##### Document Text Contents

Page 1

Yield Curve

DEFINITION of 'Yield Curve'

A line that plots the interest rates, at a set point in time, of bonds having

equal credit quality, but differing maturity dates. The most frequently reported

yield curve compares the three-month, two-year, five-year and 30-year U.S.

Treasury debt. This yield curve is used as a benchmark for other debt in the

market, such as mortgage rates or bank lending rates. The curve is also used to

predict changes in economic output and growth.

Next Up

1. SPOT RATE

2. EQUITY CURVE

3. YIELD ELBOW

4. INVERTED YIELD CURVE

5.

BREAKING DOWN 'Yield Curve'

The shape of the yield curve is closely scrutinized because it helps to give an

idea of future interest rate change and economic activity. There are three main

types of yield curve shapes: normal, inverted and flat (or humped). A normal yield

curve(pictured here) is one in which longer maturity bonds have a higher yield

compared to shorter-term bonds due to the risks associated with time.

http://www.investopedia.com/terms/c/creditquality.asp

http://www.investopedia.com/terms/n/normalyieldcurve.asp

http://www.investopedia.com/terms/n/normalyieldcurve.asp

http://www.investopedia.com/terms/i/invertedyieldcurve.asp

http://www.investopedia.com/terms/y/yieldelbow.asp

http://www.investopedia.com/terms/e/equity-curve.asp

http://www.investopedia.com/terms/s/spot_rate.asp

http://www.investopedia.com/terms/m/mortgage-rate.asp

http://www.investopedia.com/terms/b/benchmark.asp

http://www.investopedia.com/terms/u/ustreasury.asp

http://www.investopedia.com/terms/u/ustreasury.asp

http://www.investopedia.com/terms/m/maturitydate.asp

Page 2

An inverted yield curve is one in which the shorter-term yields are higher than the

longer-term yields, which can be a sign of upcoming recession. A flat (or

humped) yield curve is one in which the shorter- and longer-term yields are very

close to each other, which is also a predictor of an economic transition. The slope

of the yield curve is also seen as important: the greater the slope, the greater the

gap between short- and long-term rates.

Read more: Yield Curve Definition |

Investopedia http://www.investopedia.com/terms/y/yieldcurve.asp#ixzz3zzjaLwpO

Follow us: Investopedia on Facebook

http://ec.tynt.com/b/rf?id=arwjQmCEqr4l6Cadbi-bnq&u=Investopedia

http://www.investopedia.com/terms/y/yieldcurve.asp#ixzz3zzjaLwpO

http://www.investopedia.com/terms/y/yieldcurve.asp#ixzz3zzjaLwpO

http://www.investopedia.com/terms/y/yieldcurve.asp#ixzz3zzjaLwpO

http://www.investopedia.com/terms/r/recession.asp

http://www.investopedia.com/terms/i/invertedyieldcurve.asp

Page 20

Quantitative Methods - Net Present

Value and the Internal Rate of Return

This section applies the techniques and formulas first presented in the time value of money

material toward real-world situations faced by financial analysts. Three topics are

emphasized: (1) capital budgeting decisions, (2) performance measurement and

(3) U.S. Treasury-bill yields.

Net Preset Value

NPV and IRR are two methods for making capital-budget decisions, or choosing between

alternate projects and investments when the goal is to increase the value of the enterprise

and maximize shareholder wealth. Defining the NPV method is simple: the present value of

cash inflows minus the present value of cash outflows, which arrives at a dollar amount that

is the net benefit to the organization.

To compute NPV and apply the NPV rule, the authors of the reference textbook define a

five-step process to be used in solving problems:

1.Identify all cash inflows and cash outflows.

2.Determine an appropriate discount rate (r).

3.Use the discount rate to find the present value of all cash inflows and outflows.

4.Add together all present values. (From the section on cash flow additivity, we know that

this action is appropriate since the cash flows have been indexed to t = 0.)

5.Make a decision on the project or investment using the NPV rule: Say yes to a project if

the NPV is positive; say no if NPV is negative. As a tool for choosing among alternates, the

NPV rule would prefer the investment with the higher positive NPV.

Companies often use the weighted average cost of capital, or WACC, as the appropriate

discount rate for capital projects. The WACC is a function of a firm's capital structure

(common and preferred stock and long-term debt) and the required rates of return for these

securities. CFA exam problems will either give the discount rate, or they may give a WACC.

Example:

To illustrate, assume we are asked to use the NPV approach to choose between two

projects, and our company's weighted average cost of capital (WACC) is 8%. Project A

costs $7 million in upfront costs, and will generate $3 million in annual income starting three

http://www.investopedia.com/terms/n/npv.asp

http://www.investopedia.com/terms/c/capitalbudgeting.asp

Page 21

years from now and continuing for a five-year period (i.e. years 3 to 7). Project B costs $2.5

million upfront and $2 million in each of the next three years (years 1 to 3). It generates no

annual income but will be sold six years from now for a sales price of $16 million.

For each project, find NPV = (PV inflows) - (PV outflows).

Project A: The present value of the outflows is equal to the current cost of $7 million. The

inflows can be viewed as an annuity with the first payment in three years, or an ordinary

annuity at t = 2 since ordinary annuities always start the first cash flow one period away.

PV annuity factor for r = .08, N = 5: (1 - (1/(1 + r)N)/r = (1 - (1/(1.08)5)/.08 = (1 - (1/

(1.469328)/.08 = (1 - (1/(1.469328)/.08 = (0.319417)/.08 = 3.99271

Multiplying by the annuity payment of $3 million, the value of the inflows at t = 2 is ($3

million)*(3.99271) = $11.978 million.

Discounting back two periods, PV inflows = ($11.978)/(1.08)2 = $10.269 million.

NPV (Project A) = ($10.269 million) - ($7 million) = $3.269 million.

Project B: The inflow is the present value of a lump sum, the sales price in six years

discounted to the present: $16 million/(1.08)6 = $10.083 million.

Cash outflow is the sum of the upfront cost and the discounted costs from years 1 to 3. We

first solve for the costs in years 1 to 3, which fit the definition of an annuity.

PV annuity factor for r = .08, N = 3: (1 - (1/(1.08)3)/.08 = (1 - (1/(1.259712)/.08 =

(0.206168)/.08 = 2.577097. PV of the annuity = ($2 million)*(2.577097) = $5.154 million.

PV of outflows = ($2.5 million) + ($5.154 million) = $7.654 million.

NPV of Project B = ($10.083 million) - ($7.654 million) = $2.429 million.

Applying the NPV rule, we choose Project A, which has the larger NPV: $3.269 million

versus $2.429 million.

Problems on the CFA exam are frequently set up so that it is tempting to pick a choice that seems intuitively better (i.e. by people who are guessing), but this is wrong by NPV rules. In the case we used, Project B had

lower costs upfront ($2.5 million versus $7 million) with a payoff of $16 million, which is more than the combined $15 million payoff of Project A. Don\'t rely on what feels better; use the process to make the decision!

Yield Curve

DEFINITION of 'Yield Curve'

A line that plots the interest rates, at a set point in time, of bonds having

equal credit quality, but differing maturity dates. The most frequently reported

yield curve compares the three-month, two-year, five-year and 30-year U.S.

Treasury debt. This yield curve is used as a benchmark for other debt in the

market, such as mortgage rates or bank lending rates. The curve is also used to

predict changes in economic output and growth.

Next Up

1. SPOT RATE

2. EQUITY CURVE

3. YIELD ELBOW

4. INVERTED YIELD CURVE

5.

BREAKING DOWN 'Yield Curve'

The shape of the yield curve is closely scrutinized because it helps to give an

idea of future interest rate change and economic activity. There are three main

types of yield curve shapes: normal, inverted and flat (or humped). A normal yield

curve(pictured here) is one in which longer maturity bonds have a higher yield

compared to shorter-term bonds due to the risks associated with time.

http://www.investopedia.com/terms/c/creditquality.asp

http://www.investopedia.com/terms/n/normalyieldcurve.asp

http://www.investopedia.com/terms/n/normalyieldcurve.asp

http://www.investopedia.com/terms/i/invertedyieldcurve.asp

http://www.investopedia.com/terms/y/yieldelbow.asp

http://www.investopedia.com/terms/e/equity-curve.asp

http://www.investopedia.com/terms/s/spot_rate.asp

http://www.investopedia.com/terms/m/mortgage-rate.asp

http://www.investopedia.com/terms/b/benchmark.asp

http://www.investopedia.com/terms/u/ustreasury.asp

http://www.investopedia.com/terms/u/ustreasury.asp

http://www.investopedia.com/terms/m/maturitydate.asp

Page 2

An inverted yield curve is one in which the shorter-term yields are higher than the

longer-term yields, which can be a sign of upcoming recession. A flat (or

humped) yield curve is one in which the shorter- and longer-term yields are very

close to each other, which is also a predictor of an economic transition. The slope

of the yield curve is also seen as important: the greater the slope, the greater the

gap between short- and long-term rates.

Read more: Yield Curve Definition |

Investopedia http://www.investopedia.com/terms/y/yieldcurve.asp#ixzz3zzjaLwpO

Follow us: Investopedia on Facebook

http://ec.tynt.com/b/rf?id=arwjQmCEqr4l6Cadbi-bnq&u=Investopedia

http://www.investopedia.com/terms/y/yieldcurve.asp#ixzz3zzjaLwpO

http://www.investopedia.com/terms/y/yieldcurve.asp#ixzz3zzjaLwpO

http://www.investopedia.com/terms/y/yieldcurve.asp#ixzz3zzjaLwpO

http://www.investopedia.com/terms/r/recession.asp

http://www.investopedia.com/terms/i/invertedyieldcurve.asp

Page 20

Quantitative Methods - Net Present

Value and the Internal Rate of Return

This section applies the techniques and formulas first presented in the time value of money

material toward real-world situations faced by financial analysts. Three topics are

emphasized: (1) capital budgeting decisions, (2) performance measurement and

(3) U.S. Treasury-bill yields.

Net Preset Value

NPV and IRR are two methods for making capital-budget decisions, or choosing between

alternate projects and investments when the goal is to increase the value of the enterprise

and maximize shareholder wealth. Defining the NPV method is simple: the present value of

cash inflows minus the present value of cash outflows, which arrives at a dollar amount that

is the net benefit to the organization.

To compute NPV and apply the NPV rule, the authors of the reference textbook define a

five-step process to be used in solving problems:

1.Identify all cash inflows and cash outflows.

2.Determine an appropriate discount rate (r).

3.Use the discount rate to find the present value of all cash inflows and outflows.

4.Add together all present values. (From the section on cash flow additivity, we know that

this action is appropriate since the cash flows have been indexed to t = 0.)

5.Make a decision on the project or investment using the NPV rule: Say yes to a project if

the NPV is positive; say no if NPV is negative. As a tool for choosing among alternates, the

NPV rule would prefer the investment with the higher positive NPV.

Companies often use the weighted average cost of capital, or WACC, as the appropriate

discount rate for capital projects. The WACC is a function of a firm's capital structure

(common and preferred stock and long-term debt) and the required rates of return for these

securities. CFA exam problems will either give the discount rate, or they may give a WACC.

Example:

To illustrate, assume we are asked to use the NPV approach to choose between two

projects, and our company's weighted average cost of capital (WACC) is 8%. Project A

costs $7 million in upfront costs, and will generate $3 million in annual income starting three

http://www.investopedia.com/terms/n/npv.asp

http://www.investopedia.com/terms/c/capitalbudgeting.asp

Page 21

years from now and continuing for a five-year period (i.e. years 3 to 7). Project B costs $2.5

million upfront and $2 million in each of the next three years (years 1 to 3). It generates no

annual income but will be sold six years from now for a sales price of $16 million.

For each project, find NPV = (PV inflows) - (PV outflows).

Project A: The present value of the outflows is equal to the current cost of $7 million. The

inflows can be viewed as an annuity with the first payment in three years, or an ordinary

annuity at t = 2 since ordinary annuities always start the first cash flow one period away.

PV annuity factor for r = .08, N = 5: (1 - (1/(1 + r)N)/r = (1 - (1/(1.08)5)/.08 = (1 - (1/

(1.469328)/.08 = (1 - (1/(1.469328)/.08 = (0.319417)/.08 = 3.99271

Multiplying by the annuity payment of $3 million, the value of the inflows at t = 2 is ($3

million)*(3.99271) = $11.978 million.

Discounting back two periods, PV inflows = ($11.978)/(1.08)2 = $10.269 million.

NPV (Project A) = ($10.269 million) - ($7 million) = $3.269 million.

Project B: The inflow is the present value of a lump sum, the sales price in six years

discounted to the present: $16 million/(1.08)6 = $10.083 million.

Cash outflow is the sum of the upfront cost and the discounted costs from years 1 to 3. We

first solve for the costs in years 1 to 3, which fit the definition of an annuity.

PV annuity factor for r = .08, N = 3: (1 - (1/(1.08)3)/.08 = (1 - (1/(1.259712)/.08 =

(0.206168)/.08 = 2.577097. PV of the annuity = ($2 million)*(2.577097) = $5.154 million.

PV of outflows = ($2.5 million) + ($5.154 million) = $7.654 million.

NPV of Project B = ($10.083 million) - ($7.654 million) = $2.429 million.

Applying the NPV rule, we choose Project A, which has the larger NPV: $3.269 million

versus $2.429 million.

Problems on the CFA exam are frequently set up so that it is tempting to pick a choice that seems intuitively better (i.e. by people who are guessing), but this is wrong by NPV rules. In the case we used, Project B had

lower costs upfront ($2.5 million versus $7 million) with a payoff of $16 million, which is more than the combined $15 million payoff of Project A. Don\'t rely on what feels better; use the process to make the decision!