©2015, College for Financial Planning, all rights reserved. Session 10 Geometric, Holding Period, and Dollar Weighted Returns, Net Present Value (NPV) CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning

Session Details Module5 Chapter(s)1 LOs5-1 Explain terminology related to investment return computations, and calculate returns. 5-2 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: – = 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 = $ This means $1 would have grown to $ Then just do a simple TVM calculation for i 1 (+/-) = PV = 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 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? 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 yearInflowOutflow 1$2,000$21,000 2$9,000$4,100 3$10,000$2,100 4$10,500$2,500 5$9,000$7,

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

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,

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,

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,

©2015, College for Financial Planning, all rights reserved. Session 10 End of Slides CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning