Business Valuation Methods

Prepared by Professor Kirby D. Cochran and Eric E. Anderson, PhD

January 2014

Agenda

Three Valuation Methods Comparison of Valuation Methods The Income Approach

– Time Value of Money– Free Cash Flow– Discounted Cash Flow (DCF) Analysis– Internal Rate of Return (IRR)

Discount Rate and Cost of Capital Models– Cost of Capital Models– Risk Premium Factors

Equity Risk Premiums Exercises

2

What is Valuation?

• Valuation is an unbiased process of determining the current worth of economic value of an asset or business

• It is an appraisal that takes into account both the positives and negatives of a business

3

3 Basic Valuation Methods

• Market Approaches (Comparable Approach)– Uses The market for similar businesses, including comparable sales – Ratio methods– Direct Market Data Method (Guideline Transaction Method)– Industry rule of thumb

• Asset Approaches– Book Value– Replacement Cost– Liquidation Value

• Income Approaches– Historical Earnings - including debt-paying ability, capitalization of earnings or cash

flow (T0/(d-g)), gross income multipliers, and dividend-paying ability methods – Future Earnings – the most appropriate for stable, profitable companies

• NPV, IRR• Combination of Approaches (or Blended Approaches)

– Assets and Earnings (e.g., Excess earnings method)– Market and Income

4

Which Valuation Method is Most Appropriate?

Valuation Approach Typical Usage Pros ConsMarket Approach

• Value based on Comparing Business with its Peers (Industry & Specific Companies)

• Most valuations in stock markets are market based.

• Also known as Relative Valuation Approach or Comparable Approach

• Simpler to compute• Takes into account both

supply and demand factors and current market climate

• Many businesses are unique • Difficulty in finding

comparable businesses• Growth only implicitly

considered

Asset Approach

• Value based on adjusted net book value (Assets less Liabilities)

• Often used for Mature or Declining growth cycle businesses

• Used for Strong Asset Base companies• Liquidation Valuation

• Easier to support valuation• Good indicator of barriers to

entry for asset intensive businesses

• Serves as Sanity Check on business value

• Results are often lower than fair-market-value because the method doesn’t consider ongoing business concerns and growth

Income Approach

• Current value is function of Future value that an investor can expect to receive from purchasing some or all of business

• Use Discounted cash flow analysis to determine present value of future returns from a business (NPV, IRR)

• Used for valuing profitable businesses expected to continue operating for the foreseeable future (a going concern)

• Most accurately represents the economic value of a particular business

• Accurately models future growth

• Doesn’t require identification of comparable companies

• More difficult to compute• Requires detailed financial

model• Early stage companies

require forecast with no track record

• Must determine appropriate discount rate

5

Income Approach to Business Valuation

7

The Income Approach to Business Valuation

• The Income Approach address 2 fundamental questions associated with valuation of a business:

– What are the potential economic benefits of investing time and money into a business?– What are the risks involved in not obtaining all or part of the economic benefit on the

prescribed time schedule?• The Income Approach computes the current value of a business by discounting expected

future economic benefits to current time based on the appropriate discount rate determined by quantifying the associated risks.

• In practice, current value of future earnings is calculated based on– Historical Earnings using Capitalization of Earnings or Cash Flow method– Models of Future Earnings using Discounted Cash Flow Analysis to calculate

• The Net Present Value (NPV)• Internal Rate of Return (IRR)

• Applies to stable, profitable companies and accurately represents the value of a particular business model.

• Relies heavily on the ability to forecast future earnings and to quantify the risks associated with a business

8

The Time Value of Money

• The Time Value of Money is the principle that a certain currency amount of money today has a different buying power (value) than the same currency amount of money in the future.

• The value of money at a future point of time must take account of interest earned and inflation accrued over a given period of time. – There is an opportunity to earn interest on the money.– Inflation will drive prices up, changing the "value" of the monetary benefit streams.

• Present Value is used to account for TVOM in the evaluation of future cash flows– PV evaluates the current worth of a future sum of money or stream of cash flows

discounted at the discount rate. The higher the discount rate, the lower the PV of the future cash flows.

– Several factors can be used to determine the appropriate discount rate including cost of capital and risk factors.

9

Discounted Cash Flow Analysis

A Finite Sum of Cash Flows

• In general a typical business will generate a series of cash flows, Y1, Y2, Y3, …, Yn in years 1, 2, 3,…, n

• Discounted Cash Flow (DCF) analysis computes the Net Present Value (NPV)1,2 which is the sum of all future cash flows, each discounted by the appropriate factor determined by the discount rate, r, and the year the cash is generated.

• In this case, the NPV is given by n NPV(n) = ∑ Yi / (1+r)i

i = 1

where n is the number of years in which the future cash flows are generated

Business 3

• Assume a business yields a series of cash flows of $100 each year for the next 20 years.

• How much would you pay today for this business?

• Assume a discount rate of 10%• Use DCF analysis to evaluate the NPV of all

future cash flows from the business and determine today’s value.

10

Notes: 1. Karl Marx termed NPV, “fictitious capital” in his critique of political economy. It is introduced in chapter 29 of the third volume of Capital prepared by Friedrich Engels from notes left by Karl Marx

and published in 1894.2. NPV was formalized and popularized by Irving Fisher in his 1907 The Rate of Interest and became included in textbooks from the 1950s onwards, starting in finance texts

Discounted Cash Flow Analysis Example

11

NPV of 20 year flow with a 10% discount rate is less than half of the total flows

Estimating Free Cash Flow

• Discounted Cash Flow Analysis typically is based on Free Cash Flow – not Earnings.– A key measure value of a company is the amount of free cash (non-obligated) it generates for its

owners.– Net Income include non-cash items such as depreciation and amortization which can mask the

long term cash generation potential of a company.– Capital Expenditures and changes in Working capital necessary for the operation and growth can

greatly affect cash flow and are not reflected in net income, and need taccounted for

Calculating Free Cash Flow:1. Start with a model of the Income Statement 2. Adjust Net Income (after tax) for non-cash items included on Income statement such as amortization

and depreciation.3. Adjust for changes in necessary working capital items such as Accounts Payable (AP), Accounts

Receivable (AR) and inventory to get Cash Flow from Operations4. Adjust for Capital Items such as Capital Expenditures and gains from salvage to get Free Cash Flow5. Typically model Free Cash Flow on a yearly basis for 5-10 years.

Notes: 6. Often times interest payments are removed from (i.e., added back into) Net Income to remove from affect of a

company’s debt load on earnings. In this manner, Discounted cash flow analysis estimates total Enterprise Value. To arrive at Equity Value, balance sheet cash must be added to and total debt subtracted from EV.

12

Modeling Cash Flows to Equity

13

Value from Operations

Business

Value from investments

EquityDebt and Other

Liabilities

Value Generated

Value to Equity

Enterprise Value

Discounted Cash Flow Analysis

Performing DCF Analysis:1. Start with a model of free cash flow (FCF) typically on a annual basis for 5-10 years.2. Evaluate the risks associated with business model and calculate the annual discount rate using one of

several Cost of Capital or Build-up Methods3. Calculate the Net Present Value (NPV) of the Free Cash Flow over the model period using the discount

rate from step 2.4. Estimate the annual growth in (FCF) as a constant value for all years beyond the model period. 5. Calculate the “Terminal Value” which is an estimate of the value of all future cash flows beyond the

model period. Appropriately discount the terminal value to the present time.6. Add the model NPV result from step 7 and the discounted terminal value from step 9 to arrive at the

DCF Valuation.

Notes: 7. PV discount factors can be generalized to a mid-year convention using the appropriate fractional exponents.8. The model can be generalized to a finite number of growth periods, each with different values for growth, using

multiple terminal value.9. For finite duration businesses, terminal value is not needed and business value includes liquidation value or assets

and working capital.

14

Computing the DCF Value

• The Net Present Value (NPV) of cash flows is given by n NPV(n) = ∑ Yi / (1+r)i

i = 1

where n is the number of years in which the future cash flows are generated, Y1, Y2, Y3, …, Yn is a series of cash flows in years 1, 2, 3,…, n, and

r is the discount rate.• The Terminal Value beyond year n is given by

T0 = Yn (1 + g) / (r – g)

where Yn is the cash flow in year n,

g is the projected annual growth rate in free cash flow beyond year n, and r is the discount rate.

• Calculate the present value of the terminal value as PV(T0, n) = T0 / (1+r)n

• Finally compute the DCF value of the business as DCF(n) = NPV(n) + PV(T0 ,n)

15

DCF Valuation Analysis Example

Example:• Cash flow is given below for years 1 to 5, including initial development investment in Yr 1• Assume discount rate, r = 25%• Assume growth rate, g = 3%, for the period beyond Yr 5• NPV of cash from Yr 1 to 5 with (r = 25%) = $17.36M

• Terminal Value, T0 = 35*(1.03)/(0.22) = $163.8M

• Present value of T0 = T0/(1+0.25)^5 = $53.7M

• DCF valuation = 17.4M + 53.7M = $71.5M

16

164

Y1 Y2 Y3 Y4 Y5 T0

-20 3 15 30 35

Growth Terminal

NPVPV(T0,5)

DCFValue

DCF Analysis of Free Cash Flow ($M)

Development

DCF Analysis for XYZ Genetics – Income Statement

17

CY 2005 - 2009 Financial PlanIncome Statement Annual Trend

Y2005 Y2006 Y2007 Y2008 Y2009

Revenue 5,022 59,437 162,662 315,380 512,364 Cost of Goods Sold 2,943 26,916 63,506 113,263 168,283 - - - - Gross Profit 2,079 32,520 99,156 202,117 344,081 Operating Expenses - G & A 1,621 2,620 4,200 8,223 9,210 Sales & Marketing 1,785 8,809 16,036 27,100 37,160 R&D 4,918 12,080 24,422 42,167 33,381 Total Operating Expenses 8,324 23,509 44,658 77,490 79,751 Pretax Oper. Income (6,245) 9,011 54,499 124,626 264,329 Other I/E 429 322 376 820 2,264 PBT (5,816) 9,334 54,875 125,447 266,593 Taxes - - 19,557 50,179 106,637 Net income (5,816) 9,334 35,317 75,268 159,956

EBITDA (5,441) 10,981 80,918 186,815 382,522

Tax Rate 40% 40% 40% 40% 40%

DCF Analysis for XYZ Genetics – Balance Sheet

18

Balance Sheet

Annual

Y2005 Y2006 Y2007 Y2008 Y2009

Cash 20,711 15,328 26,708 73,690 193,483 A/R 2,362 15,903 36,577 64,248 98,431 Bad Debt Reserve (24) (159) (366) (642) (984) Inventory 1,499 5,420 11,683 18,893 30,124 Other current 192 178 168 158 130 Current assets 24,741 36,670 74,771 156,347 321,184 Fixed Assets 1,686 5,014 14,939 25,834 36,034 Accumulated Depreciation (544) (2,191) (8,677) (19,866) (29,158) Total assets 25,883 39,493 81,032 162,314 328,059 Liabilities - - - A/P & Accruals 1,611 5,888 12,110 18,123 23,939 Other current liabilities - - - - - Current liabilities 1,611 5,888 12,110 18,123 23,939 Lease obligations - - - - - Other long term payables 26 26 26 26 - Total liabilties 1,637 5,914 12,136 18,149 23,939 Shareholders equity 24,245 33,579 68,896 144,164 304,120 Liabilities & Shareholder's Equity 25,883 39,493 81,032 162,314 328,059

CY 2005 - 2009 Financial Plan

DCF Analysis for XYZ Genetics – Cash Flow

19

CY 2005 - 2009 Financial PlanStatement of Cash FlowAnnual

Y2005 Y2006 Y2007 Y2008 Y2009

Gross Cash Generation Net Income / Net Loss (5,816) 9,334 35,317 75,268 159,956 Depreciation & Amortization 206 1,647 6,486 11,190 9,292 Gross Cash Flow (GCF) (5,610) 10,981 41,803 86,457 169,248

Operating Changes Change in Accounts Receivable (2,339) (13,406) (20,467) (27,394) (33,842) Change in Inventory (1,040) (3,921) (6,263) (7,210) (11,231) Change in Other Assets (528) 14 10 10 28 Change in Trade Payables 456 4,277 6,222 6,013 5,816 Change in Other Liabilities - - - - (26) Cash Flow From Operations (CFFO) (9,060) (2,056) 21,306 57,877 129,992

Capital Expenditures (1,117) (3,328) (9,925) (10,895) (10,200) Free Cash Flow (10,177) (5,383) 11,381 46,982 119,792 Increase in Capital Lease Obligatons (CLO's) - - - - - Capital Lease Obligations Amortization - - - - - Net Capital Lease Obligations - - - - -

- - - - Common Stock Issuance of Series A - - - - - Issuance of Series B 5,573 - Issuance of Series C 23,500 - - - - Total Financing Changes 29,085 - - - -

- - - - - Net Increase / Decrease in Cash 18,908 (5,383) 11,381 46,982 119,792

-

Cash-Beginning of Period 1,803 20,711 15,328 26,708 73,690 Cash-End of Period 20,711 15,328 26,708 73,690 193,483

DCF Analysis for XYZ Genetics – Cash Flow

20

Example:• Calculate the Discounted Cash Flow on the free cash flow of XYZ Genetics using a mid-year

convention for PV discount factors.• Assume discount rate, r = 40.0%• Assume growth rate, g = 10.0%, beyond the model period

Discounted Cash Flow Analysis AnnualXYZ Genetics Discount Rate 40.0%(Currency in thousands) FCF Growth Rate beyond model period 10.0%

2005 2006 2007 2008 2009Case I

Free Cash Flow (10,177)$ (5,383)$ 11,381$ 46,982$ 119,792$ PV Factor 0.845 0.604 0.431 0.308 0.220

Discounted FCF (8,601)$ (3,250)$ 4,907$ 14,471$ 26,354$

Sum of Discounted FCFs 33,881$ PV of Terminal Value 96,633$

Total Valuation 130,514$

Internal Rate of Return

• Internal Rate of Return (IRR) or Economic Rate of Return (ERR)is the annual effective compound rate of return that yields zero net present value of future cash flows.

• I.e., the IRR is the value of the discount rate, r = IRR, such that, n NPV(n) = ∑ Yi / (1+r)i = 0 i = 1

where n is the number of years in which the future cash flows are generated, Y1, Y2, Y3, …, Yn is a series of cash flows in years 1, 2, 3,…, n, and r is the discount rate.

• The cash flows included in the IRR calculation, include all cash flows (including the investment, which is considered a negative cash flow).

• Specific, the IRR of an investment is the discount rate at which the NPV of costs (negative cash flows) of the investment equals the NPV of the benefits (positive cash flows) of the investment — In other words, the rate at which an investment breaks even.

• IRR calculations are commonly used to evaluate the desirability of investments or projects. The higher a project's IRR, the more desirable it is to undertake the project.

• A firm (or individual) should, in theory, undertake all projects or investments available with IRRs that exceed the cost of capital.

• Note: The solution of the IRR equation involves the finding roots to the expression, and requires the use of iterative numerical methods such as the secant method. See for example the Excel formula IRR(values, [guess])

21

Internal Rate of Return Analysis Example

Continuing from the previous example:• The Cash flow series is given below for years 1 to 5, and the terminal value in year 6 as

calculated in the previous example.• Using the Excel formula IRR(values,[guess]) = IRR({-20,3,15,30,35,164}) = 88.4%

• To check the answer we calculate the NPV of the cash flow series using r = IRR = 88.4% and verify that NPV = 0.

22

164

Y1 Y2 Y3 Y4 Y5 T0

-20 3 15 30 35

Growth Terminal

IRR

IRR of Free Cash Flow ($M)

Development

Solar DCF Analysis – 4.0 kW-dcTypical Usage / 20% Down / 30% Fed Tax Credit

23

Estimated System Cost and BenefitsTotal per Watt

System Installation Cost 18,000.00$ 4.50$ Local Incentive -$ -$ Fed Tax on Local Incentive -$ -$

State Incentive1 -$ -$

Fed Tax Credit2 (5,400.00)$ (1.35)$ State Tax Credit -$ -$

Depreciation Tax Savings3 -$ -$ Net Customer Cost 12,600.00$ 3.15$

Total Up Front Costs 18,000.00$ 4.50$ Down Payment 3,600.00$ 0.90$ Amount to be Financed 14,400.00$ 3.60$

Estimated Annual Elecricity Generation (kWh)

Source Before Solar With Solar4

Self-Generation - Year 1 - 7,372.00 Utility 10,000.00 2,628.00

% of Demand $/kWh avg73.7% -$ 26.3% 0.26$

Estimated Annual Elecricity Costs*Per Month Per Year

Old Utility Bill (Yr 1) 215.03$ 2,580.35$ New Utility Bill (Yr 1) 34.02$ 408.29$

Energy Savings (Yr 1) 181.00$ 2,172.06$

Financing Costs5 88.30$ $1,059.58*Old bill at $0.26.kWh, New bill avg. rate of $0.155 cents/kWh

Estimated Annual Energy Cost Savings6 (inc. financing costs)Per Month Per Year

Year 1 Savings 92.71$ 1,112.48$ Year 5 Savings 122.46$ 1,469.46$ Year 10 Savings 166.60$ 1,999.23$ Year 20 Savings 284.55$ 3,414.65$ Year 25 Savings 362.63$ 4,351.54$

Total NPV7

Net Savings - 15 years 27,203.78$ 19,790.42$ Net Savings - 20 years 42,668.68$ 25,076.48$ Net Savings - 30 years 87,551.91$ 34,576.74$

Warranty : Inv erter 10 y rs, Modules 20-25 y rs, Installation 10 y rs

Includes Monitoring Sy stem and 5 y rs Monitoring and CSI Reporting

1 Assumes NO CSI EPBB

2 30% Federal Residential Renew able Energy Tax Credit

3 Assumes at 36% total tax rate

4 Estimated Production

5 Assumes for 20 y r loan @ 4%

6 Assumes 3.78% utility inflation and 0.5% degredation

7 Assumes 6% discount rate; Cash flow s include energy cost sav ings, financing, tax credit,

depreciation, and interest ex pense deduction

System Size 4.000 kW-dc

Solar DCF Analysis – 4.0kW-dcTypical Usage / 100% Down / NO Fed Tax Credit

24

Discount Rate Old Energy

Bill

New Energy

Bill Financing

Cost Savings

(including financing)

Federal Tax

Credit Depreciation

Interest

Expense

Total Cash

Flow Benefit 10.00%

Year per year per year per year Per month Per year Cumulative NPV IRR

Net Upfront Investment (inc State Rebate if any)

(18,000.00)$

1 2,580.35$ 408.29$ $0.00 181.00$ 2,172.06$ 2,172.06$ -$ -$ $0.00 2,172.06$ (14,568.55) -88%2 2,677.88 421.60 - 188.02 2,256.28 4,428.34 - $0.00 2,256.28 (12,873.37) -58%3 2,779.11 435.34 - 195.31 2,343.77 6,772.11 - - 2,343.77 (11,272.54) -36%4 2,884.16 449.51 - 202.89 2,434.64 9,206.75 - - 2,434.64 (9,760.82) -22%5 2,993.18 464.14 - 210.75 2,529.04 11,735.79 - - 2,529.04 (8,333.24) -12%6 3,106.32 479.22 - 218.92 2,627.10 14,362.89 - 2,627.10 (6,985.13) -6%7 3,223.74 494.79 - 227.41 2,728.95 17,091.84 - 2,728.95 (5,712.05) -1%8 3,345.60 510.84 - 236.23 2,834.75 19,926.60 - 2,834.75 (4,509.84) 2%9 3,472.06 527.41 - 245.39 2,944.65 22,871.25 - 2,944.65 (3,374.55) 5%

10 3,603.30 544.49 - 254.90 3,058.81 25,930.06 - 3,058.81 (2,302.45) 7%11 3,739.51 562.11 - 264.78 3,177.39 29,107.46 - 3,177.39 (1,290.04) 8%12 3,880.86 580.29 - 275.05 3,300.57 32,408.03 - 3,300.57 (333.98) 10%13 4,027.56 599.04 - 285.71 3,428.52 35,836.54 - 3,428.52 568.86 11%14 4,179.80 618.38 - 296.79 3,561.42 39,397.96 - 3,561.42 1,421.43 11%15 4,337.80 638.32 - 308.29 3,699.48 43,097.44 - 3,699.48 2,226.55 12%16 4,501.77 658.89 - 320.24 3,842.88 46,940.32 - 3,842.88 2,986.84 13%17 4,671.93 680.10 - 332.65 3,991.83 50,932.15 - 3,991.83 3,704.81 13%18 4,848.53 701.97 - 345.55 4,146.56 55,078.71 - 4,146.56 4,382.80 13%19 5,031.81 724.52 - 358.94 4,307.28 59,386.00 - 4,307.28 5,023.05 14%20 5,222.01 747.78 - 372.85 4,474.23 63,860.23 - 4,474.23 5,627.66 14%21 5,419.40 771.76 - 387.30 4,647.64 68,507.87 - 4,647.64 6,198.60 14%22 5,624.25 796.48 - 402.31 4,827.77 73,335.64 - 4,827.77 6,737.76 15%23 5,836.85 821.97 - 417.91 5,014.88 78,350.52 - 5,014.88 7,246.90 15%24 6,057.48 848.25 - 434.10 5,209.24 83,559.76 - 5,209.24 7,727.69 15%25 6,286.46 875.34 - 450.93 5,411.12 88,970.88 - 5,411.12 8,181.71 15%26 6,524.08 903.26 - 468.40 5,620.82 94,591.70 - 5,620.82 8,610.45 15%27 6,770.69 932.05 - 486.55 5,838.64 100,430.34 - 5,838.64 9,015.33 15%28 7,026.63 961.72 - 505.41 6,064.90 106,495.25 - 6,064.90 9,397.65 15%29 7,292.23 992.31 - 524.99 6,299.93 112,795.17 - 6,299.93 9,758.69 15%30 7,567.88 1,023.83 - 545.34 6,544.05 119,339.22 - 6,544.05 10,099.63 15%

139,513.20$ 20,173.98$ -$ 9,944.94$ 119,339.22$ -$ -$ -$ 101,339.22$

Solar DCF Analysis – 4.0kW-dcTypical Usage / 100% Down / 30% Fed Tax Credit

25

Discount Rate Old Energy

Bill

New Energy

Bill Financing

Cost Savings

(including financing)

Federal Tax

Credit Depreciation

Interest

Expense

Total Cash

Flow Benefit 10.00%

Year per year per year per year Per month Per year Cumulative NPV IRR

Net Upfront Investment (inc State Rebate if any)

(18,000.00)$

1 2,580.35$ 408.29$ $0.00 181.00$ 2,172.06$ 2,172.06$ 5,400.00$ -$ $0.00 7,572.06$ (10,105.74) -58%2 2,677.88 421.60 - 188.02 2,256.28 4,428.34 - $0.00 2,256.28 (8,410.56) -38%3 2,779.11 435.34 - 195.31 2,343.77 6,772.11 - - 2,343.77 (6,809.73) -21%4 2,884.16 449.51 - 202.89 2,434.64 9,206.75 - - 2,434.64 (5,298.01) -10%5 2,993.18 464.14 - 210.75 2,529.04 11,735.79 - - 2,529.04 (3,870.43) -2%6 3,106.32 479.22 - 218.92 2,627.10 14,362.89 - 2,627.10 (2,522.32) 3%7 3,223.74 494.79 - 227.41 2,728.95 17,091.84 - 2,728.95 (1,249.24) 7%8 3,345.60 510.84 - 236.23 2,834.75 19,926.60 - 2,834.75 (47.03) 10%9 3,472.06 527.41 - 245.39 2,944.65 22,871.25 - 2,944.65 1,088.26 12%

10 3,603.30 544.49 - 254.90 3,058.81 25,930.06 - 3,058.81 2,160.36 14%11 3,739.51 562.11 - 264.78 3,177.39 29,107.46 - 3,177.39 3,172.77 15%12 3,880.86 580.29 - 275.05 3,300.57 32,408.03 - 3,300.57 4,128.83 16%13 4,027.56 599.04 - 285.71 3,428.52 35,836.54 - 3,428.52 5,031.67 16%14 4,179.80 618.38 - 296.79 3,561.42 39,397.96 - 3,561.42 5,884.24 17%15 4,337.80 638.32 - 308.29 3,699.48 43,097.44 - 3,699.48 6,689.36 18%16 4,501.77 658.89 - 320.24 3,842.88 46,940.32 - 3,842.88 7,449.65 18%17 4,671.93 680.10 - 332.65 3,991.83 50,932.15 - 3,991.83 8,167.62 18%18 4,848.53 701.97 - 345.55 4,146.56 55,078.71 - 4,146.56 8,845.61 19%19 5,031.81 724.52 - 358.94 4,307.28 59,386.00 - 4,307.28 9,485.86 19%20 5,222.01 747.78 - 372.85 4,474.23 63,860.23 - 4,474.23 10,090.47 19%21 5,419.40 771.76 - 387.30 4,647.64 68,507.87 - 4,647.64 10,661.41 19%22 5,624.25 796.48 - 402.31 4,827.77 73,335.64 - 4,827.77 11,200.57 19%23 5,836.85 821.97 - 417.91 5,014.88 78,350.52 - 5,014.88 11,709.71 19%24 6,057.48 848.25 - 434.10 5,209.24 83,559.76 - 5,209.24 12,190.50 19%25 6,286.46 875.34 - 450.93 5,411.12 88,970.88 - 5,411.12 12,644.52 20%26 6,524.08 903.26 - 468.40 5,620.82 94,591.70 - 5,620.82 13,073.26 20%27 6,770.69 932.05 - 486.55 5,838.64 100,430.34 - 5,838.64 13,478.14 20%28 7,026.63 961.72 - 505.41 6,064.90 106,495.25 - 6,064.90 13,860.46 20%29 7,292.23 992.31 - 524.99 6,299.93 112,795.17 - 6,299.93 14,221.50 20%30 7,567.88 1,023.83 - 545.34 6,544.05 119,339.22 - 6,544.05 14,562.44 20%

139,513.20$ 20,173.98$ -$ 9,944.94$ 119,339.22$ 5,400.00$ -$ -$ 106,739.22$

Solar DCF Analysis – 4.0kW-dcTypical Usage / 20% Down / 30% Fed Tax Credit

26

Discount Rate Old Energy

Bill

New Energy

Bill Financing

Cost Savings

(including financing)

Federal Tax

Credit Depreciation

Interest

Expense

Total Cash

Flow Benefit 10.00%

Year per year per year per year Per month Per year Cumulative NPV IRR

Net Upfront Investment (inc State Rebate if any)

(3,600.00)$

1 2,580.35$ 408.29$ $1,059.58 92.71$ 1,112.48$ 1,112.48$ 5,400.00$ -$ $576.00 7,088.48$ 2,585.52 97%2 2,677.88 421.60 1,059.58 99.73 1,196.70 2,309.19 - $556.66 1,753.36 3,902.85 119%3 2,779.11 435.34 1,059.58 107.02 1,284.19 3,593.38 - 536.54 1,820.73 5,146.43 128%4 2,884.16 449.51 1,059.58 114.59 1,375.07 4,968.44 - 515.62 1,890.69 6,320.40 132%5 2,993.18 464.14 1,059.58 122.46 1,469.46 6,437.91 - 493.86 1,963.32 7,428.64 133%6 3,106.32 479.22 1,059.58 130.63 1,567.52 8,005.43 471.23 2,038.75 8,474.85 134%7 3,223.74 494.79 1,059.58 139.11 1,669.37 9,674.80 447.70 2,117.07 9,462.48 134%8 3,345.60 510.84 1,059.58 147.93 1,775.18 11,449.98 423.22 2,198.40 10,394.81 134%9 3,472.06 527.41 1,059.58 157.09 1,885.08 13,335.05 397.77 2,282.84 11,274.95 134%

10 3,603.30 544.49 1,059.58 166.60 1,999.23 15,334.29 371.30 2,370.53 12,105.80 134%11 3,739.51 562.11 1,059.58 176.48 2,117.82 17,452.11 343.76 2,461.58 12,890.14 134%12 3,880.86 580.29 1,059.58 186.75 2,240.99 19,693.10 315.13 2,556.12 13,630.56 134%13 4,027.56 599.04 1,059.58 197.41 2,368.94 22,062.04 285.35 2,654.29 14,329.52 134%14 4,179.80 618.38 1,059.58 208.49 2,501.85 24,563.88 254.39 2,756.23 14,989.34 134%15 4,337.80 638.32 1,059.58 219.99 2,639.90 27,203.78 222.18 2,862.08 15,612.21 134%16 4,501.77 658.89 1,059.58 231.94 2,783.30 29,987.08 188.68 2,971.98 16,200.20 134%17 4,671.93 680.10 1,059.58 244.35 2,932.26 32,919.34 153.85 3,086.10 16,755.26 134%18 4,848.53 701.97 1,059.58 257.25 3,086.98 36,006.32 117.62 3,204.60 17,279.24 134%19 5,031.81 724.52 1,059.58 270.64 3,247.71 39,254.03 79.94 3,327.64 17,773.87 134%20 5,222.01 747.78 1,059.58 284.55 3,414.65 42,668.68 - 3,414.65 18,235.30 134%21 5,419.40 771.76 1,059.58 299.01 3,588.07 46,256.75 - 3,588.07 18,676.08 134%22 5,624.25 796.48 1,059.58 314.02 3,768.20 50,024.94 - 3,768.20 19,096.90 134%23 5,836.85 821.97 1,059.58 329.61 3,955.30 53,980.25 - 3,955.30 19,498.47 134%24 6,057.48 848.25 1,059.58 345.80 4,149.66 58,129.91 - 4,149.66 19,881.46 134%25 6,286.46 875.34 1,059.58 362.63 4,351.54 62,481.45 - 4,351.54 20,246.58 134%26 6,524.08 903.26 1,059.58 380.10 4,561.24 67,042.69 - 4,561.24 20,594.50 134%27 6,770.69 932.05 1,059.58 398.26 4,779.07 71,821.76 - 4,779.07 20,925.90 134%28 7,026.63 961.72 1,059.58 417.11 5,005.33 76,827.08 - 5,005.33 21,241.43 134%29 7,292.23 992.31 1,059.58 436.70 5,240.35 82,067.43 - 5,240.35 21,541.75 134%30 7,567.88 1,023.83 1,059.58 457.04 5,484.47 87,551.91 - 5,484.47 21,827.48 134%

139,513.20$ 20,173.98$ 31,787.32$ 7,295.99$ 87,551.91$ 5,400.00$ -$ 6,750.79$ 96,102.70$

Discount Rate and Cost of Capital Models

• The Discount Rate is used to calculate a company’s value using Discounted Cash Flow (DCF) analysis or similarly using the Capitalization of Earnings Method

• Capitalization of Earnings Method: Value = future earnings level / ( r – g ) where r = discount rate, and g = growth rate• The Discount Rate is similar to the Capitalization Rate or Cap Rate which is used to estimate the

investor's potential return on his investment based on a constant annual income: Cap Rate = Yearly Income / Total Value or Total Value = Yearly income / Cap Rate• The Cap Rate is equivalent to the discount rate of a perpetuity.• Several Cost of Capital Models are used to compute the Discount Rate

– Weighted Average Cost of Capital (WACC)– Capital Asset Pricing Model (CAPM)– Modified CAPM– Build-Up Model– Arbitrage Pricing Theory Model (APT)– Fama-French Three Factor Model

27

Value is a Subjective Quantity

28

Weighted Average Cost of Capital (WACC)

• The Discount Rate is used in Discounted Cash Flow (DCF) analysis to compute the Present Value of future returns.

• A company’s Weighted Average Cost of Capital (WACC) is often used as the discount rate• WACC is the rate that a company is expected to pay (on average) to all its security holders

to finance its assets• In the case where the company is financed with only equity and debt, the average cost of

capital is given by:

WACC = D/(D + E) Kd + E/(D+E) Ke

where D is the total debt, E is the total shareholder’s equity, Ke is the cost of equity, and Kd is the cost of debt.

• Tax effects reduce the effective cost of debt and can be incorporated into the formula by replacing Kd with Kd (1-t) where t is the effective tax rate.

29

Capital Asset Pricing Model

• Capital Asset Pricing Model (CAPM) is used to determine the expected rate of return of an asset investment given that assets “non-diversifiable” risk (or market risk)

• The CAPM rate can be used to compute the discount rate or capitalization rate for adding an asset investment to an already well-diversified portfolio.

• The CAPM dictates that the risk premium for an asset or individual security is proportional to the market risk premium,

Ri – Rf = Bi ( Rm – Rf ) or Ri = Rf + Bi ( Rm – Rf )

where Ri= expected return of the capital asset (or an individual security in the market)

Rm = expected return of the market as a whole

Rf = the risk free interest rate (such as that of government bonds) Bi = “Beta” is the sensitivity of the expected excess asset returns to the expected excess market returns and is a measure of risk arising from exposure to a market. (Statistically, Bi = Cov(Ri, Rm) / Var (Rm)))

Rm - Rf = known as the market risk premium

Ri - Rf = risk premium for a given asset of individual security

30CAPM was introduced by Jack Treynor (1961, 1962),[2] William Sharpe (1964), John Lintner (1965a,b) and Jan Mossin (1966) independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory.

Security Market Line (SML)

Average Return vs Beta

31

Modified Capital Asset Pricing Model

• The basic CAPM considers only the market risk to determine the discount or capitalization rate.• The Modified CAPM extends the CAPM to consider other risks involved in an investment as:

Ri = Rf + Bi ( Rm - Rf) + SCRP + CSRP ,

Where Ri = expected return of the capital asset (or an individual security in the market)

Rf = Risk free rate of return (Generally taken as 10-year Government Bond Yield)

Bi = Beta Value (Sensitivity of the stock returns to market returns)

Rm = Market Rate of Return

SCRP = Small Company Risk Premium, CSRP = Company specific Risk premium

• Build Up Method to determine after-tax net cash flow discount rate, which in turn yields the capitalization rate.

– Called a "build-up" method because it is the sum of risks associated with various classes of assets.

– It is based on the principle that investors would require a greater return on classes of assets that are more risky.

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Risk Premiums and the Discount Rate

33

• Discount rates are adjusted to account for the various risks involved in the realization and timing of expected returns.

• The equity discount rate is built up by adding a risk premium for each risk element to risk free rate.

– Equity Risk Premium – The excess return that an individual stock or the overall stock market provides over a risk-free rate. This excess return compensates investors for taking on the relatively higher risk of the equity market. The size of the premium will vary as the risk in a particular stock, or in the stock market as a whole, changes; high-risk investments are compensated with a higher premium.

– Industry or Market Risk Premium – High risk industries result in higher risk premiums– Company Size Premium – Generally, smaller companies are associated with higher investment risk.

Hence small company investors demand higher returns.– Company Specific Risk Premium – accounts for the unique attributes of the business itself. Business

risk factors that lead to higher premium values include unstable earnings, high leverage, customer or product concentration and low quality of management or staff.

– Liquidity Risk Premium – included to account for lack of marketability of an asset. It is highest for lightly traded securities and small issues, as well as during a bear market.

Effect of Size on the Risk Premium

34

Source: Duff and Felps, “Risk Premium Report 2013”

Annual Average Return Using 8 Measures of Company Size

35

Source: Duff and Felps, “Risk Premium Report 2013”

Average Risk Premium vs Market Value

Portfolio Rank by Size

Average Market Value ($M)

Smoothed Average Risk Premium

1 136,859 2.63%

2 39,247 4.52%

3 25,711 5.15%

… … …

24 288 11.95%

25 94 13.65%

36

Figure 13: Exhibit A-1 (abbreviated) Historical Equity Risk Premium: Average Since 1963 Data for Year Ending Dec 31, 2012 Companies Ranked by Market Value of Equity

Source: Duff and Felps, “Risk Premium Report 2013”

Discount Rate Build Up

• Example of a build up of the total equity discount rate for small business valuation:

• In this example, the total equity discount rate is 45%.

• A time varying discount profile can also be used that increases the discount rate for cash flows occurring further in the future. (This method can be used, for example, to account for the yield curve premium for long term debt.)

37

Risk Risk EvaluationRisk Premium

(e.g.)

Risk Free Rate Long Term U.S. Treasury Bond 3%

Equity Risk Publically traded equity investment 7%

Size Risk Small privately-owned Company 20%

Industry Risk Risk of investing in the particular industry the business operates 5%

Company Specific Risk Risk of investing in particular business 10%

Total Discount Rate 45%

Equity Risk Premium

38Source: http://aswathdamodaran.blogspot.com/2013/05/equity-risk-premiums-erp-and-stocks.html

39Source: http://aswathdamodaran.blogspot.com/2013/05/equity-risk-premiums-erp-and-stocks.html

Equity Risk Premium

40

Are U.S. Equity Risk Premiums Reaching an Inflection Point?

41

Rising US Treasury yields are putting pressure on US equity risk premiums, and if 10 year yields go up any more the ERP will fall below its historic average, making stocks look relatively expensive

http://www.valuewalk.com/2014/01/us-equity-risk-premium/

US Equity and Bond Yield Correlation

42

http://www.valuewalk.com/2014/01/us-equity-risk-premium/

Exercise 2 – Performing DCF Analysis• Compute DCF valuations for the cash flow series below• Assume discount rate, r = 36%• Assume growth rate, g = 10%, for the period beyond Yr 5• NPV of cash from Yr 1 to 5 with (r = 36%) = __________

• Terminal Value, T0 = Y5 cash flow*(1+g)/(d-g) = _________

• Present value of T0 = T0/(1+r)^5 = _________

• DCF valuation = _________

Company Valuation Exercises – Income Approach

43

?

Y1 Y2 Y3 Y4 Y5 T0

-100 25 60 100 110

Growth Terminal

NPVPV(T0,5)

DCFValue

DCF Analysis of Free Cash Flow ($M)

Development

Exercise 2 – Calculating the IRR• Compute IRR of the cash flow series below with terminal value in year 6 as computed in the

previous example.• Assume discount rate, r = 36% and the growth rate, g = 10%, for the period beyond Yr 5• Using the Excel formula IRR(values,[guess]), calculate the IRR = _____%

• Check the answer by calculating the NPV of the cash flow series using r = IRR calculated above and verify that NPV = 0.

• If your companies Cost of Capital is 30%, would you invest in this company?

Company Valuation Exercises – Income Approach

44

?

Y1 Y2 Y3 Y4 Y5 T0

-100 25 60 100 110

Growth Terminal

NPVPV(T0,5)

DCFValue

DCF Analysis of Free Cash Flow ($M)

Development