Finance Exam 4
Net present value: Sum of the PVs of all cash flows
the difference between an investment's market value and its cost. A measure of how much value is created or added today by undertaking an investment. If the difference between estimated total cost and estimated market cost is positive, then this investment is worth undertaking because it has a positive estimated net present value. There is risk because there is no guarantee that our estimates will turn out to be correct. NPV = n S t=0 CFt / (1+R)^t Initial cost often is CF0 and is an outflow. NPV = n S t=1 [CFt / (1+R)^t] - CF0
capital budgeting
trying to determine whether a proposed investment or project will be worth more than it costs once it is in place. *Components:* Analysis of potential projects, Long-term decisions, Large expenditures, Difficult/impossible to reverse, Determines firm's strategic direction
the expression we came up with for the constant growth case...
will work for any growing perpetuity, not just dividends on common stock. If C1 is the next cash flow on a growing perpetuity, then the present value of the cash flows is given by: PV = C1 / (R - g) = C0(1 + g) / R - g
IRR & Non-Conventional Cash Flows
"Non-conventional:" Cash flows change sign more than once *Most common:* Initial cost (negative CF), A stream of positive CFs Negative cash flow to close project. For example, nuclear power plant or strip mine. More than one IRR ....
Discounted cash flow
(a) Valuation calculating the present value of a future cash flow to determine its value today. (b) The process of valuing an investment by discounting its future cash flows.
Rationale for the NPV Method
NPV = PV inflows - Cost NPV=0 → Project's inflows are "exactly sufficient to repay the invested capital and provide the required rate of return" NPV = net gain in shareholder wealth *Rule:* Accept project if NPV > 0
Constant rate, Constant growth stock
One whose dividends are expected to grow forever at a constant rate, g. Suppose we know that the dividend for some company always grows at a steady rate. Call this growth rate g. If we let D0 be the dividend just paid, then the next dividend, D1, is: D1 = D0 X (1 + g) The dividend in two periods is: D2 = D0 X (1 + g)^2 *General Formula:* Dt = D0 X (1 + g)^t D0 = Dividend JUST PAID; D1 to Dt = Expected dividends
The dividend growth model calculates the total return as:
R = Dividend Yield + Capital Gains Yield or R = D1 / P0 + g
let P0 be the current price of the stock...
and assign P1 to be the price in one period. If D1 is the cash dividend paid at the end of the period, then: P0 = (D1 + P1) / (1 + R) where R is the required return in the market on this investment.
Estimating Dividends Special Cases
1) *Constant dividend/Zero Growth:* Firm will pay a constant dividend forever, Like preferred stock, Price is computed using the perpetuity formula 2) *Constant dividend growth:* Firm will increase the dividend by a constant percent every period 3) *Supernormal growth:* Dividend growth is not consistent initially, but settles down to constant growth eventually
NPV Method
1) *Meets all desirable criteria:* Considers all CFs, Considers TVM, Adjusts for risk, Can rank mutually exclusive projects 2) Directly related to increase in VF 3) Dominant method; always prevails
advantages of IRR
1) Closely related to NPV, often leading to identical decisions 2) easy to understand and communicate
Conflicte between NPV & IRR
1) NPV directly measures the increase in value to the firm 2) Whenever there is a conflict between NPV and another decision rule, always use NPV 3) IRR is unreliable in the following situations:Non-conventional cash flows & Mutually exclusive projects
Developing The Model
1) You could continue to push back when you would sell the stock 2) You would find that the price of the stock is really just the present value of all expected future dividends
Finding the Required Return Example
A firm's stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return? P0 = $10.50; D0 = $1; g = 5% per year. R = [D0(1+g) / P0] + g = (D1 / P0) + g => R = Dividend yield + Capital Gains yield R = 1(1.05) / 10.50 + .05 = 15%
Net present value profile
A graphical representation of the relationship between an investment's net present values and various discount rates. As the discount rate increases, the NPV declines smoothly.
Zero growth; Stock Value = PV of Dividends
A share of common stock in a company with a constant dividend is much like a share of preferred stock. We know that the dividend on a share of preferred stock has zero growth and thus is constant through time. This implies that: D1 = D2 = D3 = D = constant So, the value of the stock is: P0 = D / (1+R) + D2 / (1+ R)^2 + D3 / (1 + R)^3 + D4 / (1 + R)^4 ... Because the dividend is always the same, the stock can be viewed as an *ordinary perpetuity* with a cash flow equal to D every period. The per-share value is thus given by: P0 = D/R, where R is required return *EX:* Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price? *P0 = 0.5 / (.1/4) = $20*
mutually exclusive investment decisions
A situation where taking one investment prevents the taking of another. Two projects that are not mutually exclusive are said to be *independent.*
growing perpetuity
An asset with cash flows that grow at a constant rate forever
net present value rule
An investment should be accepted if the net present value is positive and rejected if it is negative. A direct measure of how well this project will meet the goal of increasing shareholder wealth. NPV > 0 means: (1) Project is expected to add value to the firm (2) Will increase the wealth of the owners
dividend growth model "Gordon Growth Model"
As long as the growth rate, g, is less than the discount rate, R, the present value of this series of cash flows can be written very simply as: P0 = D0(1 + g) / R - g = D1 / R - g; If we rearrange this to solve for R, we get: R = [D0(1+g) / P0] + g = (D1 / P0) + g; (D1/P0) is *dividend yield:* a stock's expected cash dividend divided by its current price & (g) is *capital gains yield:* the dividend growth rate, or the rate at which the value of an investment grows. *Def:* Model that determines the current price of a stock as its dividend next period divided by the discount rate less the dividend growth rate. The price of the stock as of time t is: Pt = Dt X (1 + g) / R - g = Dt+1 / R - g
Nonconstant + Constant growth
Basic PV of all Future Dividends Formula: P0 = D / (1+R) + D2 / (1+ R)^2 + D3 / (1 + R)^3 ... P0 = D / (1+R) + D2 / (1+ R)^2 + P2 / (1 + R)^2 *Dividend Growth Model:* Pt = Dt +1 / R-g
problems with the IRR
Can produce multiple answers, Cannot rank mutually exclusive projects, Reinvestment assumption flawed
Projected Dividends
D0 = $2.00 and constant g = 6% D1 = D0(1+g) = 2(1.06) = $2.12 D2 = D1(1+g) = 2.12(1.06) = $2.2472 D3 = D2(1+g) = 2.2472(1.06) = $2.3820
Constant Growth Model Conditions
Dividend expected to grow at g forever Stock price expected to grow at g forever Expected dividend yield is constant Expected capital gains yield is constant and equal to g Expected total return, R, must be > g Expected total return (R): = expected dividend yield (DY) + expected growth rate (g) = dividend yield + g
Example 7.3 Gordon Growth Company
Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. What is the price expected to be in year 4? P4 = D4 (1 +g) / R-g = D5 / R-g D5 = D1 (1+g)^4 P4 = 4(1+0.06)^4 / .16-.06 =$50.50
Reinvestment Rate Assumption
IRR assumes reinvestment at IRR; NPV assumes reinvestment at the firm's weighted average cost of capital(opportunity cost of capital): More realistic & NPV method is best NPV should be used to choose between mutually exclusive projects
cash flows for stockholders
If you own a share of stock, you can receive cash in two ways: (1) the company pays dividends (2) you sell your shares, either to another investor in the market or back to the company As with bonds, the price of the stock is the present value of these expected cash flows: (1) dividends -> cash income (2) selling -> capital gains
DGM - Example 1
Suppose Big D, Inc. *just paid* a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? D0= $0.50; g = 2%; R = 15% P0 = D0(1 + g) / R - g => P0 = 0.5(1 + 0.2) / 0.15 - 0.02 = $3.92
DGM - Example 2
Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price? D1 = $2.00; g = 5%; r = 20% P0 = D1 / R - g => P0 = 2/ 0.2 - 0.05 = $13.33
Nonconstant growth rate example
Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock? Remember that we have to find the PV of all expected future dividends. 1) Compute the dividends until growth levels off *D1*= 1(1.2) = $1.20; *D2*= 1.20(1.15) = $1.38; *D3*=1.38(1.05) = $1.449 2) Find the expected future price at the beginning of the constant growth period: P2 = D3 / (R - g) = 1.449 / (.2 - .05) = 9.66 3) Find the present value of the expected future cash flows P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67
One Period Example
Suppose you are thinking of purchasing the stock of Moore Oil, Inc. You expect it to pay a $2 dividend in one year. You believe you can sell the stock for $14 at that time. You require a return of 20% on investments of this risk. What is the maximum you would be willing to pay? D1 = $2 dividend expected in one year; R = 20%; P1 = $14; CF1 = $2 + $14 = $16; Compute the PV of the expected cash flows: P0 = (2 + 14) / 1.20 = $13.33
Given two or more mutually exclusive investments, which one is the best?
The best one is the one with the largest NPV. Can we also say that the best one has the highest return? As we show, the answer is no.
Internal rate of return (IRR)
The discount rate that makes the net present value of an investment zero. Conceptually is the "Expected Return on the Project." It only depends on the cash flows of a particular investment, not on rates offered elsewhere. Most important alternative to NPV, Widely used in practice, Intuitively appealing, Based entirely on the estimated cash flows, Independent of required return. *Formula:* 0= n S t=0 CFt / (1+IRR)^t *IRR rule:* an investment is acceptable if the IRR exceeds the required return. It should be rejected otherwise. The IRR on an investment is the required return that results in a zero NPV when it is used as the discount rate.
Nonconstant growth rate
The main reason to consider this case is to allow for "supernormal" growth rates over some finite length of time. As we discussed earlier, the growth rate cannot exceed the required return indefinitely, but it certainly could do so for some number of years. *As always,* the value of the stock is the present value of all the future dividends.
multiple rate of return
The possibility that more than one discount rate will make the net present value of an investment zero.
What is the price in one period, P1?
We don't know in general. Instead, suppose we somehow knew the price in two periods, P2. Given a predicted dividend in two periods, D2, the stock price in one period would be: P1 = (D2 + P2) / (1 + R) If we were to substitute this expression for P1 into our expression for P0, we would have: P0 = D1 / (1+R) + D2 / (1+ R)^2 + P2 / (1 + R)^2 Now we need to get a price in two periods. We don't know this either, so we can procrastinate again and write: P2 = (D3 + P3) / (1 + R) If we substitute this back in for P2, we have: P0 = D1 / (1+R) + D2 / (1+ R)^2 + D3/ (1 + R)^3 + P3 / (1 + R)^3
Three Period Example
What if you decide to hold the stock for three years? Now how much would you be willing to pay? D1 = $2.00; CF1 = $2.00; D2 = $2.10; CF2 = $2.10; D3 = $2.205; P3 = $15.435 P0 = 2 / 1.20 + 2.10 / (1.20)^2 + (2.205 + 15.435) / (1.20)^3 =$13.33 *In calc:* CF0= 0; C01= 2; F01= 1; C02= 2.1; F02= 1; C03= 17.64; F03= 1; Press NPV; I= 20; CPT NPV = 13.33
Two Period Example
What if you decide to hold the stock for two years? Now how much would you be willing to pay? D1 = $2.00; D2 = $2.10; CF1 = $2.00; P2 = $14.70 P0 = 2 / 1.20 + (2.10 + 14.70) / (1.20)^2 = $13.33
if the constant growth rate exceeds the discount rate, then the stock price is infinitely large.
Why? If the growth rate is bigger than the discount rate, then the present value of the dividends keeps on getting bigger and bigger. Essentially, the same is true if the growth rate and the discount rate are equal.
NPV Example
Year 0: CF = -165,000 Year 1: CF = 63,120; NI = 13,620 Year 2: CF = 70,800; NI = 3,300 Year 3: CF = 91,080; NI = 29,100 Average book value = $72,000; Your required return for assets of this risk is 12%. *NPV = n S t=0 CFt / (1+R)^t* NPV = -165,000/(1.12)0 + 63,120/(1.12)1 + 70,800/(1.12)2 + 91,080/(1.12)3 = 12,627.41 *In calc:* CF0= -165000; CF1= 63120, CF2= 70800; CF3= 91080; Click NPV; I= 12; CPT NPV= 12627.41
does the IRR and NPV rules always lead to identical decisions?
Yes, if (1) the project's cash flows must be *conventional*, meaning that the first cash flow (the initial investment) is negative and all the rest are positive. *Non-concentional:* Cash flow sign changes more than once (2) the project must be *independent*, meaning that the decision to accept or reject this project does not affect the decision to accept or reject any other. *Mutually exclusive projects:* meaning, The acceptance of one project precludes accepting the other. Initial investments are substantially different, Timing of cash flows is substantially different, Will not reliably rank projects
