Chapters Net value and marginal analysis Decision rules Example Present value analysis Reconciling present and future cash flows Discounting Figures of merit Weighted sum Delivered system capability Multiple Goal Decision Analysis I

Marginal Analysis: Definitions X – Activity level of an alternative C(X) – Cost of alternative TV(X)– Total value of alternative (in same units as cost) NV(X)– Net value of alternative NV(X) = TV(X) – C(X) MNV(X) –Marginal net value MNV(X) = = - dx d(NV) dC dx d(TV) dx

C NV max X max X2X2 Activity level x (a) TV and C Cost and Total Value TV X1X1

(b) MNV = d(TV)/dx – dC/dx Marginal Net Value X max X Activity level

X1X1 X max X2X2 Over- investment (b) NV = TV - C X NV max Net Value vs. Activity Level InvestmentProfitable

Marginal Net Value Decision Rule In the “profitable” segment –If MNV > 0, Increase activity level –If MNV < 0, Decrease activity level –If MNV = 0, Activity level is optimal MNV = d(TV) / dx – dC/dx For Option B, with V T = value of each TR/sec, C(N) = N; dC / dN = 20 TV(N) = V T (880N – 40N 2 ); d(TV) / dN = V T (880 –80N) 20 = V T (880 – 80N max ) N max = (880 V T – 20) / 80 V T = 11 – 1/(4V T )

Optimal Number of Processors vs. Transaction Value N max V T, $K N max = 11 – 1 /(4 V T )

TPS Decision Problem 3 Assuming use of composite option, we will acquire 5 processors/system and run option A for 2 years Which acquisition option should we choose: -A1: Rent processors for 2 years at $2400/Mo. -A2: Purchase processors for $100,000. Resell them for $50,000 after 2 years.

Interest Calculations Option A2 ties up $50K for 24 months How much would this be worth at an interest rate of.75%/month? V($50 K, 1) = $50 K (1.0075) V($50 K, 2) = $50 K (1.0075) (1.0075) … V($50 K, 24) = $50 K (1.0075) 24 = $59,820 For any sum X, V(X, 24) = X(1.0075) 24

Present Value Calculations What is the present value X of the $50K we will receive in 24 months? X == $41,792 $50K PV (F, r, n) = (1.0075) 24 $50K V (X, 24) = X (1.0075) 24 = $50K PV ($50K,.0075, 24) = F (1 +r) n (1.0075) 24

-Of a future cash flow F -At an interest rate per time period r -Over a number of time periods n -Using the discount rate D = PV (F, D, n ) = FD n Present Value PV (F, r, n) = F (1 +r) n F

Present Value, Series of Cash Flows In option A1, we pay $2400 at the beginning of each month How much is this worth in present value? PV S ($2400, D, 1) = $2400 PV S ($2400, D, 2) = $ $2400 D PV S ($2400, D, 3) = $2400 (1 + D + D 2 )... PV S ($2400, D, 24) = $2400 (1 + D + … + D 23 ) = $2400 (1 - D 24 ) / (1 – D ) For D = 1/ = , PV S ($2400, 1/1.0075, 24) = $52,928

Present Value of A Series of Cash Flows m equal cash flows or payments P –At the beginning of each time period Constant discount rate D PV S (P, D, m) = P [(1-D m )/(1-D)]

Present Value Analysis Results Simple Analysis Present Value Analysis Cost of A1$57,600$52,928 Cost of A2$50,000$58,208

% Interest rate per month Present value, $ Present Value Comparison vs. Interest Rate Option A2 Option A1

TPS Decision Problem 4 Choose best vendor operating system –System A – Standard OS –System A Plus Better diagnostics, maintenance features $40K added cost

Alternative TPS Operating System Characteristics Alternative CriterionSystem ASystem A Plus 1. Added Cost0$40K 2. Processor overhead Multiprocessor overhead80 4. Measurement capabilityPoorGood 5. Trace capabilityNoneAdequate 6. Diagnostics, error messagesAdequateGood 7. Maintenance supportMarginalGood 8. Accounting systemAdequateVery Good 9. Usage summariesNoneGood 10. DocumentationGoodAdequate

Meta-Decision Problems Lower CostMore Stability Lower cost More insight The system decision problem The system analysis decision problem

Weighted Sum Figure of Merit Assign weight W i to criterion i Σ i W i = 1 For each option j and criterion i, assign rating r iJ (0 < r ij < 10) Compute figure of merit for each option j F j = Σ W i r ij

TPS Operating System Figure of Merit Calculation System ASystem A Plus CriterionWeightCharacteristicRatingWeighted Rating CharacteristicRatingWeighted Rating 1. Added Cost30$010300$40K Processor overhead Multiprocessor overhead Measurement capability7Poor214Good Trace Capability8None00Adequate Diagnostics, error msgs10Adequate660Good Maintenance Support10Marginal440Good Accounting system2Adequate612Very good Usage summaries3None00Good Documentation5Good840Adequate630 Total

Delivered System Capability (DSC) Figure of Merit DSC = (SC) (DC) (AV) SC: System Capability = Σ W i r ij DC: Delivered Capacity AV: Availability

The DSC Figure of Merit Dimensionless Covers effectiveness only SC component handles many criteria DC, AV components apply multiplicatively

Reduction of $150K maintenance cost – Maintenance Support: 20% ($30K) – Diagnostics, Error Msgs.: 10% (15K) – Documentation (worse): -10% (-15K) $30K – Net Cost = $650K + 40 – 30 = $660K Delivered capacity increase via measurement: 5% 2400 tr/sec (1.05) 2520 tr/sec Availability increase via diagnostics, error messages, trace capability: 50% less downtime Gains from System A Plus - I

Gains from System A Plus - II System Capability Weight System A RatingScore System A Plus RatingScore Criteria Total Basic TPS Functions Accounting Systems Usage Summaries OS Documentation

TPS Comparison: Delivered System Capability CriterionSystem ASystem A Plus System capability (SC)0.980 Delivered capability (DC) Availability (AV) Delivered system capability (DSC)=(SC)(DC)(AV) Cost Capability/Cost ratio $650K 3.44 $660K 3.65

Revised TPS Weighted Sum Analysis System ASystem A Plus CriterionWeightCharacteristicRatingWeighted Rating CharacteristicRatingWeighted Rating 1. System capability (SC) Delivered capacity (DC) Availability (AV) Total

Comparison of Weighted Sum and DSC Figures of Merit Weighted sumDelivered system capability Relative advantages SimplerMore representative of many computer systems Better for assessing side effects of DC, AV factors Better for assessing wide variations in DC, AV factors RecommendationUse where DC, AV factors will not vary widely Use where DC, AV factors may vary widely