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Chapter 06 - Making Capital Investment Decisions
Revenue Expenditures Depreciation Restoration cost EBT Tax NI OCF
Years 1-14 $215,000 90,000 23,667
0 $101,333 34,453 $66,880 $90,547
Year 15 $215,000 90,000 23,667 80,000 $21,333 7,253 $14,080 $37,747
The OCF each year is net income plus depreciation. So, the NPV for modifying the building to manufacture Product B is:
NPV = –$355,000 + $90,547(PVIFA12%,14) + $37,747 / 1.1215 NPV = $252,054.71
Since renting has the highest NPV, the company should continue to rent the building.
We could have also done the analysis as the incremental cash flows between Product A and continuing to rent the building, and the incremental cash flows between Product B and continuing to rent the building. The results of this type of analysis would be:
NPV of differential cash flows between Product A and continuing to rent: NPV = NPVProduct A – NPVRent
NPV = $242,606.97 – 274,205.40 NPV = –$31,598.43
NPV of differential cash flows between Product B and continuing to rent: NPV = NPVProduct B – NPVRent
NPV = $252,054.71 – 274,205.40 NPV = –$22,150.69
Since the differential NPV of both products and renting is negative, the company should continue to rent, which is the same as our original result.
35. The discount rate is expressed in real terms, and the cash flows are expressed in nominal terms. We
can answer this question by converting all of the cash flows to real dollars. We can then use the real interest rate. The real value of each cash flow is the present value of the year 1 nominal cash flows, discounted back to the present at the inflation rate. So, the real value of the revenue and costs will be:
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Chapter 06 - Making Capital Investment Decisions
Revenue in real terms = $265,000 / 1.06 = $250,000.00 Labor costs in real terms = $185,000 / 1.06 = $174,528.30 Other costs in real terms = $55,000 / 1.06 = $51,886.79 Lease payment in real terms = $90,000 / 1.06 = $84,905.66
Revenues, labor costs, and other costs are all growing perpetuities. Each has a different growth rate, so we must calculate the present value of each separately. Using the real required return, the present value of each of these is:
PVRevenue = $250,000.00 / (0.10 – 0.04) = $4,166,666.67 PVLabor costs = $174,528.30 / (0.10 – 0.03) = $2,493,261.46 PVOther costs = $51,886.79 / (0.10 – 0.01) = $576,519.92
The lease payments are constant in nominal terms, so they are declining in real terms by the inflation rate. Therefore, the lease payments form a growing perpetuity with a negative growth rate. The real present value of the lease payments is:
PVLease payments = $84,905.66 / [0.10 – (–0.06)] = $530,660.38
Now we can use the tax shield approach to calculate the net present value. Since there is no investment in equipment, there is no depreciation; therefore, no depreciation tax shield, so we will ignore this in our calculation. This means the cash flows each year are equal to net income. There is also no initial cash outlay, so the NPV is the present value of the future aftertax cash flows. The NPV of the project is:
NPV = (PVRevenue – PVLabor costs – PVOther costs – PVLease payments)(1 – tC)
NPV = ($4,166,666.67 – 2,493,261.46 – 576,519.92 – 530,660.38)(1 – .34) NPV = $373,708.45
Alternatively, we could have solved this problem by expressing everything in nominal terms. This approach yields the same answer as given above. However, in this case, the computation would have been impossible. The reason is that we are dealing with growing perpetuities. In other problems, when calculating the NPV of nominal cash flows, we could simply calculate the nominal cash flow each year since the cash flows were finite. Because of the perpetual nature of the cash flows in this problem, we cannot calculate the nominal cash flows each year until the end of the project. When faced with two alternative approaches, where both are equally correct, always choose the simplest one.
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? 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 06 - Making Capital Investment Decisions
36. We are given the real revenue and costs, and the real growth rates, so the simplest way to solve this
problem is to calculate the NPV with real values. While we could calculate the NPV using nominal values, we would need to find the nominal growth rates, and convert all values to nominal terms. The real labor costs will increase at a real rate of two percent per year, and the real energy costs will increase at a real rate of three percent per year, so the real costs each year will be: Year 1 Year 2 Year 3 Year 4 Real labor cost each year $15.75 $16.07 $16.39 $16.71 Real energy cost each year $3.80 $3.91 $4.03 $4.15 Remember that the depreciation tax shield also affects a firm’s aftertax cash flows. The present value
of the depreciation tax shield must be added to the present value of a firm’s revenues and expenses to find the present value of the cash flows related to the project. The depreciation the firm will recognize each year is: Annual depreciation = Investment / Economic Life Annual depreciation = $165,000,000 / 4 Annual depreciation = $41,250,000 Depreciation is a nominal cash flow, so to find the real value of depreciation each year, we discount
the real depreciation amount by the inflation rate. Doing so, we find the real depreciation each year is: Year 1 real depreciation = $41,250,000 / 1.05 = $39,285,714.29 Year 2 real depreciation = $41,250,000 / 1.052 = $37,414,965.99 Year 3 real depreciation = $41,250,000 / 1.053 = $35,633,300.94 Year 4 real depreciation = $41,250,000 / 1.054 = $33,936,477.09 Now we can calculate the pro forma income statement each year in real terms. We can then add back
depreciation to net income to find the operating cash flow each year. Doing so, we find the cash flow of the project each year is:
Year 0 Year 1 Year 2 Year 3 Year 4 Revenues $69,300,000.00 $74,250,000.00 $84,150,000.00 $79,200,000.00 Labor cost 17,640,000.00 19,278,000.00 22,285,368.00 21,393,953.28 Energy cost 798,000.00 880,650.00 1,028,012.10 996,567.02 Depreciation 39,285,714.29 37,414,965.99 35,633,300.94 33,936,477.09 EBT $11,576,285.71 $16,676,384.01 $25,203,318.96 $22,873,002.61 Taxes 3,935,937.14 5,669,970.56 8,569,128.45 7,776,820.89 Net income $7,640,348.57 $11,006,413.45 $16,634,190.51 $15,096,181.72
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manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
OCF
Capital spending
Total CF
$46,926,062.86 $48,421,379.44 $52,267,491.45 $49,032,658.81
–$165,000,000
–$165,000,000 $46,926,062.86 $48,421,379.44 $52,267,491.45 $49,032,658.81
Chapter 06 - Making Capital Investment Decisions
We can use the total cash flows each year to calculate the NPV, which is:
NPV = –$165,000,000 + $46,926,062.86 / 1.04 + $48,421,379.44 / 1.042 + $52,267,491.45 / 1.043 + $49,032,658.81 / 1.044 NPV = $13,268,433.31
37. Here we have the sales price and production costs in real terms. The simplest method to calculate the
project cash flows is to use the real cash flows. In doing so, we must be sure to adjust the depreciation, which is in nominal terms. We could analyze the cash flows using nominal values, which would require calculating the nominal discount rate, nominal price, and nominal production costs. This method would be more complicated, so we will use the real numbers. We will first calculate the NPV of the headache only pill. Headache only: We can find the real revenue and production costs by multiplying each by the units sold. We must be
sure to discount the depreciation, which is in nominal terms. We can then find the pro forma net income, and add back depreciation to find the operating cash flow. Discounting the depreciation each year by the inflation rate, we find the following cash flows each year: Year 1 Year 2 Year 3 Sales $25,050,000 $25,050,000 $25,050,000 Production costs 12,300,000 12,300,000 12,300,000 Depreciation 7,443,366 7,226,569 7,016,086 EBT $5,306,634 $5,523,431 $5,733,914 Tax 1,804,256 1,877,967 1,949,531 Net income $3,502,379 $3,645,465 $3,784,383
Market value Taxes Total
$1,000,000 –340,000 $660,000
OCF
$10,945,744
$10,872,033
$10,800,469
And the NPV of the headache only pill is:
NPV = –$23,000,000 + $10,945,744 / 1.07 + $10,872,033 / 1.072 + $10,800,469 / 1.073 NPV = $5,542,122.70 Headache and arthritis:
For the headache and arthritis pill project, the equipment has a salvage value. We will find the aftertax salvage value of the equipment first, which will be:
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? 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 06 - Making Capital Investment Decisions
Remember, to calculate the taxes on the equipment salvage value, we take the book value minus the market value, times the tax rate. Using the same method as the headache only pill, the cash flows each year for the headache and arthritis pill will be:
Sales
Production costs Depreciation EBT Tax
Net income OCF
Year 1 $37,575,000 20,925,000 10,355,987 $6,294,013 2,139,964 $4,154,049 $14,510,036
Year 2 $37,575,000 20,925,000 10,054,356 $6,595,644 2,242,519 $4,353,125 $14,407,481
Year 3 $37,575,000 20,925,000 9,761,511 $6,888,489 2,342,086 $4,546,403 $14,307,914
So, the NPV of the headache and arthritis pill is:
NPV = –$32,000,000 + $14,510,036 / 1.07 + $14,407,481 / 1.072 + ($14,307,914 + 660,000) / 1.073 NPV = $6,363,109.18
The company should manufacture the headache and arthritis remedy since the project has a higher NPV.
38. Since the project requires an initial investment in inventory as a percentage of sales, we will
calculate the sales figures for each year first. The incremental sales will include the sales of the new table, but we also need to include the lost sales of the existing model. This is an erosion cost of the new table. The lost sales of the existing table are constant for every year, but the sales of the new table change every year. So, the total incremental sales figure for the five years of the project will be: Year 1 Year 2 Year 3 Year 4 Year 5 New $10,980,000 $11,895,000 $15,250,000 $14,335,000 $12,810,000 Lost sales –1,125,000 –1,125,000 –1,125,000 –1,125,000 –1,125,000 Total $9,855,000 $10,770,000 $14,125,000 $13,210,000 $11,685,000 Now we will calculate the initial cash outlay that will occur today. The company has the necessary
production capacity to manufacture the new table without adding equipment today. So, the equipment will not be purchased today, but rather in two years. The reason is that the existing capacity is not being used. If the existing capacity were being used, the new equipment would be required, so it would be a cash flow today. The old equipment would have an opportunity cost if it could be sold. As there is no discussion that the existing equipment could be sold, we must assume it cannot be sold. The only initial cash flow is the cost of the inventory. The company will have to spend money for inventory in the new table, but will be able to reduce inventory of the existing table. So, the initial cash flow today is: New table –$1,098,000 Old table 112,500 Total –$985,500
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? 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any
manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.