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46
COVER FEATURE
We calculate the incremental net present value (ΔNPV) as
follows:
ΔNPV = NPV − NPV P L
⇒
PT − C P
T
( 1+ IK ) T
N
L
S
P − C L T T
T
∑ + − E − +
T T
T =0 ( 1+ IK ) ( 1+ IK ) ( 1+ IR ) T
N
N
∑ ∑
T =0
T =0
⇒
C L P − CT
T
( 1+ IK ) T
N
S
L T
∑ + +
N
T =0 ( 1+ IK ) ( 1+ IR ) T
N
∑ − E.
T =0
Assuming that profit from storage is equal in both the buy and
lease cases—that is, using 1 Tbyte of storage from a purchased
disk or from a storage cloud results in the same level of
productivity—the above simplification results in the removal of
the profit term P T .
Capital cost
Three components make up the cost of purchasing storage E:
The consumer needs a disk controller to house the purchased
disks.
The consumer purchases disk drives in blocks based on
increasing storage needs.
The consumer must periodically replace disks due to
failure.
These components contribute to the future cash flow E as
follows:
E =
COMPUTER
DERIVATION OF THE DECISION MODEL
( ( ⎡⎢ V ⎤ − ⎡⎢ V ⎤ T ⎥Ω T −1⎥Ω
)∗Ω+R T )∗G T
( ) T
E T
1+ I K
⇒ E = + C
T
( 1+ IK )
E = V T ( ( ⎡⎢ ⎤ − ⎡⎢ V ⎤ T ⎥Ω T −1⎥Ω
)∗Ω+R T )∗G , T
where Ω represents the hard disk drive size in Gbytes; V T is the
storage requirement in Gbytes at year T; ⎡V T ⎤ Ω is an operator that
returns the minimum number of Ω-sized disk drives needed to
store V T ; G T is the predicted cost per Gbyte of disk storage at year
T; R T is the disk replacement in Gbytes at year T; and C is the disk
controller cost.
The important insight in this formulation is that the capital
cost isn’t all incurred at the start of the project, unlike in traditional
NPV models. Rather, it’s a time-varying formula in which
users can grow their storage systems as their requirements
evolve. We modify ΔNPV to reflect this growth in capital cost:
ΔNPV =
N
∑
T =0
S
+
1+ IK L P C − CT − ET
T
( )
( ) T
1+ I K
Operating cost
− C
LT +
N
( ) T
N
∑
T =0
1+ I R
P We estimate the operating cost of purchased storage, C , by T
calculating the electric utility cost associated with running the
+ C
disk controller and the disk units, plus the cost of a human
operator to manage the system/data. These cost components
P contribute to C as follows:
T
P C = (365⋅24)∗δ ∗ PC + P T
( ∗⎡⎢ V ⎤ D T ⎥Ω )+α∗H , T
where δ is the utility cost ($/kilowatt per hour); P is the control-
C
ler’s power requirement in kWs; P is the power requirement in
D
kWs per disk drive; and α is the proportion of the human operator
cost, H , required to maintain the system/data at year T.
T
L The operating cost for leased storage, C , only includes the
T
cost of a human operator to manage the data. Thus, we calculate
L L
C as CT = β∗HT , where β is the proportion of the human opera-
T
tor cost required to maintain the data on the leased storage at
year T. Substituting ρ for (α – β), we can modify ΔNPV to reflect the
operating costs as follows:
ΔNPV =
N
∑
T =0
−ρ∗H T − 365⋅24
( )∗δ ∗( P + P ∗⎡⎢ V ⎤ C D T ⎥Ω )− ET ( ) T
L T
1+ I K
S
− C + +
.
N
( 1+ IK ) ( 1+ IR ) T ∑
T =0
Approximating the best outcomes
N
Consumers often find it difficult to estimate their capital cost
and the lease financing rates available to them. We therefore suggest
an approximate method of evaluating the buy-or-lease
decision by deriving the best possible outcome in both the purchase
and lease cases.
From the well-known economic Law of One Price, 1 we can
derive the upper bounds for NPV P and NPV L by substituting I K and
I R with the risk-free interest rate I F . The “Corollary for Estimating
the Upper-bound Present Value” sidebar explains this in more
detail. In turn, we can estimate the risk-free interest rate, I F , from
the published return on an instrument such as government treasury
bills. We can therefore derive an approximation of the
decision criteria using these best NPVs, letting us further simplify
the currently derived version of ΔNPV to:
ΔNPV =
N
∑
T =0
( )∗δ ∗( P + P ∗⎡⎢ V ⎤ C D T ⎥Ω )− E + L T T
( ) T
−ρ∗H T − 365∗24
S
− C +
.
( 1+ IF ) N
Disk price trends
1+ I F
We haven’t yet provided a function for the term G , which we need
T
to calculate E and to estimate the cost of disk storage at year T.
T
Since April 2003, we’ve been collecting SATA disk price data
from Pricewatch.com on a weekly basis. We collected price data
for all available disk drive sizes each week—250 Gbytes, 500
Gbytes, and so on—regardless of manufacturer or model. Figure
A plots the 10 lowest prices each week for SATA disk drives across
all the available drive sizes. Approximating the observed exponential
trend line using regression analysis, we obtain the formula
′ − 0.0012 X G = 1.2984e .
X
A
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