r06 discounted cash flow applications

Quantitative Methods

Discounted Cash Flow Applications

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Graphs, charts, tables, examples, and figures are copyright 2012, CFA

Institute. Reproduced and republished with permission from CFA Institute.

All rights reserved.

Contents and Introduction

1. Introduction

2. Net Present Value Internal Rate of Return

3. Portfolio Return Measurement

4. Money Market Yields

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Lecture 140 minutes

Lecture 216 minutes

2. Net Present Value and Internal Rate of Return

• Net present value and internal rate of return are often applied in all fields of finance

• Classic application is in capital budgeting where we make decisions on how to allocate funds to long-term projects or investments

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2.1 NPV and NPV Rule

To understand the NPV concept let us consider a simple example: You invest $40 million today on a project which is expected to return $10 million every year for 5 years. The appropriate discount rate is 5%. Should you go ahead?

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What if you realize that the initial investment is actually $45 million?

Practice Question 1

A project requires an initial outlay of $750,000. It is expected to produce $200,000 in the first year, $300,000 in the second year, and $400,000 in the third year. The cost of capital for this project is 10%. What is the NPV? Should the project be accepted?

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NPV = ∑ [CFt /(1+r)t]

Compute NPV Using the Financial Calculator

A project requires an initial outlay of $750,000. It is expected to produce $200,000 in the first year, $300,000 in the second year, and $400,000 in the third year. The cost of capital for this project is 10%. What is the NPV? Should the project be accepted?

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Keystrokes Explanation Display

[2nd] [QUIT] Return to standard mode 0

[CF] [2nd] [CLR WRK] Clear CF Register CF = 0

750 [+/-] [ENTER] Initial Outlay (in 000’s) CF0 = -750

[↓] 200 [ENTER] Enter CF at T = 1 C01 = 200

[↓] [↓] 300 [ENTER] Enter CF at T = 2 C02 = 300


[↓] [NPV] [10] [ENTER] Enter discount rate I = 10

[↓] [CPT] Compute NPV -19.722

Steps for Calculating NPV

• Identify all cash flows associated with the investment

• Determine the appropriate discount rate or opportunity cost

• Find the present value of each cash flow

• Sum all present values

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NPV = ∑ [CFt /(1+r)t]

NPV Rule

• Independent projects

If NPV is positive Accept

If the NPV is negative Reject

• Mutually exclusive projects

Accept project with higher NPV as long as NPV is positive

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2.2 IRR and IRR Rule

Internal rate of return (IRR) is the discount rate that makes net present value equal to zero.

Say you invest $100 today and get $110 after one year. What is the IRR?

Invest $100 today. Get $10 at t = 1 and $110 at t = 2. What is the IRR?

NPV = CF0 + [CF1/(1+IRR)1] + [CF2/(1+IRR)2] + … + [CFN/(1+IRR)N] = 0

‘Internal’ because it depends only on the cash flows of the investment. It gives a sense for the return on the project.

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Practice Question 2

Arnold Corp wants to estimate the IRR for a proposed project. The initial investment is $150,000. Estimated cash flows for the following 3 years are $50,000 $100,000 and $40,000 respectively. What is the IRR?

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Compute IRR Using the Financial Calculator

Arnold Corp wants to estimate the IRR for a proposed project. The initial investment is $150,000. Estimated cash flows for the following 3 years are $50,000 $100,000 and $40,000 respectively. What is the IRR?


Keystrokes Explanation Display

[2nd] [QUIT] Return to standard mode 0

[CF] [2nd] [CLR WRK] Clear CF Register CF = 0

150 [+/-] [ENTER] Initial Outlay (in 000’s) CF0 = -150

[↓] 50 [ENTER] Enter CF at T = 1 C01 = 50



[↓] [ÌRR] [CPT] Compute IRR 13.11%

IRR Rule


• Independent projects

If IRR > Opportunity Cost Accept

If IRR < Opportunity Cost Reject

• Mutually exclusive projects

Accept project with higher IRR as long as IRR > opportunity cost

• IRR uses the opportunity cost of capital as the hurdle rate

Practice Problem 3


Bill is interested in a project which requires an investment of $1.5 million. The project shall pay$200,000 per year in perpetuity. The first cash flow will be received 1 year from today. The cost ofcapital is 8%. What is the IRR. Should Bill invest?

2.3 Problems with the IRR Rule

• The IRR and NPV rules give the same accept or reject decision when projects are independent

• Often projects are mutually exclusive and need to be ranked

• The IRR and NPV rules might rank projects different when:

The size or scale of the project differs

Timing of the projects’ cash flows differs


NPV and IRR of Mutually Exclusive Projects


Project Investment at t = 0 Cash flow at t = 1 IRR (%) NPV at 10%

A -100 120 20% 10

B 1,000 1,150 15% 45

Difference in size/scale

Project CF 0 CF 1 CF 2 CF 3 IRR (%) NPV at 10%

A -100 120 0 0 20% 10

C -100 0 0 170 19% 28

Difference in timing of cash flow

When there is a conflict, rank/select based on the NPV rule

3. Portfolio Return Measurement

• As an investor you need to measure portfolio returns

• Holding Period Return (HPR)

• Two types of portfolio return measurement tools:1. Money Weighted Return (IRR)

2. Time Weighted Return


3.1 Money Weighted Rate of Return

Money-weighted rate of return is effectively the IRR of the investment

Determine cash flows and then compute IRR

Example: Compute the money-weighted return for the following scenario:


Time Outlay Proceeds Cash Flow

0 $20.00 to purchase the first share

1 $22.50 to purchase the second share $0.50 dividend received on first share

2 $1.00 received ($0.50 x 2 shares) received$47.00 received from selling 2 shares @ $23.50 per share

3.2 Time Weighted Rate of Return


The time-weighted return measures the compound rate of growth of $1 initially invested in the portfolio over a stated measurement period. Example: Compute the time-weighted return for the following scenario:

Time Outlay Proceeds

0 $20.00 to purchase the first share

1 $22.50 to purchase the second share $0.50 dividend received on first share

2 $1.00 received ($0.50 x 2 shares) received$47.00 received from selling 2 shares @ $23.50 per share

Time weighted Return• Dealing with inflows/outflows during year

• Dealing with negative return


TWRR - Methodology

• Price the portfolio immediately prior to any significant addition or withdrawal of funds.

• Break the overall evaluation period into sub-periods based on the dates of cash inflows and outflows.

• Calculate the holding period return on the portfolio for each sub-period.

• Link or compound holding period returns to obtain an annual rate of return for the year (the time-weighted rate of return for the year).

• If the investment is for more than a year, take the geometric mean of the annual returns to obtain the time-weighted rate of return over that measurement period.


0 1 2 3 4 5 6 7 8

10% -5% 15% -10% -20% +30% +20% 0%

MWRR versus TWRRMoney-Weighted Rate of Return Time-Weighted Rate of Return

Simply the IRR

Return depends on timing and amount of cash flows

Not an appropriate performance measure if portfolio manager does not control timing and amount of investment

Appropriate measure if portfolio manager has control over timing and amount of investment

Compound rate of growth of $1 initially invested in the portfolio over a stated measurement period

Return does NOT depend on timing and amount of cash flows

Appropriate performance measure if portfolio manager does not control timing and amount of investment

Not an appropriate measure if portfolio manager has control over timing and amount of investment


Practice Question 4


Mariah purchases a share worth $50 on January 1, 2011. She made a subsequent purchase on January1, 2012 of a share worth $60. Each share paid a dividend of $3 at the end of the year. On January 1,2013, she sold the two shares and collected $150. Compute the time weighted and money weightedreturns?

money weighted return is 28.60%

time weighted return is 27.98%

4. Money Market Yields

• Money market is the market for short-term debt instruments

• Some instruments require issuer to pay amount borrowed + interest

• T-Bills are pure discount instruments and are quoted on a bank discount basis


Different Yield Measures

• Bank Discount Yield

• Holding Period Yield

• Money Market Yield

• Effective Annual Yield

• Bond Equivalent Yield


Bank Discount Yield


BDY = D x 360

F tWhere

D = Face value – purchase value

F = Face value of the T-bill

t = Number of days remaining to maturity

Three issues1. Interest not divided by investment amount2. Simple interest3. 360 day year

Holding Period Yield

HPY = P1-P0 +D1

P0

Where

Po = initial purchase price of the instrument

P1= price received for the instrument at its maturity

D1= interest paid by the instrument at its maturity


Money Market Yield (MMY)

MMY= HPY x 360

tWhere

HPY = Holding period yield

360 = Bank convention on number of days in a year

t = Number of days till maturity


Two issues1. Simple interest2. 360 day year

Effective Annual Yield (EAY)

EAY = (1 + HPY)365/t - 1


Practice Question 5

A 90-day T-bill is purchased for $990. The face value is $1,000. Compute:

1)Bank discount yield

2)Holding period yield

3)Money market yield

4) Effective annual yield


Practice Question 5 - Answers

Bank discount yield: [(1,000 – 990) / 1,000] x 4 = 0.04 = 4.00%

Holding period yield: (1,000 / 990) – 1 = 0.0101 = 1.01%

Money market yield: 0.0101 (360 / 90) = 0.0404 = 4.04%

Effective annual yield: (1 + 0.0101 )365/90 – 1 = 0.04160 = 4.16%


Yield Measure Conversions


MMY BDY

MMY EAY

Yield Measure Conversions


BDY MMY

BDY EAY

Bond Equivalent Yield

• BEY is two times the semi-annual yield

• Example: You purchase a bond for $1000. In return you’ll receive a $40 coupon every six months and the par value of $1,000 is returned at the end of Year 4. What is the BEY?


Summary

• Net Present Value

• Internal Rate of Return

• Portfolio Return Measurement

• Money Market Yields


Conclusion

• Review learning objectives

• Examples and practice problems from the curriculum

• Practice questions from other sources


r06 discounted cash flow applications

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