Hi, this is a 4-part question about the time value of money and project valuation. Question are on the week 3 problem set word documents and the answer template is on the student template problem set excel file. Thanks!

#2. Permian Petroleum Given: Initial Cost Annual FCF Project life Discount rate Solution: $ (300,000.00) 50,000.00 10 10% a. NPV = b. Payback period = c. IRR = d. Discount Rate years NPV 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% $12.00 $10.00 $8.00 $6.00 $4.00 $2.00 $- 0% 2% 4% 6% 8% 10% 12% 14% 16% #3. Golden State's Jarring Project (revised) Given: Initial investment Project life Incremental units Price per unit Gross profit margin Incremental sales commission Depreciation expense Tax rate Incremental investment in inventory Discount rate $ 10,000 5 years 5,000 3.50 0.23 750 2,000 40% 800 8% 0 1 2 3 4 5 1 2 3 4 5 Revenues Cost of goods sold Gross profit less: Added sales commissions Net Operating Income (NOI) less: Taxes Net Operating Profit after Taxes (NOPAT) plus: Depreciation less: Capital Expenditure (Capex) less: Working capital investment Cash Flow NPV = IRR = #4. Silverlake Fitness Given: Initial cost Annual revenues Operating expenses (excluding Depr) Depreciation expense Tax rate Discount rate Residual value a. Revenues less Operating expenses Net Operating Income (NOI) $ $ 2,000,000 1,500,000 800,000 100,000 30% 20% 1,000,000 0 6 7 8 9 10 11 12 13 14 15 16 17 less Taxes Net Operating Profit after Taxes (NOPAT) plus Depreciation less Capital Expenditures (Capex) Free Cash Flow (FCF) Cumulative cash flow b. NPV = c. IRR = d. Payback = e. Your decision years Notice that the investment cash flow is computed using a method and terms not used in the HBS online course. What we use here is a method that you can use in any capital budgeting (project evaluation) setting. Although the format looks a lot like an income statement (i.e., revenues less expenses) it is only similar. Specifically, notice that after we calculate EBIT (which is net operating income where the project does not entail any non-operating income or expense) we do not deduct interest expense. We compute taxes based on operating income instead. Once taxes have been deducted we add back Depreciation expense since this is a tax deductible expense that is not a cash outflow (the accompanying outflow occured when the asset being depreciated was purchased). Next we deduct any new capital expenditures associated with the investment. The latter consist of the $2 million initial investment and the subsequent investments of $500,000 in years 5, 10, and 15. In this case we "expense" these $500,000 expenditures 18 19 20 Problem SetWeek #3 Topics Covered Time value of money Project Evaluation Questions: 1. Time value of money exercises: a. If you deposit $1,000 that earns 4% interest annually and leave any interest you earn in the account, what will be the value of your account after five years? b. If you invest $1,000 that earns 4% in the first year, 5% in the second year, and so forth for five years, how much money will you have accumulated by the end of five years? c. You are now 40 years old and hope to retire in 25 years. A favorite uncle just died and left you $100,000. If you are able to invest your inheritance for 25 years earning 5% interest, how much will your retirement nest egg be on your retirement date? d. When you plan on retiring in 25 years you expect to live for 30 years and want to have an annual income of $100,000 per year. What sum of money must you accumulate on the date of your retirement that will support your personal income if the annual rate of interest following your retirement is 4% per year? e. Answer question d. assuming that you wish to leave an inheritance of $100,000 to each of your three children. f. Your father recently died unexpectedly and left you (his only heir) with an annuity of $30,000 per year for a period of 15 years. You plan on cashing in the annuity by selling it to a firm that purchases legal settlements and wills. After contacting the firm you learn that they are willing to pay you a current sum of $228,182.39. Since you are entitled to 15 annual installments of $30,000 this sum looked small to you. What rate of interest is the firm using to determine the amount it will pay you for the annuity? 2. Permian Petroleum is considering whether to purchase a new natural gas processing unit that will be used to separate water and other contaminants from hydrocarbons at its production units in the Haynesville, La field. The firm currently is using an older processing unit that is more costly to run. If the firm purchases the newer unit the firm expects it to last for ten years and to save the firm $50,000 a year in operating expenses. The unit will cost Permian $300,000 to purchase and install. The older unit has minimal value that is roughly equal to the cost of removing the unit. a. If Permian uses a 10% discount rate when evaluating projects of this type, what is the project's NPV? Is the project a good investment for Permian? Why or why not? b. What is the payback period for the previous exercise? c. What is the internal rate of return (IRR) for the Permian investment described in part a? d. Compute the NPV for the project using discount rates of 0 to 15% in increments of 1% and graph them with NPV on the vertical axis and the discount rate on the horizontal axis. What is the relationship between NPV and IRR? 3. Re-evaluate the Golden State jarring line investment decision after making the following adjustments (note that revenues and margins do not change): Problem Set for Week #3 (IMS) Page 1 a. Sales commissions are re-estimated to be $750 per year. b. The tax rate is now estimated to be 40% (rather than 36%). c. Depreciation expense remains at $2,000 per year. d. To operate the jarring line the firm will have to invest an added $800 in inventories today and will maintain this inventory level throughout the five year life of the investment (that is, as inventory is used up in the production process, more is purchased to replace it). However, in year 5 the firm will use up the remaining inventory which means that no added purchases are needed. This means that the firm \"recaptures\" or recoups its $800 investment in inventories. 4. The Silverlake Fitness Company operates a chain of fitness centers located throughout the Minneappolis, Mn area. The firm is contemplating whether to acquire a fitness gym in St. Paul for $2 million. The gym is expected to operate for 20 years and produce revenues of $1.5 million a year. Operating total $900,000 a year which includes annual depreciation expense of $100,000. The firm's income tax rate is 30%. At the end of 20 years the facility is expected to be worth $1 million and will have a salvage or book value of zero such that the firm expects to receive an after-tax cash inflow of $700,000. Finally, Silverlake uses a 20% discount rate to evaluate its new facilities. a. What are the annual cash flows for the new facility? b. What is the NPV for the investment? c. What is the IRR for the investment? d. What is the investment's payback period? e. Should Silverlake make the investment? Why or why not? Problem Set for Week #3 (IMS) Page 2