13.3 Discounted Cash Flow Analysis Flashcards

Question

A firm uses the net present value (NPV) method to evaluate capital projects. The firm plans to acquire a depreciable asset on January 1 of next year for $2.4 million. The new asset has an estimated service life of 4 years, a zero terminal disposal value, and will be depreciated on a straight-line basis. The new asset will replace an existing asset that is expected to be sold for $350,000. The tax basis of the existing asset is $330,000. The firm is subject to an effective income tax rate of 40% and assumes that any gains or losses affect the taxes paid at the end of the year in which the gains or losses occur. The firm uses a 10% discount rate for NPV analyses. The amount related to the new asset’s depreciation that would be included in an NPV analysis is A. $1,639,200 B. $1,141,200 C. $760,800 D. $1,902,000

Answer 1

C. $760,800 The relevant amount for depreciation used in the firm's NPV analysis can be calculated as follows: Asset cost $2,400,000 Divided by: Useful life ÷ 4 = Annual depreciation $600,000 Times: Tax rate x 0.40 = Depreciation tax shield $240,000 Times: PV Factor x 3.170 = PV of depreciation tax shield $760,800

Answer 2

B. $21,516,800 The following table derives the cash flows and NPV. Year 0 Investment: $(80,000,000) Year 1-5 Revenue: $144,000,000 Variable cost: 84,000,000 Fixed cost: 25,000,000 Depreciation: 16,000,000 Pre-tax profit: 19,000,000 Tax @36%: 6,840,000 Net profit: 12,160,000 Net cash flow Net profit (12,160,000) + Depreciation (16,000,000) 28,160,000 Present value 12% (28,160,000 x 3.605) 101,516,800 NPV = $21,516,800

Answer 3

A. Internal rate of return. A capital project’s internal rate of return is the discount rate at which the net present value of the project’s cash flows equals zero, i.e., the rate at which discounted cash inflows equal discounted cash outflows.

Answer 4

C. Implicitly assumes that the firm is able to reinvest project cash flows at the project’s internal rate of return. The IRR is the rate at which the discounted future cash flows equal the net investment (NPV = 0). One disadvantage of the method is that inflows from the early years are assumed to be reinvested at the IRR. This assumption may not be sound. Investments in the future may not earn as high a rate as is currently available.

Answer 5

B. $283,380 The firm’s most probable level of annual unit sales is calculated as follows: Annual Unit Sales x Probability = Probable Unit Sales 80,000 × 10% = 8,000 85,000 × 20% = 17,000 90,000 × 30% = 7,000 95,000 × 20% = 19,000 100,000 × 10% = 10,000 110,000 × 10% = 11,000 100% 92,000 The expected annual inflow from sales is $460,000 (92,000 units × $5 margin each). The equipment will generate an annual depreciation tax shield of $80,000 [($1,000,000 ÷ 5 years) × .40 tax rate]. The net present value of the project is calculated as follows: Annual cash inflow $ 460,000 Less: Income taxes (40%) (184,000) Net income $ 276,000 Add: Depreciation tax shield 80,000 Net cash inflows $ 356,000 Times: PV factor × 3.605 PV of cash inflows $1,283,380 Less: Initial investment (1,000,000) NPV of project $ 283,380

Answer 6

D. Be slightly understated but usable. The effect of assuming cash flows occur at the end of the year simply understates the present values of the future cash flows; in reality, they probably occur on the average at mid-year.

Answer 7

A. Accept the project since the after-tax discounted cash inflows exceed the cash outflows. Even with the higher tax rate, the IRR and NPV are still acceptable. The discounted cash flow of $255,512.38 ($58,667 × 4.3553) is greater than the $250,000 initial cost.

Answer 8

C. The future asset depreciation expense. Discounted cash flow analysis, using either the internal rate of return (IRR) or the net present value (NPV) method, is based on the time value of cash inflows and outflows. All future operating cash savings are considered, as well as the tax effects on cash flows of future depreciation charges. The cash proceeds of future asset disposals are likewise a necessary consideration. Depreciation expense is a consideration only to the extent that it affects the cash flows for taxes. Otherwise, depreciation is excluded from the analysis because it is a noncash expense.

Answer 9

D. 4.0% The correct answer is 4.0%. $10,000 = $400 ÷ IRR; IRR = 0.040 = 4.0%.

Answer 10

A. $172,800 The NPV is the difference between the present value of the estimated net cash inflows and the present value of the net cash outflows. The present value of the net cash inflows discounted at 14% is $4,172,800 [$800,000(5.216)]. Therefore, the NPV of the investment is $172,800 ($4,172,800 – $4,000,000).

Answer 11

C. The higher the discount rate and the longer the discount period, the lower the present value. As the discount rate increases, the present value decreases. Also, as the discount period increases, the present value decreases.

Answer 12

A. $74,830 The entity’s initial investment can be calculated as the present value of annual cash inflows using the project’s internal rate of return of 14%. Thus, the initial investment in this project was $8,770 ($10,000 × .877 PV factor) + 15,380 ($20,000 × .769 PV factor) + 27,000 ($40,000 × .675) + 23,680 ($40,000 × .592) = $74,830

Answer 13

C. 9% To determine the IRR: Step 1: Determine the factor Factor = Initial investment / After-tax annual cash flow = $50,000 / $7,791 = 6.418 Step 2: Determine the IRR Comparing with the factors from a PV table, a factor of 6.418 corresponds with an IRR of 9%.

Answer 14

C. Net present value is greater than zero. Given unlimited funds, all projects with an NPV greater than zero should be accepted. Thus, it is profitable to invest in any firm if the rate of return is greater than the cost of capital.

Answer 15

B. 10% Dividing the loan value by the periodic payments produces a present value factor of 3.797 ($30,000 ÷ $7,900). Consulting the row for 5 years on the present value table for an ordinary annuity reveals the closest amount to this value in the 10% column.

Answer 16

D. $(32,008) The cost of capital must be determined in order to calculate NPV. Using the Capital Asset Pricing Model to determine the cost of capital where R equals the required rate of return on equity capital, RF equals the risk-free rate, RM equals the market return, and β equals the β coefficient, then R = R + β (RM – RF) R = .05 + 1.8(.10 – .05) R = .14 The net present value of the project is thus the difference between the initial cost and the sum of the present value of an annuity of $12,000 for 10 years at 14% and the present value of $20,000 in 10 years at 14%. The present value factors are found in the tools section of CMA Test Prep. NPV = [($12,000 × 5.216) + ($20,000 × .270)] – $100,000 NPV = $67,992 – $100,000 NPV = $(32,008)

Answer 17

A. Projects III and IV only. When sufficient funds are available, any capital project whose IRR exceeds the company’s cost of capital should be accepted.

Answer 18

C. Net present value is greater than or equal to $0. The net present value of a capital project is the sum of the present values of all the cash inflows associated with the project netted against the sum of the present values of all the cash outflows. If the present value of the inflows exceeds the present value of the outflows, the project is profitable.

Answer 19

C. Method of funding the project. The NPV method computes the present value of future cash inflows to determine whether they are greater than the initial cash outflow. Future cash inflows include any salvage value on facilities. Included in the initial investment are the cost of new equipment and other facilities, and additional working capital needed for operations during the term of the project. The discount rate (cost of capital or hurdle rate) must be known to discount the future cash inflows. If the NPV is positive, the project should be accepted. The method of funding a project is a decision separate from that of whether to invest.

Answer 20

B. $1,202,450 The valuation for Bright Screens consists of the present value annual cash flow and the present value of projected terminal value. The present value of annual cash flow is $348,700 ($110,000 × 3.17 PV for an ordinary annuity at 10% for 4 periods). The present value of projected terminal value is $853,750 ($1,250,000 × 0.683 PV at 10% for 4 periods). Thus, the valuation is $1,202,450 ($348,700 + $853,750).

Answer 21

A. 9% A capital project’s internal rate of return is the discount rate at which the net present value of the project’s cash flows equals zero, i.e., the rate at which discounted cash inflows equal discounted cash outflows. For this copying machine, that rate is between 8%, at which net cash flows are positive, and 10%, at which net cash flows are negative.

Answer 22

A. Adjust for inflation / Adjust for inflation Inflation erodes the purchasing power of money over time. Therefore, both cash operating costs and the required rate of return must be adjusted for inflation.

Answer 23

B. $26,556 The NPV method discounts the expected cash flows from a project using the required rate of return. A project is acceptable if its NPV is positive. The future cash inflows consist of $170,000 of saved expenses per year minus income taxes after deducting depreciation. In the first year, the after-tax cash inflow is $170,000 minus taxes of $32,000 {[$170,000 – ($300,000 × 30%) depreciation] × 40%}, or $138,000. In the second year, the after-tax cash inflow is $170,000 minus taxes of $20,000 {[$170,000 – ($300,000 × 40%) depreciation] × 40%}, or $150,000. In the third year, the after-tax cash inflow is again $138,000. Also in the third year, the after-tax cash inflow from the salvage value is $12,000 [$20,000 × (1 – 40%)]. Accordingly, the sum of these cash flows discounted using the factors for the present value of $1 at a rate of 16% is $326,556. $138,000 × .862 = $118,956 $150,000 × .743 = 111,450 $150,000 × .641 = 96,150 Discounted cash inflows $326,556 Thus, the NPV is $26,556 ($326,556 – $300,000 initial outflow).

Answer 24

B. 14%, reject the project IRR is a discount rate at which investment's NPV = 0 IRR is rate at which initial investment = PV Annaul Cash Flows $874,200 = $300,000 x PV annuity factor PV annuity factor = $874,000 / 300,000 = 2.914

Answer 25

D. Net present value because internal rate of return assumes that project cash flows can be invested at the company's internal rate of return.

Answer 26

C. No, the internal rate of return is less than the required rate of return. Based on a 7% discount rate, the calculation is $12,000 × .935 = $11,220 19,000 × .873 = 16,587 16,000 × .816 = 13,056 Total = $40,863 The internal rate of return (IRR) is the discount rate at which the investment’s NPV equals zero. If the IRR is higher than the company’s required rate of return, the investment is desirable. Since the present value of the future cash flows when discounted at the 7% rate is less than the initial investment, the IRR must be lower than the 7% required rate of return. Consequently, the company should not purchase the equipment.

Answer 27

A. The internal rate of return must exceed the cost of capital for the project to be acceptable. If the IRR is higher than the company’s desired rate of return (cost of capital), then the investment is desirable. A company will not accept a project with an IRR that is less than the cost of capital.

Answer 28

A. $7,483 The internal rate of return (IRR) of a capital project is the rate at which the net present value (NPV) of its future cash flows equals zero. To find this project’s NPV, therefore, it is necessary to discount the cash flows at the appropriate rate (14%) as follows: Year: Net cash inflows / PV factor / Present Value 1: $1,000 / 0.877 / $ 877 2: 2,000 / 0.769 / 1,538 3: 4,000 / 0.675 / 2,700 4: 4,000 / 0.592 / 2,368 $7,483

Answer 29

C. $1,058,750 he company’s net cash flows for this product can be calculated as follows: Year 1 / Year 2 / Year 3 Per-unit selling price $80.00 / $76.00 / $72.20 Less: Per-unit materials cost (30.00) / (33.00) / (36.30) Less: Per-unit labor cost (20.00) / (21.00) / (22.05) Per-unit contribution margin $30.00 / $22.00 / $13.85 Times: Projected unit sales × 50,000 / 100,000 / 125,000 Total contribution margin $1,500,000 / $2,200,000 / $1,731,250 Less: Fixed costs (300,000) / (300,000) / (300,000) Operating income $1,200,000 / $1,900,000 / $1,431,250 Less: Income taxes (40%) (480,000) / (760,000) / (572,500) Net income $720,000 / $1,140,000 / $858,750 Add: Depreciation tax shield 200,000 / 200,000 / 200,000 Net cash flows $920,000 / $1,340,000 / $1,058,750

Answer 30

B. $434,424 net cash outflow. The firm’s net present value of acquiring the new finishing machine can be calculated as follows: With the trade-in allowance, the net cost will be $950,000. This will be depreciated over 5 years at $190,000 per year. The cash inflows consist of the $100,000 of annual cost savings, which reduces to $60,000 once taxes have been considered. Also, there will be an inflow from the depreciation shield ($190,000 × 40% tax rate, or an inflow of $76,000 per year). Combining the $60,000 after-tax savings from operations with the $76,000 of tax savings from depreciation produces a total of $136,000 of after-tax inflows annually. Discounting the five payments with the annuity factor of 3.791 (5 years at 10%) produces a present value of $515,576 ($136,000 × 3.791). Subtracting the present value of the inflows from the $950,000 initial outlay results in a net outflow of $434,424.

Answer 31

C. Risk-free rate. The rate used to discount future cash flows is sometimes called the cost of capital, the discount rate, the cutoff rate, or the hurdle rate. A risk-free rate is the rate available on risk-free investments such as government bonds. The risk-free rate is not equivalent to the cost of capital because the latter must incorporate a risk premium.

Answer 32

C. May produce different rankings from the net present value method on mutually exclusive projects. Investment projects may be mutually exclusive under conditions of capital rationing (limited capital). In other words, scarcity of resources will prevent an entity from undertaking all available profitable activities. Under the IRR method, an interest rate is computed such that the present value of the expected future cash flows equals the cost of the investment (NPV = 0). The IRR method assumes that the cash flows will be reinvested at the IRR. The NPV is the excess of the present value of the estimated net cash inflows over the net cost of the investment. The cost of capital must be specified in the NPV method. An assumption of the NPV method is that cash flows from the investment will be reinvested at the particular project’s cost of capital. Because of the difference in the assumptions regarding the reinvestment of cash flows, the two methods will occasionally give different answers regarding the ranking of mutually exclusive projects. Moreover, the IRR method may rank several small, short-lived projects ahead of a large project with a lower rate of return but with a longer life span. However, the large project might return more dollars to the company because of the larger amount invested and the longer time span over which earnings will accrue. When faced with capital rationing, an investor will want to invest in projects that generate the most dollars in relation to the limited resources available and the size and returns from the possible investments. Thus, the NPV method should be used because it determines the aggregate present value for each feasible combination of projects.

Answer 33

B. Multiple projects have unequal lives and the size of the investment for each project is different. The two methods ordinarily yield the same results, but differences can occur when the duration of the projects and the initial investments differ. The reason is that the IRR method assumes cash inflows from the early years will be reinvested at the internal rate of return. The NPV method assumes that early cash inflows are reinvested at the NPV discount rate.

Answer 34

C. $(13,265) The $35,000 of working capital requires an immediate outlay for that amount, but it will be recovered in 5 years. Thus, the net discounted cash outflow is $13,265 [$35,000 initial investment – ($35,000 future inflow × .621 PV of $1 for 5 years at 10%)].

Answer 35

C. $1,059,000 The net present value (NPV) is calculated as the present value of net savings (cash inflow) minus the initial investment. The NPVs for the project with and without an increase in sales are calculated as follows: Without sales increase: Increase in income ($5,000,000 sales – $2,500,000 variable costs): $ 2,500,000 Tax expense ($2,500,000 × 25% tax rate) : (625,000) Deprecation tax shield [($10,000,000 ÷ 10 years) × 25% tax rate]: 250,000 After-tax increase in income: $ 2,125,000 Times: PV factor (ord. annuity): × 5.6502 PV of net savings: $12,006,675 Minus: Initial investment: (10,000,000) Net present value $ 2,006,675 With sales increase: Increase in income ($5,500,000 sales – $2,750,000 variable costs): $ 2,750,000 Tax expense ($2,750,000 × 25% tax rate): (687,500) Deprecation tax shield [($10,000,000 ÷ 10 years) × 25% tax rate]: 250,000 After-tax increase in income: $ 2,312,500 Times: PV factor (ord. annuity): × 5.6502 PV of net savings: $13,066,088 Minus: Initial investment: (10,000,000) Net present value: $ 3,066,088 Thus, the NPV increased by $1,059,412 ($3,066,088 – $2,006,675). The amount of $1,059,000 is closest to the answer derived.

Answer 36

A. $13,817 Gunning uses straight-line depreciation. Thus, the annual charge is $38,000 [($160,000 + $30,000) ÷ 5 years], and the tax savings is $15,200 ($38,000 × 40%). That benefit will be received in 1 year, so the present value is $13,817 ($15,200 tax savings × .909 present value of $1 for 1 year at 10%).

Answer 37

D. Excess of the discounted cash inflows over the discounted cash outflows. The net present value of an investment project represents the excess of the discounted cash inflows over the discounted cash outflows.

Answer 38

The cash inflows of Project Y are uneven and must be discounted with individual factors for each of the 4 years as follows: Year: Net Cash Inflows x PV Factor = Present Value Required investment: $100,000 x 1 = $(100,000) Cash flow, end of Year 1: 8,000 x 0.917 = 7,336 Cash flow, end of Year 2: 6,000 x 0.842 = 5,052 Cash flow, end of Year 3: 7,000 x 0.772 = 5,404 Cash flow and return of investment, end of Year 4: 112,000 x 0.708 = 79,296 Total: $ (2,912)

Answer 39

A. $7,720 The net present value of a capital project is derived by calculating three amounts and discounting them at the appropriate interest rate: the net initial investment (for which the rate is always 0%), the annual cash inflows, and the termination cash inflows. The net initial investment itself consists of three components: the purchase of new equipment, the increase in working capital, and the proceeds from the disposal of any old equipment. For this project, this amount is $320,000 ($120,000 + $200,000 + $0). Since this amount is paid out today, its present value is $320,000, i.e., no discounting is performed. The second element of the project as a whole is the annual cash inflows. This has two components: the cash inflows from operations and the depreciation tax shield arising from the purchase of new equipment. Since the effects of income taxes are not relevant to this problem, only the first of these components requires calculation. The annual net operating revenue is $80,000 ($40,000 - $250,000 - $70,000). Discounted as an ordinary annuity for 5 years at 20%, its present value is $239,280 ($80,000 x 2.991). The third and final element is the cash flows upon termination of the project, consisting of the proceeds from the disposal of the equipment involved in the project (again, the effects of income taxes are ignored for this problem) and the recovery of working capital. For this project, this amount is $220,000 ($20,000 + $220,000). Discounted as a single amount to be received in 5 years at 20%, its present value is $88,440 ($220,000 x 0.402). The corporation's total net present value for this capital project can therefore be calculated as follows: Net initial investment $(320,000) Annual cash inflows 239,280 Termination cash inflows 88,440 Net present value $ 7,720

Answer 40

A. The project has another IRR in addition to the minus 29% rate. The multiple IRR effect states that there are as many solutions to the IRR formula as there are changes in the direction of the net cash flows. Because the cash flows change from inflows to outflows from Year 3 to Year 4, another correct solution to the IRR exists.

Answer 41

D. The direction of cash flow changes multiple times during the life of a project. One of the disadvantages of the IRR method is that multiple IRRs will exist when the direction of cash flows changes multiple times during the life of the project.

Answer 42

D. The entity should pursue Project A and Project C, only. Under the internal rate of return method, the entity should pursue any project that provides a rate of return greater than or equal to the entity's cost of capital. In this scenario, the rates of return for Projects A and C both meet or exceed the cost of capital of 6%. As such, both Projects A and C should be pursued.

Answer 43

A. $23 million. The fist step is to determine the amount that will be needed in 20 years. If the $500 million increases by 5% annually, the amount needed in years 20 would be $1,326,500,000 ($500 million × 2.653). Since there is already $100 million available in the fund, that amount will grow at 7% annually for 20 years to equal $387 million. Subtracting the $387 million from $1,326,500,000 leaves $939,500,000 to be raised. Use a future value table to find the present value of 20 equal payments that will accumulate to $939,500,000 in 20 years at 7% interest. Dividing the $939,500,000 by the future value factor of 40.995 (20 years at 7%) equals $22,917,429 per year, or approximately $23 million.

Answer 44

B. $38,321 This problem requires the use of the net present value (NPV) method of investment analysis. The objective is to determine what average annual net cash inflow will equal the initial cost when discounted at a rate of 24%. Given that the investment has an expected life of 5 years, the appropriate time value of money factor is that for the present value of an ordinary annuity for 5 years at 24%. In this case, the annual net cash inflow is unknown, but the product of the factor (2.74) and the inflow is $105,000. Thus, dividing $105,000 by 2.74 results in an average annual net cash inflow of $38,321. In other words, if annual inflows are $38,321 per year, the present value is $105,000. This present value is equal to the initial cost, and the net present value is zero. At a net present value of zero, the investor is indifferent as to whether to undertake the investment.

Answer 45

C. IRR is greater than 10%. The total cash inflows are only $70,000 (5 × $14,000). Thus, whatever the discount rate, the NPV will be less than $20,000 ($70,000 – $50,000). The return in the first year is $14,000, or 28% of the initial investment. Since the same $14,000 flows in each year, the IRR is going to be greater than 10% (actually, it is almost 14%).

Answer 46

C. Multiple positive and negative cash flows over the life of the project will yield multiple IRRs. There are as many solutions to the IRR formula as there are changes in the direction of the net cash flows. Therefore, the actual IRR needed cannot be found.

Answer 47

D. Increasing the present value of the depreciation tax shield. Accelerated depreciation results in greater depreciation in the early years of an asset’s life compared with the straight-line method. Thus, accelerated depreciation results in lower income tax expense in the early years of a project and higher income tax expense in the later years. By effectively deferring taxes, the accelerated method increases the present value of the depreciation tax shield.

Answer 48

B. Accept Project X and reject Project Y. When capital projects are mutually exclusive, the one with the highest net present value should be selected. Project X / Project Y Cash inflows: $ 47,000 / $280,000 Times: PV factor: × 3.791% / × .621% PV of cash inflows $178,177 / $173,880 Less: Net initial investment: (150,000) / (150,000) Net present value $ 28,177 / $ 23,880 Project X should be accepted ($28,177 > $23,880).

Answer 49

D. $7,000-$7,500 The NPV must be calculated without a value for the used equipment. The initial outflow is $120,000 ($100,000 machine cost plus $20,000 investment in working capital). The annual cash inflows would be $30,000, but that would be reduced by the $2,500 of income taxes. Thus, the net inflows each year would be $27,500 {[$30,000 cash inflow × (1 – .25 tax rate)] + ($20,000 depreciation × .25 tax rate)}. The inflows from termination equal the $20,000 of working capital recovered, plus the selling price of the used equipment, minus the taxes on the sale of the fully-depreciated equipment. These amounts would then be discounted at 10%, as follows: $27,500 × 3.791 = $104,252.50 20,000 × .621 = 12,420.00 Partial present value = $116,672.50 Less: Initial investment = 120,000.00 Amount needed at sale = $ 3,327.50 The $3,327.50 represents the present value of the amount needed from the after-tax sale of the used machine. In other words, (S – .25S) × .621 = $3,327.50. Dividing both sides of the equation by .621 yields .75S = $5,358.29, or S = $7,144.39.

Answer 50

A. Greater than the project’s internal rate of return. The higher the discount rate, the lower the NPV. The IRR is the discount rate at which the NPV is zero. Consequently, if the NPV is negative, the discount rate used must exceed the IRR.

Answer 51

B. $26,160 The initial investment in this project can be calculated as follows: Annual cash inflows $ 9,000 Times: PV factor × 3.240 PV of cash inflows $29,160 Less: NPV of project (3,000) Amount invested $26,160

Answer 52

A. Rate of interest for which the net present value is equal to zero. The IRR is the interest rate at which the present value of the expected future cash inflows is equal to the present value of the cash outflows for a project. Thus, the IRR is the interest rate that will produce a net present value (NPV) equal to zero. The IRR method assumes that the cash flows will be reinvested at the internal rate of return.

Answer 53

C. Approximately $(73,000); recommend not making the investment. The net initial investment in Year 0 will be $475,000 ($450,000 + $25,000 installation charges). The annual pre-tax savings per year are stated as $175,000. Therefore, the annual after-tax savings will be $105,000 [$175,000 × (1 – .40)]. The depreciation tax shield for each year is calculated as follows: Year 1: $475,000 × .25 = $118,750 × .40 = $47,500 Year 2: $475,000 × .38 = $180,500 × .40 = $72,200 Year 3: $475,000 × .37 = $175,750 × .40 = $70,300 Now solve for the NPV using the PV factors at 12%: (–$475,000) + [($105,000 + $47,500) × .893] + [($105,000 + $72,200) × .797] + [($105,000 + $70,300) × .712] = –$72,776 Because the NPV is negative, the firm should not make the investment.

Answer 54

B. Cash inflow stream #1. The concept of present value gives greater value to inflows received earlier in the stream. Thus, the declining inflows are superior to increasing inflows or even inflows.

Answer 55

C. Building X and Building Y only. The relevant calculations for each building are Building X: ¥450,000 discounted for 4 years = ¥450,000 × 3.1699 = ¥1,426,455 Building Y: ¥650,000 discounted for 2 years = ¥650,000 × 1.7355 = ¥1,128,075 Building Z: ¥615,000 discounted for 3 years = ¥615,000 × 2.4869 = ¥1,529,444 (rounded) The leases for Buildings X and Y meet management’s criteria and therefore should be accepted.

Answer 56

D. Net present value because internal rate of return assumes that project cash flows can be invested at the firm’s internal rate of return. Since the firm knows the required rate of return, it would be better to use the NPV, as it assumes that funds are reinvested at the required rate of return even if that changes from year to year. They will not be reinvested at the internal rate of return.

Answer 57

B. $31,632 The NPV of the electric bus is $31,632, which is greater than that of two gas-powered buses bought 4 years apart. The NPV for the $90,000 electric bus involves multiplying the $28,000 annual cash flows times the present value factor of 4.344, which equals $121,632. Deducting the $90,000 initial cost results in an NPV of $31,632. The NPV for the two gas-powered buses is $10,208, calculated as follows: $22,000 × 4.344 $95,568 Less: First bus (55,000) Less: Second bus ($55,000 × .552) (30,360) NPV $10,208

Answer 58

C. Accept Project A because at a 10% discount rate, it has an NPV that is greater than that of Project B. Net present value (NPV) is the most satisfactory method of evaluating competing capital projects. At a hurdle rate of 10%, Project A has the higher NPV and is therefore the more desirable project.

Answer 59

C. Z, Y, X. The net present value (NPV) nets the expected cash streams related to a project and then discounts them at the hurdle rate. The cost of capital is equal to 10%. Therefore, the NPV for each project can be calculated using the PV factors of $1 at 10% as follows: Periods: PV Factor at 10% 0: 1.00000 1: 0.90909 2: 0.82645 3: 0.75131 4: 0.68301 Project X: (–$7,000 × 1) + ($0 × .90909) + ($4,000 × .82645) + ($2,000 × .75131) + ($5,000 × .68301) = $1,224 Project Y: (–$7,000 × 1) + ($2,000 × .90909) + ($3,000 × .82645) + ($4,000 × .75131) + ($2,000 × .68301) = $1,668 Project Z: (–$7,000 × 1) + ($5,000 × .90909) + ($0 × .82645) + ($2,000 × .75131) + ($4,000 × .68301) = $1,780 The NPVs can be ranked in descending order as Z ($1,780), Y ($1,668), and X ($1,224).