value of Money
Ref Sullivan Ch 4
1
Time Value of Money
Capital – refers to wealth in the form of money or property that can be used to produce more wealth. Engineering economy – studies involve the commitment of capital for extended periods of time.
3
Computation of Simple Interest
Interest – fee paid for the use of borrowed money, or money earned on deposited funds.
The total interest, I, earned or paid may be computed using the formula below.
I (P) (N) (i)
P = principal amount lent or borrowed N = number of interest periods (e.g., years) i = interest rate per interest period The total amount repaid at the end of N interest periods is P + I.
• Cash flow depends on point of view
– The direction of arrows will be reversed from a lender’s point of view vs. the borrower’s
11
Cash-Flow Diagram
12
Cash-Flow Diagram
• Using these elements we can “move” cash flows so that we can compare them at particular points in time.
• Interest and profit pay the providers of capital for forgoing its use during the time the capital is being used.
• Interest and profit are payments for the risk the investor takes in letting another use his or her capital. • Any project or venture must provide a sufficient return to be financially attractive to the suppliers of money or property.
5
Compound Interest
Compound Interest – occurs when the interest earned is added to the principal, so that from that point on the interest and principal both earn interest.
A dollar today is worth more than a dollar one or more years from now
2
Capital Return
• Return of capital in the form of interest and profit is an essential ingredient of engineering economy studies.
years years
SOLUTION Draw the cash flow diagram Year Positive Negative 0 $0 -$10,000 1 $5,310 -$3,000 2 $5,310 -$3,000 3 $5,310 -$3,000 4 $5,310 -$3,000 5 $7,310 -$3,000
Period 1
2 3
$1,100 $1,210
$110 $121
$1,210 $1,331
7
Compound Interest Example
8
Economic Equivalence
• Allows us to compare alternatives on a common basis.
• Each alternative can be reduced to an equivalent basis dependent on
Net -$10,000 $2,310 $2,310 $2,310 $2,310 $4,310
15
16
Cash-Flow Diagrams in Excel
Cash flow tables and column charts may be used to model engineering cash flow problems in Excel.
13
14
Cash-Flow Diagram in Excel
Cash flow diagrams may be represented in Excel with column charts corresponding to the cash flow tables.
EX 4-1 Before evaluating the merits of a proposed investment XYZ insists that they develop a cash flow diagram for the proposal. Initial Investment Annual Revenue Annual Revenue Period Market Recovery Value Market Recovery Point Annual Expense $10,000 $5,310 5 $2,000 5 $3,000
– Downward arrows represent disbursements or negative cash flows (cash outflows) – Upward arrows represent receipts or positive cash flows (cash inflows)
• For the following example, assume $1,000 is invested at 10% compound interest
6ຫໍສະໝຸດ Baidu
Compound Interest Example
(1) Amount owed at beginning of period $1,000 (2)=(1)x10% Interest amount for period $100 (3)=(1)+(2) Amount owed at end of period $1,100
17
Compound Interest Formula
18
Compound Interest Formulas
Using the standard notation, we find that a present amount, P, can grow into a future amount, F, in N time periods at interest rate i according to the formula below.
4
Simple Interest Example
If $5,000 were loaned for five years at a simple interest rate of 7% per year, the interest earned would be
So, the total amount repaid at the end of five years would be the original amount ($5,000) plus the interest ($1,750), or $6,750.
• F = future sum of money; equivalent value of one or more cash flows at a reference point in time; the future
• A = end-of-period cash flows in a uniform series continuing for a certain number of periods, starting at the end of the first period and continuing through the last
• Rule 2. To move a cash flow forward in time by one time unit, multiply the magnitude of the cash flow by ( 1 + i), where i is the interest rate that reflects the time value of money. • Rule 3. To move a cash flow backward in time by one time unit, divide the magnitude of the cash flow by ( 1 + i).
F P (1 i)
N
In a similar way we can find P given F by
P F (1 i)
-N
F N (1 i)
19
Basic Cash Flow Rules
• Rule 1. Cash flows cannot be added or subtracted unless they occur at the same point in time.
9
Cash Flow Notation
• i = effective interest rate per interest period
• N = number of compounding (interest) periods • P = present sum of money; equivalent value of one or more cash flows at a reference point in time; the present
10
Cash-Flow Diagram
Cash Flow Diagram – a tool used by accountants and engineers to represent the transactions which will take place over the time scale of a given project which may include initial investments, maintenance costs, projected earnings or cost savings resulting from the project, as well salvage and resale value of equipment at the end of the project. • Horizontal Line: time scale • Arrows: cash flows
• Compound interest reflects both the remaining principal and any accumulated interest.
• Compound interest is commonly used in personal and professional financial transactions.
Time Value of Money
Ref Sullivan Ch 4
1
Time Value of Money
Capital – refers to wealth in the form of money or property that can be used to produce more wealth. Engineering economy – studies involve the commitment of capital for extended periods of time.
3
Computation of Simple Interest
Interest – fee paid for the use of borrowed money, or money earned on deposited funds.
The total interest, I, earned or paid may be computed using the formula below.
I (P) (N) (i)
P = principal amount lent or borrowed N = number of interest periods (e.g., years) i = interest rate per interest period The total amount repaid at the end of N interest periods is P + I.
• Cash flow depends on point of view
– The direction of arrows will be reversed from a lender’s point of view vs. the borrower’s
11
Cash-Flow Diagram
12
Cash-Flow Diagram