Lecture Notes: Part II
Finance 302 Spring 2009
Capital Budgeting and Risk: Chapter 10
Topics:
WACC
Asset Betas
When you can (can’t) use the WACC as a discount rate.
A firm’s value can be stated as the sum of the value of the assets; PV of cash flows that accrue (sooner or later) to bondholders and stockholders. I.e.,:
Firm value = PV of cash flows assets produce for security holders (debt, PS, CS)
Example of projects of differing risk:
What would happen if we used the WACC to evaluate ALL projects (both high and low risk)?
Company Cost of Capital (COC) is based on the average beta of the assets. The average Beta of the assets is based on the % of funds in each asset
Example
1/3 New Ventures =2.0
1/3 Expand existing business =1.3
1/3 Plant efficiency =0.6
AVG of assets = 1.3
R2 = .27
β = 1.61
Price data: Dec 97 - Apr 04
Issue: How stable is beta?(What we really want in the future beta.) Can we estimate it using past data? Beta Stability: Chart: percentage of stocks in same risk category 5-years later. Notes:
The Weighted Average Cost of Capital:
WACC: for a firm with only D & common E: (Text generally leaves tax issues for later chapters to focus on the intuition in Chapter 10)
(1-Tc)D/(D+E) rD + E/(D+E) rE
The WACC measures req rate for projects of:
a)All risks
b)Average risk
c)Some risk (not riskless)
Why does the WACC use the after-tax cost of debt?
EXG: $1000, 10% bond. Tc = 40% How much after-tax cash flows could have been used to pay bond’s interest?
EBT 100(could be used to pay “I” of $100)
Less Tax-40
= NI 60 (10% before tax payoutequivalent to a 6%
After-tax payout. )
COC = rportfolio = rassets
rassets
assets
requity
IMPORTANT:E, D, and V are all market values.
debt < asset < equity
•Concept:
–Balance sheets balance in:
•Book value (accounting)
•Market value (V = D + E)
•Risk (&): Beta of assets is weighted average beta of debt & equity
•Expected rates of return
–Expected return on assets = weighted average of expected rate on debt + equity.
Projects that are not of average risk:
•Easier to assess risk when measured RELATIVE to your typical project
•Make an ad-hoc adjustment to your WACC, and use as a discount rate
Characteristics that affect market risk (beta) of a project:
1)Cyclicality of cash flows
2)Fixed operating costs
Discussion: Are the following risks mostly Diversifiable or Undiversifiable (Market) risk?
•|Risk that an oil well will come up dry
•Risk that a new drug to cure baldness will not be approved by the FDA
•Risk to Sheraton that their hotel in Lebanon will be bombed by terrorists
•Risk that people, worried about job security, delay purchase of a new SUV
•Risk that people, worried about the price of oil, delay the purchase of a new SUV.
•Risk that the Fed will raise interest rates, thus reducing the volume of sales of spring clothing made on (variable rate) credit cards.
International Project Risk
Which risks should be incorporated into the discount for international projects rate?
Does it matter that US investors tend not to be optimally diversified internationally?
Which is riskier for an investor in the US – the S&P composite or the stock market in Egypt?
Egyptian stocks have more total risk (Var), but a lower beta than US stocks, because they have a lower return correlation to US stocks
International Risk:
σ Ratio - Ratio of standard deviations, country index vs. S&P composite index
•EXG:
–Carrefour, a French retailing giant is considering opening stores in the US. The beta for such a project is 1.1 for such stores in France. Similarly, for US firms, the beta for opening a new store in the US is also 1.1.
–The market risk premium for French stocks in 7%. Carrefour therefore determines that the correct discount rate for their new US store is: Euro i-rate + 1.1(7%) = 7.7% above euro rate. Is this correct? Are there other considerations?
Chapter 6:Introduction to NPV analyses
If we assume “efficient markets,” should positive NPV projects exist?
Sources of positive NPV:
1) Special skills of employees
2) Duopoly or monopoly investment powers
3) Technological innovation
4) New untapped markets
5) Brand loyalty
6) Cost Advantage
Beware: Math error on part of analyst or persons providing cash flow estimates.
•Note: Sometimes NPV is NOT the best method to value an asset. I.e., when there is an active secondary market for the asset, it is often better to consider market prices to best represent asset value.
i.e., Rental properties
Commercial Aircraft
Land for development
Part I: Identifying Incremental Cash Flows
Incremental Cash Flows
•Cash flows that occur as a result of accepting the project, which would not be incurred were the project to be rejected (or discontinued).
Where does the financial manager obtain the numbers to use in capital budgeting?
Cash flow review
Total Revenues
-Total expenses
- Depreciation
=EBT
- taxes
=Net Income
+ Deprecation
CASH FLOW
Why do we subtract depreciation, only to add it back in later on?
What is the impact on a project’s cash flows if $10,000 in depreciation weremistakenly excluded from the analysis… Assume Tc = 30%
Depreciation tax shield:
The tax savings from depreciation
= Tc x $deprec
Side Effects:
Impact of your project on firm’s other cash flows
May be positive or negative “cannibalization”
Examples:
1) Impact on book sales of having a coffee shop in the store
2) Impact on tire sales for doing muffler work
3) Impact on Toyota Sienna (minivan) sales for producing Toyota Sequoia (large SUV
Should side-effects be included in our analysis?
Sunk Costs: Money which has already been spent; can’t be recovered if the project is halted, rejected or discontinued at the time of the analysis.
Should sunk-costs be included in our analysis?
Opportunity Costs: Cost of using an asset that your firm already owns – measured by its value when put to its next best use.
Examples:
Use of warehouse your firm already owns
Use of machine your firm already owns
Use of some stored furniture that your firm already owns
Should opportunity costs be included in our analysis?
How do you value an opportunity cost?
•Use asset’s highest value when put to an alternative use.
•Opportunity costs arecash outflows, i.e., they represent a cash flow that the firm will notreceive when the asset is used in an alternative way.
Other cash flows and special valuation techniques:
1)Change in NWC (Net Working Capital)
NWC = current assets - current liabilities
Current Assets (CA): Cash, Accts Rec., Inventory
Current Liabilities (CL): Accts Payable
1) Suppose the change in NWC is positive. Is this a net inflow or outflow?
2) In general, will the change in NWC be positive or negative at the start of the project?
…at the end of the project?
3) What if the asset is to be replaced with a like asset at the end of the project? Should weconsider any change in NWC to occur at the end of the life of the project?
2) Treatment of Inflation: Should we consider the impact of inflation (or other expected changes in price) when estimating future cash flows?
(Note: Some products may be expected to decline in price over the life of a project: I.e., high tech products like Plasma TVs. This will affect future revenue estimates.)
Other than revenues, which cash flows would also likely be affected by changes associated with inflation?
3) Treatment of cash flows of varying risk:
The objective of NPV analyses is to discount cash flows by a rate which reflects the riskiness of the cash flows. Are SOME cash flows in a project riskier (less certain) than others? What types of cash flows MIGHT be known with certainty?
4) Valuing projects with cash flows of unequal risk: Discount riskless cash flows by risk free rate, and risky cash flows by risky rate (or WACC if appropriate).
Example:Initial outlay: $100,000, no salvage value
Dep = $20,000 for 5 yrs, riskless cash flow
Revenues (risky) $60,000 for 5 yrs
Expenses (risky) $20,000 for 5 yrs
Expenses (riskless – contracted labor) $10,000 for 5 yrs
Riskless rate = 5%
Risky rate = 10%
Tax rate = 30%
time/PV / aft tax / 0 / 1 / 2 / 3 / 4 / 5-100000 / -100000 / init outlay / -100000
Revs / 60000 / 60000 / 60000 / 60000 / 60000
227447 / 159213 / PV of rev / 54545 / 49587 / 45079 / 40981 / 37255
Exp (risky) / -20000 / -20000 / -20000 / -20000 / -20000
-75816 / -53071 / PV of exp / -18182 / -16529 / -15026 / -13660 / -12418
Exp (riskless) / -10000 / -10000 / -10000 / -10000 / -10000
-43295 / -30306.3 / PV of exp / -9524 / -9070 / -8638 / -8227 / -7835
Dep Tax shield / 6000 / 6000 / 6000 / 6000 / 6000
25977 / 25977 / PV of DTS / 5714 / 5442 / 5183 / 4936 / 4701
NPV / 1813
Practice Problems 1: SPROCKETS
Compute the NPV of the following project:
A project to manufacture SPROCKETS is being considered.
a)Initial outlay is $100,000 to be depreciated straight line down to $0 in 10 years. The machine will be sold in year 5 for 70,000 and the project will end at that time.
b)Revenues are expected to be $50,000, and decrease at a rate of 5% per year.
c)Actual expenses associated with the project are expected to be 20% of the expected revenues for each year.
d)Working capital will increase by $5,000 at time 0, increase by another $2000 in year 1, and decrease by $7,000 at the end of 5 years.
e)This project will decrease the sales revenue of the WIDGET division by $1000 (before tax) per year but will increase sales of the GADGET division by $2000 per year (before tax). All expenses associated with these divisions will remain unchanged.
f)The Sprocket project will be funded using a 100,000 10% bond issue.
g)The firm discounts risky cash flows by the risky rate, and riskless cash flows by the riskfree rate of 5%. The depreciation tax shield is the only riskless cash flow.
h)The corporate tax rate is 30%
i)If the project is accepted, the firm will hire consultants to decide how to market the SPROCKETS, at a cost of $4000 in year 1 (before tax)
j)The firm’s WACC is 12%. The above project is of average risk to the firm.
Practice problem 2: Compute the NPV of the following projectto make widgets. The project will involve the following outlays:
A) A $25,000 study conducted last month determined that the Widgets project will produce annual revenues of $600,000, and require annual expenses of $200,000 at the end of year 1. Revenues will increase at the rate of inflation of 5% per year, starting in year 2. Costs will increase at 8% per year, starting in year 2. The project will continue through year 5.
B) Cost of the Widget machine: $1,000,000, to be incurred at the start of the project (time = 0) & depreciated as a 7-year class asset using MACRS . The Widget machine will be sold for $100,000 at the end of year 5.
MACRS depreciation schedule:
1 / 2 / 3 / 4 / 5 / 6 / 7 / 814% / 25% / 17% / 13% / 9% / 9% / 9% / 4%
C) At the start of the project, cash will increase by $50,000, Accounts Receivable will increase by $40,000, and inventory will increase by $50,000. Accounts Payable will increase by $20,000. At the end of year 5, there is a 95% probability that the widget machine will be replaced by a new widget machine, which will require similar levels of cash, accounts receivable and inventory and have similar amounts of accounts payable as that associated with the old machine. However, if the widget project were not to be continued, the working capital would be recaptured at the end of year 5.
D) The widget project will be housed in a warehouse that the company already owns, and has fully depreciated. If the warehouse were not used to house this project, it could be leased for (before tax) revenues of $50,000 per year, to be paid at the end of years 1-5.
E) [Note: “Cogs” in this question refers to a piece of machinery, not “cost of goods sold”] Since Widgets and Cogs are interchangeable parts, the widget project will decrease the sales revenues of Cogs by $50,000 per year, but decrease costs of manufacturing Cogs by $20,000 per year. Since Cogs are produced by contracted laborers, the costs will be unaffected by inflation – however, Cog revenues increase at the inflation rate, starting in year 2.
F) The project will be funded through a 1,000,000 10% 5-year bond issue, with interest paid annually, at the end of each year.
G) The project will take up 10% of the area in the warehouse, and associated costs will be allocated by the firm’s accountants to the firm’s widget division, based on 10% of the total warehouse overhead. Overhead to keep the warehouse heated, and electricity to keep the warehouse operational is $100,000 per year, total. However, the actual cost of the utilities to run the widget machine = $20,000 per year.
H) The firm’s cost of debt (before tax) is 10%. The firm’s cost of equity is 16%, and the riskless rate is 6%. The firm’s debt/asset ratio is 40%. The firm discounts riskless cash flows by the riskless rate. The project is of average risk for the firm – however the firm’s discounts riskless cash flows by the riskless rate. Riskless cash flows are any contracted cash flows and the depreciation tax shield.
Assume a corporate tax rate of 30%.
Practice Problem III: Compute the NPV of the following project to make Gadgets.
1)ABC Corp is considering a 5-year project to manufacture GADGETS. They anticipate the following cash flows. The corporate tax rate is 25%.The firm discounts all cash flows by a rate of 15%, except for riskless cash flows, which they discount at a rate of 6%. Only the depreciation tax shield and other cash flows listed as “known with certainty” are discounted at the riskless rate.
2)The GADGET machine will cost $1.5 million– to be paid in two installments; $1 million at the time of purchase and $500,000 at the end of the first year.
3)The GADGET project is somewhat unusual, in that it will DECREASE net working capital by $50,000 at time=0 and INCREASE net working capital by $50,000 at time = 5, when NWC is recaptured. However, the firm expects to buy another GADGET machine at the end of year 5, causing NWC to decrease by $50,000 at that time.
4)The GADGET machine will be depreciated, straight line, over 10 years, down to 0. However, the GADGET machine will be sold at the end of year 5 for $600,000. At this time, the project will be discontinued.
5)Revenues associated with this project are expected to be $900,000 in year 1, and will increase at a rate of 8% per year. The gadgets are contracted to be sold to the military, so the revenues are known with certainty.
6)Expenses associated with the project (excluding utilities) are expected to be 40% of revenues in year 1 (only), and increase at a rate of 5% per year, thereafter. Unlike revenues, expenses are not known with certainty.
7)The GADGET project will be housed in a warehouse that the company already owns. If the GADGET project were not housed there, the warehouse could be leased to NBC Co on a five-year lease, for $200,000 per year, before taxes.
8)The GADGET project will occupy 10% of the floor space in the warehouse. 10% of the warehouse’s total utilities (of $10,000 per year – including the GADGET machine) will be allocated to the division producing the GADGETS. However, actual warehouse utility bills will increase by $50,000 as a direct result of the GADGET project.
9)The firm’s net revenues of “thingamajigs” will decrease by $100,000 in year 1, as a direct result of the gadget project. If the firm decides not to produce Gadgets, net revenues of thingamajigs would increase at a rate of 5% per year.
10)If the project is accepted, the firm will contract with quality control consultants for $100,000 at time=1, to ensure sufficient quality control, as per government contract specifications.
11)The project will be funded with an equity issue, requiring $20,000 in additional dividends per year.
5) Valuing projects with unequal lives:
Valuation method: Compute the NPV of the projects, assuming that the projects are extended for a given number of lives, so that both projects end at the same time. (# of lives will be lowest common denominator of the two projects’ lives.)
Example 1Projects A and B are mutually exclusive. Project A requires an initial outlay of $100, and will produce a cash inflow of 30 for 5 years
Project B requires an initial outlay of $132, and will produce a cash inflow of $25 for 10 years. Both projects will be replaced, ad-infinitum.
Which project should you accept? The cost of capital is 12%
YEAR / 0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
A / initial outlay / -100 / -100
net cash flows / 30 / 30 / 30 / 30 / 30 / 30 / 30 / 30 / 30 / 30
PV / -100.00 / 26.79 / 23.92 / 21.35 / 19.07 / -39.72 / 15.20 / 13.57 / 12.12 / 10.82 / 9.66
B / initial outlay / -132
net cash flow / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25
PV / -132.00 / 22.32 / 19.93 / 17.79 / 15.89 / 14.19 / 12.67 / 11.31 / 10.10 / 9.02 / 8.05
NPV (A) = / 12.76
NPV (B) = / 9.26
On your own:
Practice Problem 1Projects A and B are mutually exclusive. Project A requires an initial outlay of $10, and will produce a cash inflow of $4 for 6 years
Project B requires an initial outlay of $12, and will produce a cash inflow of $7 for 4 years. Both projects will be replaced, ad-infinitum.
Which project should you accept? The cost of capital is 10%
Practice Problem 2
Projects X and Y are mutually exclusive. Project X requires an initial outlay of $60, and will produce a cash inflow of $35 for 6 years
Project Y requires an initial outlay of $80, and will produce a cash inflow of $25 for 10 years. Both projects will be replaced, ad-infinitum.
Which project should you accept? The cost of capital is 8%
Practice Problem 3
Projects K and L are mutually exclusive. Project K requires an initial outlay of $4000, and will produce a cash inflow of $800 for 10 years
Project L requires an initial outlay of $700, and will produce a cash inflow of $600 for 2 years. Both projects will be replaced, ad-infinitum.
Which project should you accept? The cost of capital is 12%
Reference formulas
A) Cost of Debt: rD: cost at which debt of similar maturity (to the project) could be issued. Most firms match maturity of the debt to that of the assets (except for banks).
B) Cost of Preferred stock: rPE
Dps / P0
C) Cost of Common Equity: rS
1) From the CAPM:
rS= Rf + [Rm - Rf]
[Rm - Rf] = Market Risk Premium
Rm = Expected rate of return on the Market
2) Solving the formula: P0= D1 /(rS-g) for “rS”:
rS= D1/P0 + g
What is the difference (if any) between the cost of debt, equity and preferred stock for the firm, and the required rate of return on debt, equity and preferred stock (for the investors)?
Although not explicitly noted in the above formulas, all costs measured by the above formulas are net of floatation costs.
Chapter 11: Sensitivity Analysis / Monte-Carlo Simulation