FV = (-$395) (1.10) = -$435 The cost of the old autoclave in terms of end-of-year 2 dollars is $435. Bradley Company's required rate of return is 14%. Remember that the salvage value is expressed in nominal terms, and thus must be discounted by the nominal discount rate, 0.20. PV(Savings) = C1 ATr = $120,000 A50.11 = $443,507 The NPV of the mixer is the sum of the above cash flows. Since it is more expensive to operate the old autoclave ($620) than to purchase the new one ($615), Klious should purchase the new autoclave at the end of year 3. Irrational behavior: The text examines how limitations in cognitive abilities and biases in assessing abilities of key players can affect valuation. Since the resale value ($638,140.78) is higher than the book value ($0), the firm must pay capital gains taxes on the difference. 7.31 Mixer X The first step is to find the NPV of the savings associated with Mixer X. Found inside – Page viiiPrinciples and Solutions D S Hira ... Investment Analysis Break-Even Analysis Payback Period Method Average (Accounting) Rate of Return Method Time-Adjusted or Discounted Cash Flow (DCF) Methods Net Present Value (NPV) Method Internal ... In the case of the internal rate of return method, the cost of capital is . 7.30 To evaluate the word processors, compute their equivalent annual costs (EAC). Present value, commonly referred to as PV, is the calculation of what a future sum of money or stream of cash flows is worth today given a specified rate of return over a specified period of time.. Found inside – Page 833( a ) 6 % per year , N = 5 years , present value ( PV ) = $ 10,000 , future value ( FV ) = $ 13,382 . ... Accept the program . 7. Cash Budget for Care for the Homeless : January Solutions to Exercises 833. Solution (a) Payback method. Found inside – Page xiii96 97 98 5 5.2.5 4.19 Capacity Planning Exercise Generators—Solution 4.20 Bottling Plant Exercise Solution . ... 5.2.1 Interest Rate 5.2.2 Present Value (PV) 5.2.3 Discount Factor 5.2.4 Net Present Value (NPV) . Since it is cheaper to operate the old autoclave ($477) than to purchase the new one ($615), Klious should continue to operate the old machine in year 3. Also, no inflation adjustment is needed for either the depreciation charge or the recovery of net working capital since these items are already expressed in nominal terms. A/T-NCF - $775,000 $345,000$501,000 * The capital loss arises because the resale value ($40,000) is less than the net book value ($300,000). Since there are no capital gains taxes, the PV is just that cash flow, discounted back three periods. 7.5 Compute the NPV of both alternatives. Net present value (NPV) is the difference between the present value of cash inflows and outflows of an investment over a period of time. Investment 13. Net present value, or NPV, is used to calculate today's value of a future stream of payments. C1 = $120,000 The real discount rate is 11%. XX40 Find the present value of both the initial cash outlay and the maintenance expenses. 1+ Real Discount Rate = (1+ Nominal Discount Rate) / (1+ Inflation Rate) Real Discount Rate = [(1.14) / (1.05)] 1 = 0.0857 Find the equivalent annual cost (EAC) of each of the copiers. Present Value Index = Amount to Be Invested Total Present Value of Net Cash Flow Present value index of the sewing machine: $360,000 $453,097 = 1.26 Present value index of the packing machine: $120,000 $179,480 = 1.50 c. Therefore, applying the annuity formula to a stream of cash flows that begins four years from today will generate the present value of that annuity as of the end of year three. The following represents a different approach to solving present-value break-even problems, unlike the EAC method used in problems 8.8 and 8.7. After-Tax Salvage Value = Salvage Value Tc (Salvage Value Book Value) = $1,000,000 0.34 ($1,000,000 $0) = $660,000 The salvage value must then be discounted in order to find the PV. PV of cash outflows from RH45 = $900 + $110 A50.0857 = $1,333 $1,333 = EAC * A50.0857 EAC = $339 The equivalent annual cost of model RH45 is $339. Once the after-tax value is calculated, the value must be discounted back five years to the present (year 0). Remember to account for taxes. The discount rate is the rate for one period, assumed to be annual. Solve for the payment amount, which is the equivalent annual cost. The problem also indicates that 5 million packages will be sold in each of the next three years. See Present Value Cash Flows Calculator for related formulas and calculations. This approach yields the same answer. $43,507 = EAB * A50.11 EAB = $11,772 The equivalent annual benefit of Mixer X is $11,772. Since net income will be lower by $200,000 per year due to this expense, the firms tax bill will also be lower. PV(Salvage Value) = C8 / (1 + r)8 = $500 / (1.11)8 = $217 The NPV of the computer is the combination of the above cash flows. Taxes at 34%40,80040,80040,46039,72938,54910. / C D R S g h ~ ¢ £ § ® . (If the net present value is negative, use either anegative sign preceding the number eg -45 or parentheses eg (45).Round computations and final answer for present value to 0 decimalplaces, e.g. The present value is an important concept of Financial Management.It is concerned with the present value of cash flows that are taking place in some future. Present value is the value right now of some amount of money in the future. Note that nominal cash flows must be discounted by nominal rates. Use a five-year annuity, discounted at 12 percent to find the present value of the costs. Found inside – Page 263This new architecture , much like Hewlett - Packard's Series 80 VisiCale PLUS , which is advertised to analyze business problems , evaluate solutions , to calculate Net Present Value , Internal Rate of Return and statistical analysis ... 7.25 In order to find equivalent annual cost, first find the net present value of all costs related to the investment, net of any benefits the investment may yield. $200,000*(1.03)4 = $225,102. a. Less than the total cash flow without the net present value applied C. - It considers the time value of money. Pretax Income [6-7]120,000120,000119,000116,850113,3839. Annual Depreciation Expense = $60,000 / 5 = $12,000 Annual Depreciation Tax Shield = (Tc) (Annual Depreciation Expense) = (0.35) ($12,000) = $4,200 To find the PV of the annual depreciation tax shields, use the formula for a five-year annuity. Net Working Capital- 25,000 $25,0008. NPV = -Initial Investment PV(Maintenance) + PV(Depreciation Tax Shield) + PV(Salvage) = -$45,000 - $7,926 + $12,249 + $4,698 = -$35,979 In order to calculate the equivalent annual cost, set the NPV of the equipment equal to an annuity with the same economic life. / A B T U c k , 1 D F e õòëõëõëõëõëåòåòëåòåòåòåòåòåÜåòõëõòëÓëòÏòÏòÏòËòÏòËòÏòËòÏòÏòÏòÏòÏòåëÓëÓëÓëõòëòëòÏò CJ H*CJ H*B*CJ H*ph 56CJ \] Annual Depreciation Tax Shield = Tc (Annual Depreciation Expense) = 0.34 ($8,000,000) = $2,720,000 Remember that depreciation is a nominal quantity, and thus must be discounted at the nominal rate. Find the NPV of one SAL 5000, and later, when finding the equivalent annual cost (EAC) of the decision, multiply the final answer by 10. Determine the cash flows pertaining to the sale of the existing equipment, the purchase of the new equipment, the future incremental benefits that the new equipment will provide to the firm, and the sale of the new equipment in eight years. Apply the annuity formula to the string of annual tax shields to find the present value of the taxes saved. Since the project has an economic life of 10 years and is discounted at 10 percent, the NPV is equal to a 10-year annuity, discounted at 10 percent. The firm will choose the option with the higher NPV. Pretax Income [1-2-3]$300,000$300,0005. 7.26 Since the cash flows are given in real terms, they must be discounted at the real discount rate. If neither of the projects has a positive NPV, the correct recommendation is to reject both projects and continue renting the building to the current occupants. NPV = -Investment + PV(Revenues) - PV(Costs) + PV(Depreciation Tax Shield) + PV(Salvage Value) = -$6,000,000 + $7,364,645 - $582,479 + $1,220,170 + $169,260 = $2,171,596 These calculations could also have been performed in a single step: NPV = -$6,000,000 + (1 - 0.34) ($3.15) (1,000,000) A50.20, 0.1025 (1 - 0.34) ($.2625) (1,000,000) A50.20, 0.071 + 0.34 ($6,000,000 / 5) A50.20 + [$638,140.78 - 0.34 ($638,140.78 - $0)] / (1.20)5 = $2,171,596 The NPV of the project is $2,171,596. To find the present value, discount the after-tax salvage value by five periods. Therefore, the after-tax salvage value of the asset is $19,800 [= $30,000 0.34($30,000 0)]. Solution: (1). The net present value (NPV) of an investment proposal is the present value of the proposal's net cash flows less the proposal's initial cash outflow. NPV = -Initial Investment PV(Maintenance) + PV(Tax Shield) = -$60,000 - $7,661 + $15,787 = -$51,874 In order to calculate the equivalent annual cost (EAC), set the NPV of the equipment equal to an annuity with the same economic life. Annual Depreciation Tax Shield = (Tc) (Annual Depreciation Expense) = (0.34) ($280,000) = $95,200 Apply the annuity formula to calculate the PV of the annual depreciation tax shields. PV Delayed Annuity = (ATr) / (1+r)T-1 = ($1,250,000 A100.1236) / (1.1236)3 = $4,906,457 Thus, the total PV of his three-year contract is: PV = $1,400,000 + $2,950,000 A30.1236 + ($1,250,000 A100.1236) / (1.1236)3 = $1,400,000 + $7,041,799 + $4,906,457 = $13,348,256 The present value of the contract is $13,348,256. PV(Maintenance) = -$450 / (1.10)1 = -$409 PV(Resale Value) = $600 / (1.10)1 = $545 The NPV of keeping the old autoclave through the fourth year is the combination of the above cash flows. The net cash inflow for each year of life of both the proposals is given below: Required: Compute the present value of cash inflows generated by both the proposals assuming a discount rate of 18%. Facility 1: The first step is to find the NPV of the project. Apply the five-year annuity formula, discounted at 0.10 to calculate the PV of the maintenance costs. Chapter 13 Class Exercises Solution 1. Present Value Formula - Example #3. by . Net Present Values Problems With Solutions. The initial investment is not discounted because it occurs today (year 0). NPV = - Initial Investment + PV(Revenues) PV(Costs) + PV(Tax Shield) + PV(Resale Value) = -$12,000,000 + $62,334,429 $26,492,132 + $2,926,496 + $457,413 = $27,226,206 These calculations could also have been performed in a single step: NPV = -$12,000,000 + (1 - 0.34) $40,000,000 A30.13 (1 - 0.34) $17,000,000 A30.13 + 0.34 ($4,000,000) A30.1865 + [$1,000,000 0.34 ($1,000,000 $0)] / (1.13)3 = $27,226,206 Pill, Inc. should produce the Headache and Arthritis medicine since it has the higher NPV. The initial investment is not discounted because it occurs today (year 0). The present value of this annuity is: PV(Depreciation Tax Shield) = Tc (Annual Depreciation) ATr PV(Depreciation Tax Shield) = 0.34 ($4,000,000) A30.1865 = $2,926,496 Unlike the Headache-only medicine equipment, the Headache and Arthritis medicine equipment has a resale value of $1 million at the end of three years. • Strategy A: To bring to market in 1 year, invest $1 B (billion) now and returns $500 M (million), $400 M and $300 M in The net present value determined by using the calculative rate of interest (capital profit sacrifice cost) - the minimum required yield, the value of which can be derived from the market - shows the amount of the increase in assets that was created by the investment during Net Present Value = ＄518.18 - ＄500 = ＄18.18. The price at which the firm sells the equipment is a cash inflow, and any difference between the book value of the equipment and its sale price will create gains or losses that result in either a tax credit or liability. Found inside – Page 1COMPOUND INTEREST : CONCEPTS AND APPLICATIONS Questions , Exercises , Problems , and Cases : Answers and Solutions ... A.6 The discount rate that sets the net present value of a stream of payments equal to zero is the implicit rate for ... PV(Remainder of Lease Payments) = C0(1- 0.34)(1.03)(GA190.12, 0.03)* * The notation GATr, g represents a growing annuity consisting of T payments growing at a rate of g per payment, discounted at r. Annual depreciation, calculated by the straight-line method (Initial Investment / Economic Life of Investment), is $200,000 (= $4,000,000 / 20). If both of the projects have positive net present values, recommend the one with the higher NPV. Since the NPV of Option 2 is higher than the NPV of Option 1, the firm will choose to sell the old equipment and purchase new equipment in five years. PV(Initial Investment) = -$10,200,000 Find the PV of the revenues if the headache-only medicine were produced. Solution: Yes, the two projects are comparable because both the projects require equal amount of initial investment. The so-called anomalies that arise in the computation and interpretation of the Net Present Value ( NPV) and the In-. Found inside – Page 8-5EXERCISE. 8.5. New. car. John Smith wants to buy a new car worth 35,000 euro. He can't pay in cash, ... Calculate the effective annual interest rate and the net present value of each solution, using a 2% interest rate and considering ... After-Tax Salvage Value = Salvage Value Tc (Salvage Value Book Value) = $10,000 0.34 ($10,000 $0) = $6,600 The after-tax salvage value must be discounted back three periods to find its present value. After-Tax Salvage Value = Sale Price TC(Sale Price Net Book Value) = $500,000 0.34($500,000 0) = $330,000 PV(Salvage Value) = $330,000 / (1.12)5 = $187,251 NPV(Option 1) = $1,660,000 - $3,000,000 - $1,189,576 + $735,374 + $187,251 = -$1,606,950 The net present value (NPV) of selling the old machine and purchasing the new machine now is -$1,606,950. Principles of Managerial Finance. NET PRESENT VALUE (NPV) Topic: Net Present Value Calculation. In order to find the after-tax present value, multiply revenues by (1-TC). The machine would cost $136,700, including invoice cost, freight, and training of employees to operate it. Remember to adjust the maintenance cost for taxes. EVF Find the net present value of the costs associated with this model of word processor. Annual Costs Headache and Arthritis = -$1.70 * 10,000,000 = -$17,000,000 PV(Headache and arthritis costs) = (1 - Tc) C1 ATr, = (1 - 0.34) -$17,000,000 A30.13 = -$26,492,132 Since Pill, Inc. has positive income, it will benefit from a depreciation tax shield. Present Value = $3,000 / (1 + 5%/2) 4*2 Present Value = $2,462.24 Therefore, David is required to deposit $2,462 today so that he can withdraw $3,000 after 4 years.. Because of this depreciation tax shield, the firm has more cash on hand at the end of the year than it would have had without expensing depreciation. Keeping the old autoclave through Year 3: The foregone resale value is already stated as of the beginning of the year, and therefore does not need further discounting. 7.14 Notice that the problem provides the nominal values at the end of the first year, so to find the values for revenue and expenses at the end of year 5, compound the values by four years of inflation, e.g. Remember to account for taxes. NPV = Net Cash In Flowt1 / (1+r)t1 + Net Cash In Flowt2 / (1+r)t2 + …. NPV calculates the net present value (NPV) of an investment using a discount rate and a series of future cash flows.
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