Valuation by PE ratio, including cash flow from existing assets. The existing as
ID: 2708989 • Letter: V
Question
Valuation by PE ratio, including cash flow from existing assets. The existing assets of the firm are expected to yield an EBITDA of y million dollars in the current year. After the disruption is over, this EBITDA will grow at the growth rate of sales revenue. (The existing assets are not affected by marketing campaign.) The annual depreciation on the existing assets is $4 million. The annual capital expenditure is $4 million. The current PE ratio of 15 is considered a fair reflection of the market as well as industry and will continue for the life of the machine. Use the original project of XC-750. Calculate the (market) price expected at the end of each year during the life of the machine.
Year 0 1 2 3 4 5 6 7 8 9 10 11 Revenues Growth 5.50% 5.14% 4.77% 4.41% 4.05% 3.68% 3.32% 2.95% 2.59% 2.23% 1.86% 1.50% Marketing Growth 2.00% 2.50% 2.50% 1.50% 0.50% Total Revenue Growth 5.50% 7.14% 7.27% 6.91% 5.55% 4.18% 3.32% 2.95% 2.59% 2.23% 1.86% 1.50% New Machine Total Revenue Growth 5.50% 7.14% 7.27% 7.91% 6.55% 5.18% 4.32% 3.95% 3.59% 3.23% 2.86% 1.50% Incremental Revenues $ (5,000.00) $ 10,713.64 $ 11,492.81 $ 12,401.79 $ 13,213.54 $ 13,898.24 $ 14,498.39 $ 15,071.74 $ 15,612.95 $ 16,116.82 $ 16,578.35 $ 16,827.03 Incremental COGS rate of Sales 70% 69% 68% 67% 66% 65% 65% 65% 65% 65% 65% 65% Incremental Costs of Goods Sold $ (3,500.00) $ 7,392.41 $ 7,815.11 $ 8,309.20 $ 8,720.94 $ 9,033.86 $ 9,423.96 $ 9,796.63 $ 10,148.42 $ 10,475.94 $ 10,775.93 $ 10,937.57 Incremental Gross Profit $ (1,500.00) $ 3,321.23 $ 3,677.70 $ 4,092.59 $ 4,492.60 $ 4,864.38 $ 5,074.44 $ 5,275.11 $ 5,464.53 $ 5,640.89 $ 5,802.42 $ 5,889.46 Selling, General, and Administrative $ 2,142.73 $ 2,298.56 $ 2,480.36 $ 2,642.71 $ 2,779.65 $ 2,899.68 $ 3,014.35 $ 3,122.59 $ 3,223.36 $ 3,315.67 $ 3,365.41 Marketing Expenses $ 254.27 $ 269.86 $ 288.04 $ 40.00 $ 40.00 $ - $ - $ - $ - $ - $ - Depreciation Rate 10.00% 18.00% 14.40% 11.52% 9.22% 7.37% 6.55% 6.55% 6.56% 6.55% 3.28% 0.00% Depreciation Expense $ (300.00) $ (540.00) $ (432.00) $ (345.60) $ (276.60) $ (221.10) $ (196.50) $ (196.50) $ (196.80) $ (196.50) $ (98.40) $ - EBIT $ (1,800.00) $ 384.23 $ 677.28 $ 978.60 $ 1,533.30 $ 1,823.64 $ 1,978.26 $ 2,064.26 $ 2,145.14 $ 2,221.02 $ 2,388.35 $ 2,524.05 Income Tax (35%) $ (630.00) $ 134.48 $ 237.05 $ 342.51 $ 536.65 $ 638.27 $ 692.39 $ 722.49 $ 750.80 $ 777.36 $ 835.92 $ 883.42 Incremental Earnings $ (1,170.00) $ 249.75 $ 440.23 $ 636.09 $ 996.64 $ 1,185.36 $ 1,285.87 $ 1,341.77 $ 1,394.34 $ 1,443.67 $ 1,552.43 $ 1,640.64 Add Back Depreciation $ 300.00 $ 540.00 $ 432.00 $ 345.60 $ 276.60 $ 221.10 $ 196.50 $ 196.50 $ 196.80 $ 196.50 $ 98.40 $ - Purchase of Equipment $ (4,250.00) $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - $ - Receivables (Sales/Receivables Turnover) $ (750.00) $ 1,607.05 $ 1,723.92 $ 1,860.27 $ 1,982.03 $ 2,084.74 $ 2,174.76 $ 2,260.76 $ 2,341.94 $ 2,417.52 $ 2,486.75 $ - Payables (CGS/Payables Turnover) $ (350.00) $ 739.24 $ 781.51 $ 830.92 $ 872.09 $ 903.39 $ 942.40 $ 979.66 $ 1,014.84 $ 1,047.59 $ 1,077.59 $ - Inventory (Sales/Inventory) $ (500.00) $ 1,071.36 $ 1,149.28 $ 1,240.18 $ 1,321.35 $ 1,389.82 $ 1,449.84 $ 1,507.17 $ 1,561.30 $ 1,611.68 $ 1,657.84 $ - Cash (Sales/Cash Turnover) $ (750.00) $ 1,607.05 $ 1,723.92 $ 1,860.27 $ 1,982.03 $ 2,084.74 $ 2,174.76 $ 2,260.76 $ 2,341.94 $ 2,417.52 $ 2,486.75 $ - NWC $ (1,650.00) $ 3,546.21 $ 3,815.61 $ 4,129.79 $ 4,413.32 $ 4,655.91 $ 4,856.96 $ 5,049.03 $ 5,230.34 $ 5,399.14 $ 5,553.75 $ - NWC cghange $ (1,650.00) $ 5,196.21 $ 269.40 $ 314.18 $ 283.53 $ 242.59 $ 201.05 $ 192.07 $ 181.31 $ 168.80 $ 154.61 $ (5,553.75) Incremental Free Cash Flows $ (3,470.00) $ (4,406.47) $ 602.83 $ 667.51 $ 989.71 $ 1,163.87 $ 1,281.32 $ 1,346.20 $ 1,409.84 $ 1,471.37 $ 1,496.22 $ 5,553.75 NPV $ (3,470.00) $ (4,005.88) $ 498.21 $ 501.51 $ 675.99 $ 722.67 $ 723.27 $ 690.81 $ 657.70 $ 624.00 $ 576.86 $ 1,946.55 WACC 10.000% 1-8 NPV Total $ 141.70 IRR 10.304%Explanation / Answer
The payoff from the call option is $17 if the stock price rises and $12 if the stock price falls. From the binomial pricing model we can create a replicating portfolio with the following two equations:
$17 = ($47 × x) + (1.05 × y)
$12 = ($42 × x) + (1.05 × y)
x = 1 share of stock
y = –28.57 of risk free bonds
The value of the option is the value of the replicating portfolio:
(1 × $45) + (–28.57) = $16.43
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