Cost–Benefit with Risk Analysis

Abstract

There are a myriad of methods that are available in calculating the design added value (DAV) of given design features. The central methodology we recommend for this purpose is cost–benefit analysis with risk. In this chapter, our mission is to describe specific techniques to implement classic cost–benefit analysis methods that can be effective in analyzing DAV features.

Exercise 4

The table below contains formulae that can be used to estimate the values for cost–benefit analysis, risk analysis, VBD analysis, NPV analysis, correction coefficients, and multiple dimensions of risk. Familiarize yourself with these formulations and select one to apply to data about a building delivery case found either in your own sources or ones provided in this text.

Formulas for cost–benefit and risk analysis calculations
1. The norm: $\left\{\alpha \left(B,t\right)\;B(t)-\beta \left(C,t\right)\;C(t)\right\};$where B is benefit, C is cost, at time t, with α and β as coefficients of conversion into a common unit, for benefit and cost, respectively, for a given design feature and stakeholder
2. Value of a design decision-making strategy with risk: $\left\{\alpha \left(B,t\right)\;B(t)-\beta \left(C,t\right)\;C(t)-\gamma \left(R,t\right)\;R(t)\right\};$where t is time; and α, β, and γ are coefficients of conversion into a common unit, for benefit, cost, and risk, respectively, for a given design feature and benefiting stakeholder
3. Objective of Value Based Design: $\max \left\{{\varSigma}_{k,l}\;\left[{\varSigma}_{j,i}\;\left({B}_d-{C}_d\right)\;{R}_d\right]\right\};$ where Bd are the benefits subject to risk R of a decision d, Cd are the cost subject to the same risks, and Rd are the risk factor involved in a decision d, k and l define the range of costs and i and j the range of benefit involved with the decisions.
4. Objective of Value Based Design with correction coefficients: $\max \left\{{\varSigma}_j\;\left[{\varSigma}_l\;\left(\alpha {B}_d-\beta {C}_d\right)\;\phi {R}_d\right]\right\};$where α, β, and Φ are correction coefficients to map Bd, Cd, and Rd into a common cardinal scale
5. The C-BA of the Net Present Value (NPV) of a Value Based Design feature: $\mathrm{NPV}={\varSigma}_{t=0},T\;{D}_t\;\left\{\alpha \left(B,t\right)\;\left[{B}_t-\beta \left(C,t\right)\;{C}_t\right]\;\gamma \left(R,t\right)\;{R}_t\right\};$where B, C, R = {benefit, cost, risk}; Bt, Ct, Rt = {benefit, cost, risk} at time t; α(B, t), β(C, t), γ(R, t) = factors, one for each, to convert the values of {benefit, cost, risk} onto a common scale so that their relative values can be added, subtracted, etc.; Dt = discount value of {benefit, cost, risk} adjusted for time t, i.e., the value of a benefit B1t may be less at a future time t’ by a Facto r of Dt−t’; D(t) 1/(1 + r) (t−t’)
6. The C-BA of the Net Present Value in Value Based Design feature representing multiple cost-benefits-risks for different stakeholders (i, j, …): $\mathrm{NPV}=\sum t=0,T\sum j\sum i\;D{j}_t\;\left\{\alpha j\;\left( Bji,t\right)\; Bj{i}_t-\beta j\;\left( Cji,t\right)\; Cj{i}_t-\gamma j\;\left( Rji,t\right)\; Rj{i}_t\right\}$
7. Estimating the differences between multiple dimensions of risk with constant costs and benefits: $\mathrm{NPV}1-\mathrm{NPV}2=\sum t=0,T\;\left\{\varSigma j\;\varSigma i\;D{j}_t\;\gamma j\;\left( Rji1,t\right)\; Rj{i}_t-\varSigma j\;\varSigma i\;D{j}_t\;\gamma j\;\left( Rji2,t\right)\; Rj i{2}_t\right\}$