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10-1A.
(a) Tax payments associated with the sale for $35,000
Recapture of depreciation
= ($35,000-$15,000) (0.34) = $6,800
(b) Tax payments associated with sale for $25,000
Recapture of depreciation
= ($25,000-$15,000) (0.34) = $3,400
(c) No taxes, because the machine would have been sold for its book value.
(d) Tax savings from sale below book value:
Tax savings = ($15,000-$12,000) (0.34) = $1,020
10-2A.
New Sales $25,000,000
Less: Sales taken from
existing product lines - 5,000,000
$20,000,000
10-3A. Change in net working capital equals the increase in accounts receivable and inventory less the increase in accounts payable = $18,000 + $15,000 - $24,000 = $9,000.
The change in taxes will be EBIT X marginal tax rate = $475,000 X.34 = $161,500.
A project’s free cash flows =
Change in earnings before interest and taxes
- change in taxes
+ change in depreciation
- change in net working capital
- change in capital spending
= $475,000
- $161,500
+ $100,000
- $9,000
$0
= $404,500
10-4A. Change in net working capital equals the increase in accounts receivable and inventory less the increase in accounts payable = $8,000 + $15,000 - $16,000 = $7,000.
The change in taxes will be EBIT X marginal tax rate = $900,000 X.34 = $306,000.
A project’s free cash flows =
Change in earnings before interest and taxes
- change in taxes
+ change in depreciation
- change in net working capital
- change in capital spending
= $900,000
- $306,000
+ $300,000
- $7,000
- $0
= $887,000
10-5A. Given this, the firm’s net profit after tax can be calculated as:
Revenue $2,000,000
- Cash expenses 800,000
- Depreciation 200,000
= EBIT $1,000,000
- Taxes (34%) 340,000
= Net income $ 660,000
OCF Calculation: Pro Forma Approach
Operating Cash Flows =
Change in Earnings Before Interest and Taxes
- Change in Taxes
+ Change in Depreciation
= $1,000,000 - $340,000 + $200,000 = $860,000
Alternative OCF Calculation 1: Add Back Approach
Operating Cash Flows = Net income + Depreciation
= $660,000 + $200,000 = $860,000
Alternative OCF Calculation 2: Definitional Approach
Operating Cash Flows = Change in revenues - Change in cash expenses –
Change in Taxes
= $2,000,000 - $800,000 -$340,000 = $860,000
Alternative OCF Calculation 3: Depreciation Tax Shield Approach
Operating Cash Flows = (Revenues – cash expenses) X (1 – tax rate) +
(change in depreciation X tax rate)
= ($2,000,000 - $800,000) X (1-.34) + ($200,000 X.34)
= $860,000
You’ll notice that interest payments are nowhere to be found, that’s because we ignore them when we’re calculating operating cash flows. You’ll also notice that we end up with the same answer regardless of how we work the problem.
10-6A. Given this, the firm’s net profit after tax can be calculated as:
Revenue $3,000,000
- Cash expenses 900,000
- Depreciation 400,000
= EBIT $1,700,000
- Taxes (34%) 578,000
= Net income $1,122,000
As you can see, regardless of which method you use to calculate operating cash flows, you get the same answer:
OCF Calculation: Pro Forma Approach
Operating Cash Flows = Change in Earnings Before Interest and Taxes - Change in
Taxes + Change in Depreciation
= $1,700,000 - $578,000 + $400,000 = $1,522,000
Alternative OCF Calculation 1: Add Back Approach
Operating Cash Flows = Net income + Depreciation
= $1,122,000 + $400,000 = $1,522,000
Alternative OCF Calculation 2: Definitional Approach
Operating Cash Flows = Change in revenues - Change in cash expenses –
Change in Taxes
= $3,000,000 - $900,000 -$578,000 = $1,522,000
Alternative OCF Calculation 3: Depreciation Tax Shield Approach
Operating Cash Flows = (Revenues – cash expenses) X (1 – tax rate) +
(change in depreciation X tax rate)
= ($3,000,000 - $900,000)X(1-.34) + ($400,000 X.34)
= $1,522,000
You’ll notice that interest payments are no where to be found, that’s because we ignore them when we’re calculating operating cash flows. You’ll also notice that we end up with the same answer regardless of how we work the problem.
10-7A. (a) Initial Outlay
Outflows:
Purchase price $1,000,000
Increased Inventory 50,000
Net Initial Outlay $1,050,000
(b) Differential annual cash flows (years 1-9)
First, given this, the firm’s net profit after tax can be calculated as:
Revenue $1,000,000
- Cash expenses 560,000
- Depreciation* 100,000
= EBIT $340,000
- Taxes (34%) 115,600
= Net income $224,400
A project’s free cash flows =
Change in earnings before interest and taxes
- change in taxes + change in depreciation
- change in net working capital
- change in capital spending
= $340,000
- $115,600
+ $100,000*
- $0
- $0
= $324,400
*Annual Depreciation on the new machine is calculated by taking the purchase price ($1,000,000) and adding in costs necessary to get the new machine in operating order (in this case $0) and dividing by the expected life.
(c) Terminal Cash flow (year 10)
Inflows:
Free Cash flow in year 10 $324,400
Recapture of working capital (inventory) 50,000
Total terminal cash flow $374,400
(d) NPV = $324,400 (PVIFA10%,9 yr.) + $374,400 (PVIF10%, 10 yr.) - $1,050,000
= $324,400 (5.759) + $374,400 (.386) - $1,050,000
= $1,868,220 + $144,518 - $1,050,000
= $962,738
10-8A.
(a) Initial Outlay
Outflows:
Purchase price $5,000,000
Increased Inventory 1,000,000
Net Initial Outlay $6,000,000
(b) Differential annual cash flows (years 1-4)
First, given this, the firm’s net profit after tax can be calculated as:
Revenue $5,000,000
- Cash expenses 3,500,000
- Depreciation* 1,000,000
= EBIT $ 500,000
- Taxes (34%) 170,000
= Net income $ 330,000
A project’s free cash flows =
Change in earnings before interest and taxes
- change in taxes
+ change in depreciation
- change in net working capital
- change in capital spending
= $500,000
- $170,000
+ $1,000,000*
- $0
- $0
= $1,330,000
*Annual Depreciation on the new machine is calculated by taking the purchase price ($5,000,000) and adding in costs necessary to get the new machine in operating order ($0) and dividing by the expected life.
(c) Terminal Cash flow (year 5)
Inflows:
Free Cash flow in year 5 $1,330,000
Recapture of working capital (inventory) 1,000,000
Total terminal cash flow $2,330,000
(d) NPV = $1,330,000 (PVIFA10%,4 yr.) + $2,330,000 (PVIF10%, 5 yr.) - $6,000,000
= $1,330,000 (3.170) + $2,330,000 (.621) - $6,000,000
= $4,216,100 + $1,446,930 - $6,000,000
= -$336,970
Since the NPV is negative, this project should be rejected.
10-9A.
(a) Initial Outlay
Outflows:
Purchase price $100,000
Installation Fee 5,000
Increased Working Capital Inventory 5,000
Net Initial Outlay $110,000
(b) Differential annual free cash flows (years 1-9)
A project’s free cash flows =
Change in earnings before interest and taxes
- change in taxes
+ change in depreciation
- change in net working capital
- change in capital spending
= $35,000
- $11,900
+ $10,500*
- $0
- $0
= $33,600
* Annual Depreciation on the new machine is calculated by taking the purchase price ($100,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life.
(c) Terminal Free Cash flow (year 10)
Inflows:
Free Cash flow in year 10 $33,600
Recapture of working capital (inventory) 5,000
Total terminal cash flow $ 38,600
(d) NPV = $33,600 (PVIFA15%,9 yr.) + $38,600 (PVIF15%, 10 yr.) - $110,000
= $33,600 (4.772) + $38,600 (.247) - $110,000
= $160,339.20 + $9,534.20 - $110,000
= $59,873.40
Yes, the NPV > 0.
10-10A.(a) Initial Outlay
Outflows:
Purchase price $ 500,000
Installation Fee 5,000
Training Session Fee 25,000
Increased Inventory 30,000
Net Initial Outlay $560,000
(b) Differential annual free cash flows (years 1-9)
A project’s free cash flows =
Change in earnings before interest and taxes
- change in taxes
+ change in depreciation
- change in net working capital
- change in capital spending
= $150,000
- $51,000
+ $50,500*
- $0
- $0
= $149,500
*Annual Depreciation on the new machine is calculated by taking the purchase price ($500,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life.
(c) Terminal Free Cash flow (year 10)
Inflows:
Free Cash flow in year 10 $149,500
Recapture of working capital (inventory) 30,000
Total terminal cash flow $ 179,500
(d) NPV = $149,500 (PVIFA15%,9 yr.) + $179,500 (PVIF15%, 10 yr.) - $560,000
= $149,500 (4.772) + $179,500 (.247) - $560,000
= $713,414 + $44,336.50 - $560,000
= $197,750.50
Yes, the NPV > 0.
10-11A.(a) Initial Outlay
Outflows:
Purchase price $ 200,000
Installation Fee 5,000
Training Session Fee 5,000
Increased Inventory 20,000
Net Initial Outlay $230,000
(b) Differential annual cash flows (years 1-9)
A project’s free cash flows =
Change in earnings before interest and taxes
- change in taxes
+ change in depreciation
- change in net working capital
- change in capital spending
= $50,000
- $17,000
+ $20,500*
- $0
- $0
= $53,500
*Annual Depreciation on the new machine is calculated by taking the purchase price ($200,000) and adding in costs necessary to get the new machine in operating order (the installation fee of $5,000) and dividing by the expected life.
(c) Terminal Cash flow (year 10)
Inflows:
Free Cash flow in year 10 $53,500
Recapture of working capital (inventory) 20,000
Total terminal cash flow $ 73,500
(d) NPV = $53,500 (PVIFA10%,9 yr.) + $73,500 (PVIF10%, 10 yr.) - $230,000
= $53,500 (5.759) + $73,500 (.386) - $230,000
= $308,106.50 + $28,371 - $230,000
= $106,477.50
Yes, the NPV > 0.
10-12A
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| END-OF-CHAPTER QUESTIONS | | | Section I. Calculate the change in EBIT, Taxes, and Depreciation (this becomes an input in the calculation of Operating Cash Flow in Section II). |