CHAPTER 9
MAKING CAPITAL INVESTMENT DECISIONS
4.
To find the OCF, we need to complete the income statement as follows:
Sales
$ 687,500
Variable costs 343,860
Depreciation
110,000
EBIT
$ 233,640
Taxes@35%
81,774
Net income $ 151,866
The OCF for the company is:
OCF = EBIT + Depreciation – Taxes
OCF = $233,640 + 110,000 – 81,774
OCF = $261,866
The depreciation tax shield is the depreciation times the tax rate, so:
Depreciation tax shield = tcDepreciation
Depreciation tax shield = .35($110,000)
Depreciation tax shield = $38,500
The depreciation tax shield shows us the increase in OCF by being able to expense
depreciation.
14. First, we will calculate the annual depreciation of the new equipment. It will be:
Annual depreciation charge = $850,000/5
Annual depreciation charge = $170,000
The aftertax salvage value of the equipment is:
Aftertax salvage value = $180,000(1 – 0.35)
Aftertax salvage value = $117,000
Using the tax shield approach, the OCF is:
OCF = $310,000(1 – 0.35) + 0.35($170,000)
OCF = $261,000
Now we can find the project IRR. There is an unusual feature that is a part of this
project. Accepting this project means that we will reduce NWC. This reduction in
NWC is a cash inflow at Year 0. This reduction in NWC implies that when the
project ends, we will have to increase NWC. So, at the end of the project, we will
have a cash outflow to restore the NWC to its level before the project. We must also
include the aftertax salvage value at the end of the project. The IRR of the project is:
NPV = 0 = –$850,000 + 75,000 + $261,000(PVIFAIRR%,5) + [($117,000 – 75,000) /
(1+IRR)5]
IRR = 21.28%
21. First, we will calculate the depreciation each year, which will be:
D1 = $480,000(0.2000) = $96,000
D2 = $480,000(0.3200) = $153,600
D3 = $480,000(0.1920) = $92,160
D4 = $480,000(0.1152) = $55,296
The book value of the equipment at the end of the project is:
BV4 = $480,000 – ($96,000 + 153,600 + 92,160 + 55,296)
BV4 = $82,944
The asset is sold at a loss to book value, so this creates a tax refund.
After-tax salvage value = $55,000 + ($82,944 – 55,000)(0.34)
After-tax salvage value = $64,500.96
Using the depreciation tax shield approach, the OCF for each year will be:
OCF1 = $205,000(1 – 0.34) + 0.34($96,000) = $167,940
OCF2 = $205,000(1 – 0.34) + 0.34($153,600) = $187,524
OCF3 = $205,000(1 – 0.34) + 0.34($92,160) = $166,634
OCF4 = $205,000(1 – 0.34) + 0.34($55,296) = $154,101
Now, we have all the necessary information to calculate the project NPV. We need
to be careful with the NWC in this project. Notice the project requires $21,000 of
NWC at the beginning, and $3,000 more in NWC each successive year. We will
subtract the $21,000 from the initial cash flow, and subtract $3,000 each year from
the OCF to account for this spending. In Year 4, we will add back the total spent on
NWC, which is $30,000. The $3,000 spent on NWC capital during Year 4 is
irrelevant. Why? Well, during this year the project required an additional $3,000, but
we would get the money back immediately. So, the net cash flow for additional
NWC would be zero. With all this, the equation for the NPV of the project is:
NPV = – $480,000 – 21,000 + ($167,940 – 3,000)/1.15 + ($187,524 – 3,000)/1.152
+ ($166,634 – 3,000)/1.153 + ($154,101 + 30,000 + 64,500.96)/1.154
NPV = $31,683.79
24. The marketing study and the research and development are both sunk costs and should be
ignored. The initial cost is the equipment plus the net working capital, so:
Initial cost = $18,400,000 + 1,100,000
Initial cost = $19,500,000
Next, we will calculate the sales and variable costs. Since we will lose sales of the expensive
clubs and gain sales of the cheap clubs, these must be accounted for as erosion. The total
sales for the new project will be:
Sales
New clubs
Exp. clubs
Cheap clubs
$650  60,000 = $39,000,000
$1,100  (–10,000) = –11,000,000
$300  15,000 =
4,500,000
$32,500,000
For the variable costs, we must include the units gained or lost from the existing clubs. Note
that the variable costs of the expensive clubs are an inflow. If we are not producing the sets
anymore, we will save these variable costs, which is an inflow. So:
Var. costs
New clubs
Exp. clubs
Cheap clubs
$340  60,000 = $20,400,000
$550  (–10,000) = –5,500,000
$100  15,000 = 1,500,000
$16,400,000
The pro forma income statement will be:
Sales
Variable costs
Costs
Depreciation
EBT
Taxes
Net income
$32,500,00
0
16,400,000
9,000,000
2,628,571
4,471,429
1,788,571
$
2,682,857
Using the bottom up OCF calculation, we get:
OCF = NI + Depreciation
OCF = $2,682,857 + 2,628,571
OCF = $5,311,429
So, the payback period is:
Payback period = 3 + $3,565,713/$5,311,429
Payback period = 3.67 years
The NPV is:
NPV = –$18,400,000 – 1,100,000 + $5,311,429(PVIFA14%,7) + $1,100,000/1.147
NPV = $3,716,625.90
And the IRR is:
0 = –$18,400,000 – 1,100,000 + $5,311,429(PVIFAIRR%,7) + $1,100,000/IRR7
IRR = 19.91%