MIE 353 Engineering Economics Todays Goals

1
MIE 353 Engineering EconomicsTodays Goals

• Correctly include taxes when calculating PW.
• Review interest calculations
• HW8 Due Wed Dec. 5 Using PW, calculate the EVPI
  on the cash flow of the stock in problem 18.27
  16.27, 17.40 (use either computer or by hand)

2
Method (a very simply 2 year example)
I initial investment A annual revenue MV market
value of project B basis of project di
depreciation in year i BV book value
3
Groupwork Example

• A firm is considering purchasing machinery for
  the manufacture of chemicals. The cost of the
  machinery is 180,000. It will reduce net annual
  operating expenses by 36,000 per year for 10
  years and have a MV of 30,000 at the end of 10
  years. The after-tax MARR is 10. The effective
  tax rate is 40. They are required to use GDS.
• What is the PW of this project, using after-tax
  calculations?
• What is PW using before-tax calculations?

4
Groupwork ExampleSteps

• Determine the depreciation for each year.
• Determine the cash flow for each year.
• Before tax cash flow income tax
• Note that in year 10 you will have a gain. That
  will be added to the taxable income for that
  year.
• Calculate the PW using after-tax MARR.
• Calculate the before-tax PW simply using
  before-tax cash flows and the before tax MARR
  (which you need to calculate).

5
Solution
Should the firm invest in the machinery?
6
Solution
Cash flow given in problem
Should the firm invest in the machinery?
7
86.40 34.56 51.84
Rates from table
Cash flow given in problem
0.32 180 57.60
Should the firm invest in the machinery?
8
86.40 34.56 51.84
Rates from table
Cash flow given in problem
0.32 180 57.60
BTCF - dk
Should the firm invest in the machinery?
9
86.40 34.56 51.84
Rates from table
Cash flow given in problem
0.32 180 57.60
BTCF - dk
MV book value 30 0 0
10
Solution
Before tax use MARR 105/(1-40) 16.67. NPV
-3.81K
11
Example 2

• Consider the same problem, but say that the firm
  intends to sell the machinery after 3 years, and
  estimate a market value of 140K.

12
Example 2

• Consider the same problem, but say that the firm
  intends to sell the machinery after 3 years, and
  estimate a market value of 140K.

13
Example 2

• Consider the same problem, but say that the firm
  intends to sell the machinery after 3 years, and
  estimate a market value of 140K.

Gain 140 51.84 88.16
14
Interest calculations

• With single cash flows use annual effective
  interest rate.
• When cash flows and compounding periods are the
  same, use i r/M and N total number of
  compounding periods.
• With cash flows different from compounding
  period, use the effective rate for the cash flow
  period, and N total number of cash flow periods.

15

• Work on worksheets for about 5 minutes.

16
Cash flow ? compounding

• 1. Jane makes quarterly deposits of 100 into a
  savings account that pays interest of 6 per
  year, compounded monthly. How much will be in the
  account after 5 years?
• Compounding is monthly
• Cash flow is quarterly
• i (1 .06/12)3 1
• 12 is the number of compounding periods per year
• 3 is the number of compounding periods per cash
  flow
• N 5 4 20 quarters
• The number of cash flow periods
• FW 100(F/A, i, 20)

17
Annual cash flows

• A company made deposits of 10,000 at the end of
  year 2, 25,000 at the end of year 3, and 30,000
  at the end of year 5. What is the future worth,
  at the end of year 5, of the deposits at an
  interest rate of 16 per year compounded
  semiannually?
• compounding is semiannally (twice a year)
• cash flows are annual
• i (1.16/2)2 -1
• N depends on each payment (3, 2, and 0) years
• FW 10,000 (F/P, i, 3) 25,000 (F/P, i, 2)
  30,000

18
Annual cash flows alternate method

• A company made deposits of 10,000 at the end of
  year 2, 25,000 at the end of year 3, and 30,000
  at the end of year 5. What is the future worth,
  at the end of year 5, of the deposits at an
  interest rate of 16 per year compounded
  semiannually?
• compounding is semiannally (twice a year)
• cash flows are annual
• i .16/2 .08 per half year
• N number of half years (6, 4, and 0) years
• FW 10,000 (F/P, i, 6) 25,000 (F/P, i, 4)
  30,000

19
Compounding cash flow

• A service is available at a cost of 2.99 for 48
  hours. A company uses the service an average of
  96 hours per month. What is the present worth of
  the rental costs for 10 months at an interest
  rate 18 nominal compounded monthly?
• compounding is monthly
• cash flow is monthly
• i .18/12 .015
• N 10 months
• PW 2.99 96/48 (P/A, i, 10)

20
Cash flow compounding

• A modest e-commerce package is available for
  20,000. If the company wants to recover the cost
  in 2 years, what is the equivalent amount of
  income that must be realized each quarter, if the
  MARR is 12 nominal, compounded quarterly.?
• compounding is quarterly (4 times a year, every 3
  months)
• cash flow is quarterly.
• i .12/4 .03
• N 2 4 8 quarters
• They want to recover the cost in two years means
  that they want the PW of the income to be equal
  to the investment of 20K for 2 years worth of
  income.
• 20,000 PW income (P/A, i, 8)
• income 20,000/ (P/A, i, 8)

21
Cash flow ? compounding

• A manufacturer expects the cost of an input to
  increase by 2 every 6 months. If the cost for
  the first semiannual period is expected to be
  80, what is the present worth of the costs for a
  4-year time period for a MARR of 12 nominal
  compounded monthly?
• compounding is monthly
• cash flows are every 6 months
• i (1 .12/12)6 1
• N 4 2 8 6-month periods
• PW 80 (P/A, i, 8) 2 (P/G, i, 8)