DCF Calculate Example Exercise: Steves Sub Shop Steves Sub Shop - - PowerPoint PPT Presentation

DCF – Calculate

Example Exercise: Steve’s Sub Shop

Steve’s Sub Shop (Steve’s) is considering investing in toaster ovens for each of its 120 stores located in the southwestern United

• States. The high-capacity conveyor toaster ovens, manufactured

by Lincoln, will require an initial investment of $15,000 per store plus $500 in installation costs, for a total investment of $1,860,000. The new capital (including the costs for installation) will be depreciated over five years using straight-line depreciation toward a zero salvage value. In addition, Steve’s will also incur additional maintenance expences totaling $120,000 per year to maintain the ovens. At present, firm revenues for the 120 stores total $9,000,000, and the company estimates that adding the toaster feature will increase revenues by 10%. ◮ If Steve’s faces a 30% tax rate, what expected project FCFs for each of the next five years will result from the investment in toaster ovens? ◮ If Steve’s uses a 9% discount rate to analyze its investments in its stores, what is the project’s NPV?

Example Exercise: Steve’s Sub Shop

Solution Invest 1860 Increase revenues by 900/year Maintenance costs 120 Annual Tax Calculation: Revenue 900 less Maintenance 120 less depreciation 372 Taxable income 408 tax 122 Annual FCF 900 − 120 − 122 = 658

Example Exercise: Steve’s Sub Shop

t Ct −1860 1 658 2 658 3 658 4 658 5 658

Example Exercise: Steve’s Sub Shop

NPV = − 1860 + 658 (1 + 0.09)1 + 658 (1 + 0.09)2 + 658 (1 + 0.09)3 + 658 (1 + 0.09)4 + 658 (1 + 0.09)5 = $699.391 ≈ 700

Example exercise - Best Manufacturing

Best Manufacturing Ltd is considering a new investment. Financial projections for the investment are tabulated here. The corporate tax rate is 28%. Assume all sales revenue is received in cash, all

• perating costs and income taxes are paid in cash, and all cash

flows occur at the end of the year. All net working capital is recovered at the end of the project, and the investment is sold at its residual value after depreciation. Year 1 2 3 4 Investment 10,000

• Sales revenue
• 7,000

7,000 7,000 7,000 Operating Costs

• 2,000

2,000 2,000 2,000 Depreciation

• 2,500

1,875 1,406 1,055 Net working capital spending 200 250 300 200

• 1. Suppose the appropriate discount rate is 12%. What is the

NPV of the project?

• 2. Suppose additionally that the project requires an initial

investment of working capital of 3,000 and the fixed asset will have a market value of 2,100 at the end of the project. What is the new NPV?

Example exercise - Best Manufacturing, solution

Tax rate 0.28

1 2 3 4 Investment 10000 Sales revenue 7000 7000 7000 7000 Operating costs 2000 2000 2000 2000 Depreciation 2500 1875 1406 1055 Total depreciation 2500 4375 5781 6836 Residual value investment 10000 7500 5625 4219 3164 WC spending 200 250 300 200 Taxable income 2500 3125 3594 3945 Tax 700 875 1006.32 1104.6 Cash flow from operations 4300 4125 3993.68 3895.4 Total WC 200 450 750 950 950 Change WC 200 250 300 200

• 950

Sale investment 3164 FCF 10200 4050 3825 3793.68 8009.4 PV $14,456 NPV $4,256

Example exercise - Best Manufacturing

Additional WC 3000 Sale value of fixed asset 2100

1 2 3 4 Investment 10000 Sales revenue 7000 7000 7000 7000 Operating costs 2000 2000 2000 2000 Depreciation 2500 1875 1406 1055 Total depreciation 2500 4375 5781 6836 Residual value investment 10000 7500 5625 4219 3164 WC spending 200 250 300 200 Taxable loss sale of residual investment 1064 Taxable income 2500 3125 3594 2881 Tax 700 875 1006.32 806.68 Cash flow from operations 4300 4125 3993.68 4193.32 Total WC 3200 3450 3750 3950 3950 Change WC 3200 250 300 200

• 3950

Sale investment 2100 FCF 13200 4050 3825 3793.68 10243.3 PV $15,875 NPV $2,675

Example Exercise: Red Cat

Red Cat Inc. is a non-listed company that has expected perpetual Free Cash Flow of $8 million per year. Red Cat has issued a perpetual bond with face value of $50 million and annual coupon

• f 5.2632%. The debt-to-equity ratio for Red Cat is 1.0. Red Cat

has 4 million common shares outstanding. An industry analyst has collected the following information about traded comparables: Traded Stock Debt-to-equity comparable beta (βE) ratio (D/E) Green Cat 1.105 0.5 Yellow Cat 1.440 1.0 Black Cat 1.520 1.0 The cost of debt for Red Cat and the compararable firms is 5%

• annually. The market risk premium and the risk free rate is also

5% per year. The tax rate is 40%

• 1. Estimate the value of common equity for Red Cat using the

Adjusted Present Value approach.

• 2. Estimate the value of common equity for Red Cat using the

Total Enterprise Value (WACC) approach.

• 3. Red Cat currently has one owner. This owner plans to sell out

Example Exercise: Red Cat, solution

APV calculation Traded Stock Debt-to-equity Unlevered comparable beta (βE) ratio (D/E) beta Green Cat 1.105 0.5 0.85 Yellow Cat 1.440 1.0 0.9 Black Cat 1.520 1.0 0.95 Average 0.90 The unleverered cost of equity: r = rf +βU(Market Risk Premium) = 0.05+0.9×0.05 = 0.095

Example Exercise: Red Cat, solution

Value of debt D = 0.052632 × 50 0.05 = 52.63mill Enterprise value TEV = FCF rU + τD = 8 0.095 + 0.4 · 52.63 = 105.26mill Value of equity E = TEV − D = 105.26 − 52.63 = 52.63mill

WACC calculation Levered beta βE =

• 1 − (1 − τ) D

E

• τ = (1 − (1 − 0.4)1.0)0.9 = 1.44

Levered cost of equity rE = rf + βE(E[rm] − rf ) = 0.05 + 1.44 × 0.05 = 0.122 The WACC WACC = 0.5 · 0.1122 + 0.5(1 − 0.5)0.05 = 0.076 Enterprise value TEV = FCF WACC = 8 0.076 = 105.25mill Value of equity E = TEV − D = 105.26 − 52.63 = 52.63mill

Per share value of Red Cat assuming it was liquid and listed on a stock exchange is Pa = 52.63 4 = 13.16 Since the stock will be non-listed, you should demand a discount. Let us say 15%. Pb = Pa(1 − 0.15) = 11.18 Maybe you would also like to negotiate a discount to reflect the fact that the current ower will have control, say 5%. PC = Pb(1 − 0.05) = 10.62 In sum, you should demand a discount to reflect the illiquidity of the stock and the control held by the majority owner.

DCF: Sensitivity of value

Need to investigate sensitivity of value estimate. Typically investigate questions like ◮ Which growth/sales assumptions are critial? ◮ What are the consequences of changes in cost of capital? (NPV profile)

Exercise

The company EZ computers has developed a new high speed computer specially for simulations in the oil industry. The company expects to keep the edge on the competition for the next three years, and sell 100 units a year. Each machine sells for 10 million, and has a production cost of 8 million. Startup costs in production are estimated at 400 million. The cost of capital for the project is 10%. ◮ Calculate the NPV of the project There is uncertainty about the number of units that can be sold per year. ◮ Determine the minimum number of units per year that maintains profitability. ◮ Plot the NPV of the project as a function of units sold. ◮ Plot the NPV profile, NPV as a function of the cost of capital.

Exercise solution

NPV t = 1 2 3 Ct = −400 200 200 200 NPV = −400+ 200 (1 + 0.1)1 + 200 (1 + 0.1)2 + 200 (1 + 0.1)3 = 97.3704

Exercise solution ctd

NPV as a function of units sold

• 150
• 100
• 50

50 100 150 200 60 70 80 90 100 110 120

• 400 + 2*x/(1.1) + 2*x/(1.1**2) + 2*x/(1.1**3)

Exercise solution ctd

NPV profile

• 20

20 40 60 80 100 120 140 160 0.05 0.1 0.15 0.2 0.25

• 400 + 200/(1+x) + 200/((1+x)**2) + 200/((1+x)**3)

Sheridan Titman and John D Martin. Valuation. The art and science of corporate investment decisions. Pearson, third edition, 2016.