Upload
sarah-victorio
View
226
Download
0
Embed Size (px)
Citation preview
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
1/20
Chapter 7 - Rate of
Return AnalysisClick here for Streaming Audio To
Accompany Presentation (optional)
EGR 403 Capital Allocation Theory
Dr. Phillip R. Rosenkrantz
Industrial & Manufacturing Engineering Department
Cal Poly Pomona
http://video.csupomona.edu/PRRosenkrant/EGR403Lecture-09.asxhttp://video.csupomona.edu/PRRosenkrant/EGR403Lecture-09.asxhttp://video.csupomona.edu/PRRosenkrant/EGR403Lecture-09.asxhttp://video.csupomona.edu/PRRosenkrant/EGR403Lecture-09.asx8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
2/20
EGR 403 - Cal Poly Pomona - SA9 2
EGR 403 - The Big Picture Framework:Accounting& Breakeven Analysis
Time-value of money concepts - Ch. 3, 4
Analysis methods
Ch. 5 - Present Worth
Ch. 6 - Annual WorthCh. 7, 8 - Rate of Return (incremental analysis)
Ch. 9 - Benefit Cost Ratio & other techniques
Refining the analysisCh. 10, 11 - Depreciation & Taxes
Ch. 12 - Replacement Analysis
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
3/20
EGR 403 - Cal Poly Pomona - SA9 3
Three Major Methods of
Economic Analysis PW - Present Worth
AW - Annual Worth
IRR - Internal Rate of Return
If P = A(P/A, i, n)
Then (P/A, i, n) = P/A
Solve for (P/A, i, n) and look up
interest in Compound Interest Tables
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
4/20
EGR 403 - Cal Poly Pomona - SA9 4
Internal Rate of Return (IRR)
The interest rate paid on the unpaid balance of a
loan such that the payment schedule makes the
unpaid loan balance equal to zero when the final
payment is made. Ex: P = $5000, i = 10%, n = 5
Year Principal Prin. Paid Int Paid Payment
1 5000.00 818.99 500.00 1318.99
2 4181.01 900.89 418.10 1318.99
3 3280.13 990.97 328.01 1318.994 2289.15 1090.07 228.92 1318.99
5 1199.08 1199.08 119.91 1318.99
6 0.00 0.00
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
5/20
EGR 403 - Cal Poly Pomona - SA9 5
Calculating Rate of Return
The IRR is the interest rate at which the
benefits equal the costs. IRR = i*
PW Benefit - PW Cost = 0
PW Benefit/PW Cost = 1
NPW = 0
EUAB - EUAC = 0PW Benefit = PW Cost
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
6/20
EGR 403 - Cal Poly Pomona - SA9 6
Calculating IRR - Example 7-1
PWB/PWC = 1 2000(P/A, i, 5)/8200 = 1
(P/A, i, 5) = 8200/2000 =
4.1
From Table, IRR =7%
3.9938%
4.1007%
4.2126%
(P/A,i,5)Interest rate
From Compound Interest Tables
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
7/20
EGR 403 - Cal Poly Pomona - SA9 7
Calculating IRR - Example 7-2
Sometimes we have more than one factor in our equation.
When that happens we cannot solve for just one factor.
If we use: EUAB - EUAC = 0
100 + 75(A/G, i, 4) - 700(A/P, i, 4) = 0
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
8/20
EGR 403 - Cal Poly Pomona - SA9 8
Calculating IRR - Example 7-2 (contd) No direct method for calculating. Use trial and error
and iterate to get answer.
Try i = 5%:
100 + 75(A/G, 5%, 4) - 700(A/P, 5%, 4) = + 11
+ 11 is too high. The interest rate was too low Try i = 8%
100 + 75(A/G, 8%, 4) - 700(A/P, 8%, 4) = - 6
- 6 is too low. The interest rate was too high
Try i = 7%
100 + 75(A/G, 8%, 4) - 700(A/P, 8%, 4) = 0
Therefore IRR = 7%
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
9/20
EGR 403 - Cal Poly Pomona - SA9 9
Calculating IRR - Example 7-3
Example 7-3 shows a series of cash flows that does not match any
of our known patterns. We must use trial and error. Using NPW = 0, suppose we start with i = 10% . NPW = + 10.16,
which is too high.
Using i = 15%, NPW = - 4.02. IRR is between 10% & 15%
The iterations may be graphed and the true IRR will be indicatedat the point where the NPW curve = 0.
Yr CF
0 - 100
1 + 20
2 + 203 + 30
4 + 40
5 + 40
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
10/20
EGR 403 - Cal Poly Pomona - SA9 10
Calculating IRR - Example 7-3 (Contd)
We can use linear interpolation to find estimatethe point where the curve crosses 0.
IRR = i* = 10% + (15%-10%)[10.16/(10.16 +
4.02)] = 13.5% This is a linear interpolation of a non-linear
function so the answer is slightly inaccurate,
but good enough for decision making here(after all, the guesswork in our future cash
flows introduces uncertainty in the analysis).
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
11/20
EGR 403 - Cal Poly Pomona - SA9 11
Calculating IRR - Example 7-3 (Contd)
-100
20
30
2040
40
13.47%
To get an exact answer, we can use the IRR function in EXCEL
Select the IRR function from the fx icon.
Block the column on the spreadsheet that has the cash flows for
all years.
The function returns the IRR.
=IRR(A1:A6)
The IRR function in
EXCEL allows you to
evaluate the return ofinvestments very easily
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
12/20
EGR 403 - Cal Poly Pomona - SA9 12
Calculating IRR for a Bond- Example 7-4a
Bond Costs and Benefits:Purchase price = $1000
Dividends = $40 every six months
Sold after one year for $950
Calculation of Periodic interest rate & IRR:m = 2 compounding periods/year
1000 = 40(P/A, i, 2) + 950(P/F, i, 2)
By trial and error and interpolation i* 1.5%
IRR Nominal rate = 2 x 0.015 = 0.03 (3%)
IRR Effective rate = (1 + 0.015)2- 1 = 0.0302 (3.02%)
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
13/20
EGR 403 - Cal Poly Pomona - SA9 13
Example 7-4a EXCEL Solution
Period Buy/sell Dividend Total0 -1000 -1000
1 40 40
2 950 40 990
1.52% periodic3.04% nominal
3.06% effective
Use IRR function to find periodic IRR (i) Find nominal using r = i * m
Use EFFECT function to find effective interest rate
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
14/20
EGR 403 - Cal Poly Pomona - SA9 14
Rate Of Return (ROR) Analysis
Most frequently used measure of merit in
industry.
More accurately called Internal Rate ofReturn (IRR).
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
15/20
EGR 403 - Cal Poly Pomona - SA9 15
Calculating ROR
Where two mutually exclusive alternatives will
provide the same benefit, ROR is performed using anincremental rate of return(ROR)on the difference
between the alternatives.
You cannot simply choose the higher IRR alternative.
Choose lower-cost
alternative
DROR < MARR
Choose higher-cost
alternative
DROR MARR
DecisionTwo-alternative
situation
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
16/20
EGR 403 - Cal Poly Pomona - SA9 16
The Minimum Attractive Rate of
Return (MARR) The MARR is a minimum return the
company will accept on the money it invests
The MARR is usually calculated byfinancial analysts in the company and
provided to those who evaluate projects
It is the same as the interest rate used forPresent Worth and Annual Worth analysis.
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
17/20
EGR 403 - Cal Poly Pomona - SA9 17
ROR on Alternatives With Equivalent Benefits
Year
Cash flow -
alternative
A (Leaseco)
Cash flow -
alternative
B (Saleco)
Cash flow -
alternative
B - A
0 -$1,000.00 -$2,783.00 -$1,783.00
1 $200.00 $1,200.00 $1,000.00
2 $200.00 $1,200.00 $1,000.00
3 $1,200.00 $1,200.00 $0.00
4 $1,200.00 $1,200.00 $0.00
5 $1,200.00 $1,200.00 $0.00
IRR/period 48.72% 32.60% 8.01%
Example 7-5: Consider the lease vs. buy situation. MARR = 10%
Leasco: Lease for five years for 3 annual payments of $1000 each
Saleco: Purchase up front for $2783
Both alternatives have a $1200/year benefit for 5 years
8/13/2019 RATE OF RETURN ANALYSIS (Chap7)
18/20
EGR 403 - Cal Poly Pomona - SA9 18
Example 7-5 (Contd)
Cannot simply pick the highest IRR if alternatives have
different investment costs
Must examine the incremental cash flows!!
Subtract the cash flows for the Lower First Costalternative from the cash flows of the Higher First Cost
alternative to obtain the Incremental Cash Flow or D.
Compute the IRR on the incremental cash flow. This is
the DROR. For this problem the DROR is 8.01% which is