Making Capital Investment Decisions
(Part 2)
Today’s Topics
Alternative Definitions of OCF
Special Cases of DCF Analysis
Alternative Definitions of OCF
Alternative Definitions of OCF
• Assume an all-equity firm (no debt, no interest expense)
•
Tax shield benefit from interest expense deduction is reflected in the cost of debt
𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
𝑇𝑇𝑇𝑇𝑇𝑇 = 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 × 𝑡𝑡𝐶𝐶
𝑂𝑂𝑂𝑂𝑂𝑂 = 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 − 𝑇𝑇𝑇𝑇𝑇𝑇
Alternative Definitions of OCF Continued
• The Bottom-Up Approach
•
Start with net income that appears at the bottom line of income statement
𝑂𝑂𝑂𝑂𝑂𝑂 = 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 − 𝑇𝑇𝑇𝑇𝑇𝑇
= (𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 − 𝑇𝑇𝑇𝑇𝑇𝑇) + 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
= 𝑁𝑁𝑁𝑁𝑁𝑁 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 + 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
Alternative Definitions of OCF Continued
• The Top-Down Approach
•
Start from the top of the income statement (sales and costs)
𝑂𝑂𝑂𝑂𝑂𝑂 = 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 − 𝑇𝑇𝑇𝑇𝑇𝑇
= 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 + 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 − 𝑇𝑇𝑇𝑇𝑇𝑇
= 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − 𝑇𝑇𝑇𝑇𝑇𝑇
Alternative Definitions of OCF Continued
• The Tax Shield Approach
•
•
OCF has two components
(OCF in the absence of depreciation) + (tax shield benefit of depreciation)
𝑂𝑂𝑂𝑂𝑂𝑂 = 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 + 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 − 𝑇𝑇𝑇𝑇𝑇𝑇
= 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − 𝐷𝐷𝐷𝐷𝐷𝐷. + 𝐷𝐷𝐷𝐷𝐷𝐷. −(𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − 𝐷𝐷𝐷𝐷𝐷𝐷. ) × 𝑡𝑡𝐶𝐶
= 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 × 1 − 𝑡𝑡𝐶𝐶 + 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 × 𝑡𝑡𝐶𝐶
Depreciation Tax Shield
• Tax after depreciation
𝑇𝑇𝑇𝑇𝑇𝑇 = 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − 𝐷𝐷𝐷𝐷𝐷𝐷. × 𝑡𝑡𝐶𝐶
• Tax without depreciation
𝑇𝑇𝑇𝑇𝑇𝑇 = 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 × 𝑡𝑡𝐶𝐶
• Tax shield benefit of depreciation
∆𝑇𝑇𝑇𝑇𝑇𝑇 = 𝐷𝐷𝐷𝐷𝐷𝐷. × 𝑡𝑡𝐶𝐶
Special Cases of DCF Analysis
Three Common Special Cases
• Setting the bid price
• Evaluating Equipment Options with Different Lives
• The General Decision to Replace
Setting the Bid Price
•
•
•
•
Imagine we are in the business of buying stripped-down truck platforms and then
modifying them to customer specifications for resale. A local distributor has
requested bids for five specially modified trucks each year for the next four years, for
a total of 20 trucks in all.
Suppose we can buy the truck platforms for $10,000 each. The facilities we need can
be leased for $24,000 per year. The labor and material cost to do the modification
works out to be about $4,000 per truck.
We will need to invest $60,000 in new equipment. This equipment will be
depreciated straight-line to a zero salvage value over the four years. It will be worth
about $5,000 at the end of that time. We will also need to invest $40,000 in raw
materials inventory and other working capital items. The relevant tax rate is 21
percent.
What price per truck should we bid if we require a 20 percent return on our
investment?
Setting the Bid Price continued
Year
(1) Operating cash flow
(2) NWC
(3) Change in NWC
(4) Capital spending
(5) Depreciation
(6) Acc. Dep.
(7) Book value
(8) Total cash flow [(1)+(3)+(4)]
0
1
2
$40,000
−40,000
−60,000
60,000
−100,000
+OCF
$40,000
15,000
15,000
45,000
+OCF
+OCF
$40,000
15,000
30,000
30,000
+OCF
Aftertax salvage value = 5,000 – 0.21 x (5,000 – 0) = 5,000 – 1,950 = $3,950
Yearly straight-line depreciation = 60,000/4 = 15,000
3
4
+OCF
+OCF
$40,000
40,000
3,950
15,000
15,000
45,000
60,000
15,000
+OCF +OCF + 43,950
Setting the Bid Price continued
𝑂𝑂𝑂𝑂𝑂𝑂
𝑂𝑂𝑂𝑂𝑂𝑂
𝑂𝑂𝑂𝑂𝑂𝑂
𝑂𝑂𝑂𝑂𝑂𝑂 + 43,950
+
𝑁𝑁𝑁𝑁𝑁𝑁 = −100,000 +
+
+
=0
2
3
4
1.2
1.2
1.2
1.2
𝑂𝑂𝑂𝑂𝑂𝑂
𝑂𝑂𝑂𝑂𝑂𝑂
𝑂𝑂𝑂𝑂𝑂𝑂
𝑂𝑂𝑂𝑂𝑂𝑂
+
𝑁𝑁𝑁𝑁𝑁𝑁 = −78,805 +
+
+
=0
2
3
4
1.2
1.2
1.2
1.2
𝑁𝑁𝑁𝑁𝑁𝑁 = −78,805 + 𝑂𝑂𝑂𝑂𝑂𝑂 × 2.58873 = 0
𝑂𝑂𝑂𝑂𝑂𝑂 = $30,442
−78805 PV , 4 N , 20 {I/YR}, {PMT}
=𝑃𝑃𝑃𝑃𝑃𝑃(0.2, 4, −78805)
Setting the Bid Price continued
𝑂𝑂𝑂𝑂𝑂𝑂 = $30,442
𝑵𝑵𝑵𝑵𝑵𝑵 𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰𝑰 = 𝑂𝑂𝑂𝑂𝑂𝑂 − 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷
= 30,442 − 15,000 = $15,442
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 = 24,000 + 5 × 10,000 + 4,000 = $94,000
𝑁𝑁𝑁𝑁𝑁𝑁 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 = 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 − 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 × 1 − 𝑡𝑡𝐶𝐶
= 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 − 94,000 − 15,000 × 1 − 0.21 = $15,442
𝑺𝑺𝑺𝑺𝑺𝑺𝑺𝑺𝑺𝑺 = $128,546
𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝑜𝑜𝑜𝑜 𝑎𝑎 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 128,546⁄5 = $25,709
Equipment with Different Lives
•
•
•
•
•
The Downtown Athletic Club must choose between two mechanical tennis ball
throwers. Machine A costs less than Machine B but will not last as long.
The aftertax cash outflows from the two machines are shown in the table below.
Assume that machine A will be replaced at Date 4 (no loss of revenue at Date 4)
Revenues per year are assumed to be the same, regardless of machine, so they are
ignored in the analysis
Which machine should the firm purchase? Which one is cheaper?
DATE
MACHINE
A
B
0
$500
600
1
$120
100
2
$120
100
3
$120
100
4
$100
Equipment with Different Lives continued
• PV of costs (does not consider machine A’s cost at Date 4)
$120 $120
$120
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐴𝐴 ∶ 500 +
+
+
= $798.42
2
3
1.1
1.1
1.1
$100 $100
$100
$100
+
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐵𝐵 = $600 +
+
+
= $916.99
2
3
4
1.1
1.1
1.1
1.1
• Need to compare on a per-year basis → Obtain annuity payment
Annuity
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐴𝐴: $798.42 = 𝐶𝐶 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃10%,3 = 𝐶𝐶 × 2.4869
Factor
𝐶𝐶 = $321.06
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐵𝐵: $916.99 = 𝐶𝐶 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃10%,4 = 𝐶𝐶 × 2.4869
𝐶𝐶 = $289.28
Equipment with Different Lives continued
• This per-year annuity payment = equivalent annual cost (EAC)
•
It is now obvious that the firm should choose machine B
DATE
MACHINE
A
B
0
$500
600
1
$120
100
2
$120
100
3
$120
100
2
$321.06
289.28
3
$321.06
289.28
4
$100
DATE
MACHINE
A
B
0
1
$321.06
289.28
4
$289.28
General Decision to Replace
•
•
•
Consider the situation of BIKE, which must decide whether to replace an existing
machine. The replacement machine costs $9,000 now (net of old machine’s salvage
value) and requires maintenance of $1,000 at the end of every year for eight years. At
the end of eight years, the machine would be sold for $2,000.
The existing machine requires increasing amounts of maintenance each year, and its
salvage value falls each year, as shown in the table below.
If BIKE faces an opportunity cost of capital of 15 percent, when should it replace the
machine? Immediately or a year later? Assume that BIKE currently pays no tax.
YEAR
Present
1
2
3
4
MAINTENANCE
$
0
1,000
2,000
3,000
4,000
SALVAGE
$4,000
2,500
1,500
1,000
0
General Decision to Replace continued
• Equivalent Annual Cost (EAC) of New Machine (annual rental price)
𝑃𝑃𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
2,000
= 9,000 + 1,000 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃15%,8 −
= $12,833.5
8
1.15
𝑃𝑃𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 × 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃15%,8
$12,833.5 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 × 4.4873
𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝐸𝐸𝐸𝐸𝐸𝐸 = $2,860
• Cost of keeping the Old Machine for 1 year
𝑃𝑃𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
1,000 2,500
= 4,000 +
−
= $2,696
1.15
1.15
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑎𝑎𝑎𝑎 𝑡𝑡𝑡𝑡𝑡 𝑒𝑒𝑒𝑒𝑒𝑒 𝑜𝑜𝑜𝑜 𝑌𝑌𝑌𝑌𝑌𝑌𝑌𝑌 1 = 2,696 × 1.15 = $3,100
General Decision to Replace continued
• Comparison on a per-year basis (assume replacement every 8 years)
•
It is now obvious that it is better to replace the machine now
Immediate Replacement
Next-year Replacement
YEAR 1
$2,860
YEAR 1
$3,100
YEAR 2
$2,860
YEAR 2
$2,860
YEAR 3
$2,860
YEAR 4
$2,860
…
…
YEAR 3
$2,860
YEAR 4
$2,860
…
…