FINANCE 101Lecture 7

Professor Jianfeng HU

1

2

Net Present Value and Other Investment Criteria

Chapter Nine

3

Decision Rules Once we have an estimate of cash flows, three types of

decisions can be made: Accept a project Reject a project Pick one project from many

Common criteria for decision making NPV Payback Period Discounted Payback Internal Rate of Return Profitability Index

4

Net Present Value

NPV=PV(All Future CFs) – Initial Investment

C = Cash Flow (positive or negative), C0 is usually negative (initial investment)

t = time period of the investmentr = discount rate, required rate of return, opportunity cost of capital

The NPV rule: Accept a project if NPV > 0

N PV C Cr

Cr

Crt

t

0

11

221 1 1( ) ( )

. . .( )

5

Net Present Value

ExampleYou have the opportunity to purchase an officebuilding. You have a tenant lined up that will generate$16,000 per year in cash flows for three years. At theend of three years you anticipate selling the buildingfor $450,000. If the building is being offered for saleat a price of $350,000, would you buy the building?The discount rate is 7%.

(NPV=59)

6

Advantages of NPV decision rule

Accounts for time value of money There is an objective cut-off point ( >0, < 0) Considers all the cash flows

7

Payback Period A project’s payback period is the number of years it

takes to repay the initial investment. The payback rule: Accept a project if payback period

is within some specified number of years

8

Payback period—example Assume we will accept the project if it pays back within two

years. Initial investment: -165,000;

Cash flow in year 1: 63,120; Cash flow in year 2: 70,800; Cash flow in year 3: 91,080 -165,000 + 63,120 = -101,880 still to recover -101,880 + 70,800 = -31,080 still to recover -31,080 + 91,080 = 60,000 The project pays back in 2+31080/91080= 2.34 years.

Do we accept or reject the project?

Advantages and Disadvantages of Payback

Advantages Easy to

understand/use Biased toward

liquidity/ short-termprojects: tend to favor investments that free up cash quickly

Disadvantages Ignores the time value

of money Requires an arbitrary

cutoff point Ignores cash flows

beyond the cutoff date Biased against long-

term projects

9

10

Discounted Payback Period

Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis

Decision Rule - Accept a project if it pays back on a discounted basis within the specified time

11

Discounted Payback—example Assume we will accept the project if it pays back

on a discounted basis in 2 years. Compute the PV for each cash flow and

determine the payback period using discounted cash flows -165,000 + 63,120/1.121 = -108,643 -108,643 +70,800/1.122 = -52,202 -52,202 +91,080/1.123 = +12,627 project pays back in

year 3 Payback 2+52,202/(91,080/1.123) =2.81

Do we accept or reject the project?

12

Advantages and Disadvantages ofDiscounted Payback Advantages

Includes time value of money

Easy to understand Does not accept

negative estimated NPV investments

Biased towards liquidity

Disadvantages May reject positive

NPV investments Requires an

arbitrary cutoff point Ignores cash flows

beyond the cutoff point

Biased against long-term projects

13

Internal Rate of Return

This is the most important alternative to NPV The internal Rate of Return (IRR) is the rate of

return for which the NPV is equal to zero. Decision Rule: Accept a project if the IRR is

greater than the required return (discountrate)

14

Internal Rate of Return

Example What is the IRR on project A?

IRR=21.86%

Year 0 1 2 3 4A -200 80 80 80 80

15

Problems of the IRR –Non-Conventional Cash FlowsNon-Conventional Cash FlowsCertain cash flows can generate NPV=0 at two

different discount rates.Example

Suppose an investment will cost $90,000 initially and will generate the following cash flows: 132,000 in one year, 100,000 in two years, and -150,000 in three years. The required return is 15%. What is the IRR of the project?

16

Problems of the IRR –Non-Conventional Cash Flows

($10,000.00)

($8,000.00)

($6,000.00)

($4,000.00)

($2,000.00)

$0.00

$2,000.00

$4,000.00

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

Discount Rate

NPV

17

Problems of the IRR –Non-Conventional Cash Flows

When does a project have more than one IRR?

A rule of thumb A project typically has more than one IRR, if its cash

flow stream changes sign more than once. In the previous example, its cash flows are

-90K, 132K, 100K, -150K.

18

Problems of the IRR –Mutually Exclusive Projects

Period Project A

Project B

0 -500 -400

1 325 325

2 325 200

IRR 19.43% 22.17%

NPV 64.05 60.74

The required return for both projects is 10%.

Which project should you accept ?

19

Conflicts Between NPV and IRR

NPV directly measures the increase in value to the firm Whenever there is a conflict between NPV and another

decision rule, you should use NPV IRR is unreliable in the following situations

Non-conventional cash flows Mutually exclusive projects

Caveat: We do not assume financing constraint here.

20

20

Advantages and Disadvantages of IRR Advantages

Closely related to NPV, often leading to identical decisions

Disadvantages May result in multiple

answers or not deal with nonconventional cash flows

May lead to incorrect decisions in comparisons of mutually exclusive investments

21

Profitability Index

Profitability Index ( PI ) =

Benefit/Cost ratio

Decision Rule: Accept a project if PI > 1

If a project has a positive NPV, the PI will be greater than 1.

PV(Cash Inflows)PV(Cash Outflows)

22

Problem with PI

PI has problems ranking mutually exclusive projects. Project 1: PV(cash inflow)=75; PV(cash outflow)=50

NPV=25 PI=1.5 Project 2: PV(cash inflow)=10; PV(cash outflow)=5

NPV=5 PI=2

23

Advantages and Disadvantages of Profitability Index Advantages

Closely related to NPV, generally leading to identical decisions

Disadvantages May lead to incorrect

decisions in comparisons of mutually exclusive investments

24

Consider an investment that costs $100,000 initially and has a cash inflow of $25,000 every year for 5 years, starting at year 1. The required return is 9%, and required payback is 4.5 years.

What is the payback period? Accept the project? (4 yr)

Will you accept the project if using discounted payback method? (PV=97.24)

What is the NPV? Accept the project? (-2.76)

What is the IRR? Accept the project? (7.93%)

Practice

Cost of Capital

Chapter Fourteen

25

Cost of Equity The cost of equity is the return required by EQUITY

investors given the risk of the cash flows from the firm

There are two major methods for determining the cost of equity Dividend growth model CAPM

26

Dividend Growth Model Start with the dividend growth model formula and

rearrange to solve for RE

P0 = D0(1+g)/(RE -g) = D1/(RE -g)

RE = D1/ P0 +g

27

Dividend Growth Model Example Suppose that your company is expected to pay a dividend

of $1.50 per share next year. There has been a steady growth in dividends of 5.1% per year. The current price is $25. What is the cost of equity?

RE = D1/ P0 +g=1.50/25+0.051=0.111

28

Pros and Cons of Dividend Growth Model Advantage – easy to understand and use

Disadvantages Only applicable to companies currently paying dividends Not applicable if dividends aren’t growing at a reasonably

constant rate Extremely sensitive to the estimated growth rate – an

increase in g of 1% increases the cost of equity by 1% Does not explicitly consider risk Assume current price is correct price

29

CAPM Approach Use the following information to compute our cost of

equity Risk-free rate, Rf

Market risk premium, E(RM) – Rf

Systematic risk of asset,

E(RE) = Rf + E(E(RM) – Rf)

30

Example

Suppose your company has an equity beta of .58 and the current risk-free rate is 6.1%. If the expected market risk premium is 8.6%, what is your cost of equity capital?

RE = 6.1 + .58(8.6) = 11.1%

31

Pros and Cons of CAPM

Advantages Explicitly adjusts for systematic risk Applicable to all companies, as long as we can compute beta

Disadvantages Have to estimate the expected market risk premium, which

does vary over time Have to estimate beta, which also varies over time We are relying on the past to predict the future, which is not

always reliable

32

Example – Cost of Equity Suppose our company has a beta of 1.5. The market risk

premium is expected to be 9% and the current risk-free rate is 6%. We have used analysts’ estimates to determine that the market believes our dividends will grow at 6% per year and just paid dividend was $2. Our stock is currently selling for $15.65. What is our cost of equity?

Using CAPM: RE = 6% + 1.5(9%) = 19.5% Using DGM: RE = [2(1.06) / 15.65] + .06 = 19.55%

33

Cost of Debt The cost of debt is the required return on the company’s

debt

The required return is best estimated by computing the yield-to-maturity on the existing debt.

34

Example: Cost of Debt Suppose we have a bond issue currently outstanding that

has 25 years left to maturity. The coupon rate is 9% and coupons are paid semiannually. The bond is currently selling for $908.72 per $1000 bond. What is the cost of debt?

YTM = 5*2= 10%

35

Cost of Preferred Stock Reminders

Preferred generally pays a constant dividend every period Dividends are expected to be paid every period forever

Preferred stock is a perpetuity, so we take the perpetuity formula, rearrange and solve for RP

RP = D / P0

36

Example: Cost of Preferred Stock

Your company has preferred stock that has an annual dividend of $3. If the current price is $25, what is the cost of preferred stock?

RP = 3 / 25 = 12%

37

Weighted Average Cost of Capital

We can use the individual costs of capital that we have computed to get our “average” cost of capital for the firm.

This “average” is the required return on our assets, based on the market’s perception of the risk of those assets.

The weights are determined by how much of each type of financing that we use.

38

Capital Structure Weights

Notation E = market value of equity = # outstanding shares times price

per share D = market value of debt = # outstanding bonds times bond

price V = market value of the firm = D + E

Weights wE = E/V = percent financed with equity wD = D/V = percent financed with debt

39

Example: Capital Structure Weights

Suppose you have a market value of equity equal to $500 million and a market value of debt = $475 million.

What are the capital structure weights?

o V = 500 million + 475 million = 975 million

o wE = E/V= 500 / 975 = .5128 = 51.28%

o wD = D/V = 475 / 975 = .4872 = 48.72%

40

Taxes and the WACC We are concerned with after-tax cash flows, so we need to

consider the effect of taxes on the various costs of capital

Interest expense reduces our tax liability This reduction in taxes reduces our cost of debt After-tax cost of debt = RD(1-TC)

WACC = wERE + wDRD(1-TC)

41

Practice – WACC

42

Equity Information50 million shares

$80 per share

Beta = 1.15

Market risk premium = 9%

Risk-free rate = 5%

Debt Information1 million in outstanding

debt contractsCurrent price per contact=

1100Coupon rate = 9%,

semiannual coupons15 years to maturity

Tax rate = 40%

Flotation Costs

Flotation costs – the cost of issuing new securities. Underwriting fees, Legal fees, Registration fees

These costs should be taken into account when evaluating a new project.

Basic ApproachCompute the weighted average flotation cost

Use the target weights because the firm will issue securities in these percentages over the long term

43

Example: NPV and Flotation Costs Your company is considering a project that will cost $1 million. The

project will generate after-tax cash flows of $250,000 per year for 7 years. The required return is 15%. The flotation cost for equity is 5% and for debt is 3%. What is the NPV for the project after adjusting for flotation costs? Weight of 0.375 for debt and 0.625 for equity.

Positive NPV of 40,105 without considering flotation costs.

With flotation costs: fA = (.375)(3%) + (.625)(5%) = 4.25%PV of future cash flows = 1,040,105NPV = - 1,000,000/(1-0.0425) + 1,040,105 = -4,281

Once we consider the cost of issuing new securities, the NPV becomes negative.

44

Example: if a firm sells new shares of common stock for $25 per share but incurs transaction costs of $5 per share, then the cost of capital for the new common equity is increased.

Assume that the investor’s required return = 15% for each $25 share. Then 0.15 * 25 = $3.75 must be earned each year to satisfy the investor’s required return. (assume, payout ratio = 100%, growth rate = 0)

However the firm has only $20 to invest, the cost of capital (k) is calculated as the rate of return that must earn on $20 net proceeds, which has to produce a dollar return of $3.75; that is

20 * k = 25 * 0.15 = 3.75

k = 3.75/20 = 0.1875 = 18.75%

Dividend Growth Model

knc = + g

Cost of External Equity

D1NPo

Net proceeds to the firmafter flotation costs!

Example: The expected dividend is $2.50 for a share of stock

priced at $25. What is the cost of retained earnings if the long-term growth in dividends is projected to be 8%?

K = (D1/V) +g = (2.5/25) + 8% = 18%

To increase the value of firm, the firm’s manager has to find a project that gives return higher than 18%.

When flotation cost = 0, investor’s require return on equity = cost of common equity.