CERTIFIED FINANCIAL PLANNER CERTIFICATION
PROFESSIONAL EDUCATION PROGRAM
Investment Planning
Session 10
Geometric, Holding
Period, and Dollar
Weighted Returns, Net
Present Value (NPV)
©2015, College for Financial Planning, all rights reserved.
Session Details
Module
5
Chapter(s) 1
LOs
5-1
5-2
Explain terminology related to investment
return computations, and calculate returns.
Calculate various measures of periodic returns
or pricing of securities.
10-2
Weighting Methods
Equally weighted
• Gives small-cap stocks as much influence as
large-cap stocks (Value Line)
Price weighted
• Gives high-priced stocks more influence than
low-priced stocks (Dow Jones Industrials)
Capitalization weighted
• Gives large-cap stocks more
influence than small-cap stocks
(most indexes―capitalization
weighted indexes are the ones
used in MPT)
10-3
Arithmetic & Geometric Average Returns
Arithmetic return
• Assumes no
compounding
• Each year is
independent
• Always higher than
geometric return
Geometric return
• Assumes compounding
• Always lower than
arithmetic return
10-4
Arithmetic & Geometric Average Returns
Annual returns of 8%, 15%, -7%, and 12%
• Arithmetic return: 8 + 15 – 7 + 12 = 28
28/4 = 7% (or solve for mean return on
calculator)
• Geometric (time-weighted) return:
$1.00 x 1.08 x 1.15 x 0.93 x 1.12 = $1.2937
This means $1 would have grown to $1.2937
Then just do a simple TVM calculation for i
1 (+/-) = PV
1.2937 = FV
4=n
i = 6.65%
10-5
The Holding Period Return (HPR)
• The percentage earned on an investment
•
•
during a period of time
Simply the profit divided by the amount
invested
S = sale price, I = income (subtract costs, such
as margin interest), Pc = purchase cost
S  I  Pc
HPR 
Pc
10-6
HPR Example
Victor purchases 1,000 shares at $50
per share using a 50% margin. The
stock pays a $1.00 dividend and Victor
pays $450 in margin interest. He sells
the shares for $60 per share.
What is his holding period return?
60,000  1,000  450  50,000
25,000 *
 10,550/25,000  .422  42.2%
10-7
Dollar- & Time-Weighted Return
Dollar weighted
• Client returns are dollar
•
weighted
This reflects the actual
return to the client
Time weighted
• Investment manager
•
•
returns are time weighted
This reflects the actual
performance of a manager
over a specified time period
AIMR required
10-8
Dollar Weighted Problems
George and Thelma Blake purchased a stock six
months ago for $4,600. At the end of the third month,
the Blakes received $104 in dividends. Today, they
sold the stock for $4,900. What is the annual internal
rate of return on this investment?
Set calculator for 12 P/YR, end mode
Note: For the HP12C the first cash flow entry will always be CFo, then CFj
will be used, also after solving for IRR the number will need to be
multiplied by 12 in order to arrive at the correct answer since this is
monthly compounding.
10-9
Timeline
10-10
Dollar Weighted Problems
John Baker purchased a plot of land for
$100,000. He had the following inflows and
outflows associated with the investment. At
the end of Year 5 John sold the land for
$127,000.
What was the internal rate of return on his investment ?
End of year
Inflow
Outflow
1
$2,000
$21,000
2
$9,000
$4,100
3
$10,000
$2,100
4
$10,500
$2,500
5
$9,000
$7,200
10-11
Timeline
10-12
Net Present Value
• Net present value (NPV) is the present value of
future cash flows using an appropriate discount
rate, and then subtracting the investment’s cost.
• A positive NPV means the investor will earn a
return higher than the discount rate used, and the
investment should be purchased.
• A zero NPV means the investor will earn the same
return as the discount rate used, and the
investment should be purchased.
• A negative NPV means the investor will
earn a return lower than the discount
rate used, and the investment should
be rejected.
10-13
NPV & PV Calculation
A real estate property is being offered for
$250,000 and is expected to have cash flows of
$26,000, $31,000, $34,000, and $38,000 at the
end of each of the next four years. At the end of
Year 4 the property is expected to be worth
$320,000.
If an investor has a required rate
of return of 12%, what are the PV
and NPV of the property?
10-14
Timeline
10-15
PV & NPV Calculation
First we will calculate the PV of the cash flows
(disregard the purchase price for this calculation):
12 = i
(this is our discount rate)
0 = CFj
26,000 = CFj
31,000 = CFj
34,000 = CFj
358,000 = CFj
SHIFT, NPV - $299,643
10-16
PV & NPV Calculation
Next we will calculate the NPV of the investment
(enter the purchase price):
12 = i
250,000 (+/-) = CFj
26,000 = CFj
31,000 = CFj
34,000 = CFj
358,000 = CFj
SHIFT, NPV = $49,643
10-17
PV & NPV Calculation
Note that the present value we came up with for
the cash flows was $299,643.
Note also that the NPV of the investment was
$49,643.
Another way to look at it:
$299,643 present value
Less
$250,000 purchase price
Equals
$49,643 net present value
10-18
Question 1
How are indices calculated when used for
modern portfolio theory analysis?
a. value weighted
b. price weighted
c. equal weighted
d. geometrically weighted
10-19
Question 2
Which one of the following methods of
computing investment returns should be used
to evaluate the performance of investment
managers?
a. internal rate of return
b. arithmetic weighted average return
c. dollar-weighted return
d. time-weighted return
10-20
Question 3
When computing the interest rate that equates
the present value of an investment’s cash flows
with the cost of investment, which one of the
following methods of computing interest is
used?
a. arithmetic average return
b. internal rate of return
c. geometric average return
d. time-weighted return
10-21
Question 4
Robert “The Magnificent” purchased a fireworks business for
$85,000 from his cousin. He expects the following cash flows
from the business over the next three years:
End of Year 1: $45,000 inflow, $20,000 outflow
End of Year 2: $55,000 inflow, $25,000 outflow
End of Year 3: $65,000 inflow, $35,000 outflow
Robert plans to sell the business at the end of the third year
for $100,000. If these projections are correct, what will be
Robert’s internal rate of return on this investment?
a. 22.4%
b. 26.2%
c. 32.7%
d. 36.9%
10-22
Question 5
Laura is considering buying some foreclosed real estate
property for $150,000. She expects to receive, at year
end, net cash benefits of $6,000 the first year, $6,500
the second year, and $7,000 the third year. At the end
of the third year she anticipates a better housing
market, and hopes to sell the property for $200,000.
If her projections are correct, what would be the
internal rate of return on this investment?
a. 12%
b. 13%
c. 14%
d. 15%
10-23
Question 6
You are considering an investment in Moose
Industries, and want to know the geometric
return over the past five years. Total returns for
the past five years have been +22%, -8%,
+13%, +4%, and -7%.
What is the annual compound rate of return
(geometric average) for Moose Industries?
a. 4.17%
b. 4.80%
c. 5.58%
d. 7.57%
10-24
Question 7
Theo has been offered a parcel of vacant land for
$50,000. Taxes and upkeep (at the end of each
year) are anticipated to be $2,000 per year for the
next five years. At the end of five years, Theo
hopes to sell the land for $100,000.
If Theo’s required rate of return is 9%, should he
purchase the property?
a. yes, because the NPV is positive
b. yes, because the NPV is negative
c. no, because the NPV is positive
d. no, because the NPV is negative
10-25
Question 8
Alice is considering the purchase of some antiques.
She anticipates spending the following amounts at
the end of each of the following three years on
restoration: $9,000, $7,000, and $6,500. At the end
of the third year, she anticipates selling the
antiques for $45,000.
If her required rate of return is 18%, what is the
most she should pay for the antiques?
a. $6,600
b. $10,778
c. $22,500
d. $27,665
10-26
CERTIFIED FINANCIAL PLANNER CERTIFICATION
PROFESSIONAL EDUCATION PROGRAM
Investment Planning
Session 10
End of Slides
©2015, College for Financial Planning, all rights reserved.