Comm 221 Extra NPV problems
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1 Woodlot NPV problem considering sustainability A woodlot is for sale for a price of 15 million dollars. You estimate that next year, the lot will harvest 2 million board feet of good quality lumber. If you use optimized sustainable practices in managing the lot you believe that this amount can grow by 3% per year. Following a sustainable process requires a monthly investment of $85,000 in perpetuity. If instead, you follow an unsustainable process, you think the output will instead decline by 2% per year. If you do not follow a sustainable process, you can clear cut some sections and receive an immediate (time 0) cashflow of $200K for some lower value scrap lumber. You have forecasted the inflation adjusted value of the lumber at $1.25/board foot for the long foreseeable future. Similar forestry projects have been capitalized at a rate of 1% effective monthly. To simplify your analysis, you may assume that you receive all revenues in single lump sum at the end of each year. Should you buy the woodlot and if you do, should you use sustainable or non-sustainable practices? With sustainable practices: NPV = value of growing annuity of lumber –
cost of wood lot –
cost of sustainable practice Convert EMR to EAR to match cashflow, (1+EMR)^12-1 = EAR = 12.6825% D1 = first sale at end of year = 2 million feet * 1.25 a foot = $2.5M Value of annuity now, P0 = D1/(r-g) = 2.5/(0.126825-0.03) = $25.819M Cost of sustainable practice, perpetuity formula = monthly pmt/EMR = 85K/0.01 = $8.5M Total value = 25.819M-15M-8.5M = $2.319M > 0 , this is profitable, we could pursue this
2 Without sustainable practices: NPV = value of shrinking annuity of lumber + clear cut scrap lumber –
cost of wood lot Value of shrinking annuity now, P0 = D1/(r-g) = 2.5/(0.126825-(-0.02)) = 2.5/0.146825 = 17.027M NPV = 17.027M + 0.2M –
15M = $2.227M > 0, this is profitable, we could pursue this So now we have a choice of do nothing (spend 0, get 0), do the sustainable for an estimated net benefit of 2.319M or do the unsustainable for a benefit of 2.227M Between these two choices, for the current situation, the sustainable project appears to be more profitable, we should do that.
3 NPV of a Delayed growing/shrinking/ending annuity project You are launching a new toy, the fidget-blinder, which should be a rage. You estimate that once you start production, in 3-months time, you will earn a revenue stream at the end of the 4
th
month equal to $100K. From there, you expect sales to rise meteorically, at an effective rate of 6% per year for 2 full years. After that, once people realize that this toy is stupid and can leave them blind, sales are expected to plummet by 25% per month until the end of time. Projects like this are risky and so you estimate that the appropriate discount rate is 15% APR compounded monthly. Given that it will cost $750K for three consecutive months, at the START OF EACH month, to build the manufacturing facility, should you pursue this project? Approach: This problem requires many slow thought-out calculations to ensure everything is correct in terms of time. The rough sketch is: NPV = SUBTRACT annuity due for 3 payments to build facility ADD growing annuity from month 4 to eternity. SUBTRACT growing annuity paying in month 28 (2 years + 4 months, value in month 27) to eternity (cutting off the tail) ADD shrinking annuity paying from month 28 to eternity (2 years + 4 months, value in month 27)
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