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