Technology investment decision-making under uncertainty

If there’s any issue that routinely frustrates executives in many organizations, it’s how to get a true fix on the value that information technology adds to the businesses it serves. IT is undoubtedly central to creating value and therefore continues to account for a rising share of total investment.

Michael Bloch, Director, European Insurance Operations & Technology Practice and Andres Hoyos-Gomes, Principal, Business Technology, McKinsey and Company [13].

Our stochastic cost function for IT development projects incorporates the technical and input cost uncertainties of Pindyck’s model (1993) [61], but also considers the fact that the investment costs of some IT projects might change even if no investment takes place. In contrast to other models in the real options literature in which benefits are summarized in the underlying asset value, our model for IT acquisition projects represents these benefits as a stream of stochastic cash flows.

Eduardo S. Schwartz and Carlos Zozaya-Gorostiza, Management Science [68].

Abstract

Innovations involving information technology (IT) provide potentially valuable investment opportunities for industry and government organizations. Significant uncertainties are associated with decision-making for IT investment though, a problem that senior executives have been concerned about for a long time. The uncertainties include consumer, market and regulatory responses, IT-driven changes in operational and transactional performance, technology standards and competition, and future market conditions. All these things have an impact on organizations’ willingness to adopt. As a result, traditional capital budgeting, investment experience, and intuition have not been very effective in IT investment decision-making. We propose a new option-based stochastic valuation modeling approach for IT investment under uncertainty that incorporates a mean reversion process to capture cost and benefit flow variations over time. We apply the proposed approach in two industry settings: to a large-scale IT investment in the consolidation of data marts at a major airline, and to a mobile payment system infrastructure investment on the part of a start-up. The applications supported the evaluation of the proposed methods, and offered some illustrations about the kinds of managerial insights that can be obtained. We also report on several extensions that demonstrate how the creation of useful management findings from the modeling approach can be supplemented with project value sensitivity analysis and the use of simulation-based least-squares Monte Carlo valuation. The findings are useful to assess the power and value of the approach.

Appendices

Appendix 1: Modeling notation and definitions

Math	Definition	Comments
V, B	Investment value, benefit flow at time t	PV of future benefit flows B, that fluctuate over time
I, ROV	Firm’s investment cost I, real option value	For technology investment, for the deferral option
$\bar{B}$, $\bar{I}$	Long-term mean benefit, investment cost	B, I tends to revert to the level of $B$, $\bar{I}$ in the long term
α B , α I	Speed of mean reversion for benefits, costs	Subject to the exponential mean reversion process
σ B , σ I	Standard deviation of B, I	Affects volatility of benefit flows, investment costs
g, d	Mean benefit growth rate, decay rate	Subject to the mean benefit growth curve and decay rate
ρ BI	Correlation between B and I	ρ BI  = 0, equates with uncorrelated cost-benefit
r f	Risk-free discount rate	Discounts future benefits and costs
dz	Wiener increment	Defines a standard mean reversion process
t, T	Time; maximum deferral time, or # periods in which cash flows occur	dt is a small increment in time; bounds option’s exercise time; cash flows can be benefits or costs for firms
L	Length of technology lifecycle	Capture the length of period the technology is available
λ	Mean # of jumps per unit of time	In dt, probability that a jump will occur is λdt
B max , $\bar{B}_{L}$	Maximal mean benefits, mean benefit at L	The expected maximal benefits, mean benefit level at L
Y	Δ value, random variable	Measures after-shock change in value
dq	Shock-led value jump process	Changes in value of dq follow a Poisson process

Appendix 2: Simulation parameters and procedure

See Table 7.

Table 7 Simulation parameters used in the base case

1.1 Simulation assumptions and procedure

The firm knows the current investment cost I ₀  = $10 million, the expected long-run cost $\bar{I}$ = $5 million to which I tends to revert, and the speed of cost reversion α _I  = 0.1. In addition, the cost volatility is σ _I  = 50 %. The investment decision must be made prior to the end of the investment time horizon T. Assume that L = 3 years and T = 5 years, which is a reasonable length of time for the technology to be available. Once the investment decision is made at time t, the benefit flows will be received up to time T. This benchmark case uses the same assumption as the data mart consolidation project for the change in mean benefit flows. The maximal expected benefit flow is $1,982,759. The estimated benefit growth rate g is 1.5, and its decay rate d is 1.37. The mean benefit flow reverting speed is α _B  = 1.5, and the volatility σ _B of this benefit flow is 50 %. In addition, we assume that the discount rate is 7 %.

We used Matlab to code the simulations and run the numerical analysis. Based on the parameters we selected, we first simulated 100,000 sample paths for the state variables I and B. We used a large number of sample paths to make sure that the distributions of the timing and the payoffs were close enough to the expected technology investment outcome. Future profit at time t can be calculated by adding the discounted cash flows from t to T, and the value of m-payment investment project is the present value of future profits minus the current investment cost at time t. The goal is to compare the discounted present value of the payoff at each time and then determine the optimal investment time based on the simulated values associated with all of the paths that occur.

Appendix 3: Sensitivity analysis results for key input parameters

Parameter	Max payoff	Min payoff	Mean payoff	Average timing (Year)
Base case	$24,222,392	−$1,872,303	$5,483,276	0.68
T = 4 years	$18,984,991	−$4,087,170	$1,463,879	0.44
T = 6 years	$28,826,814	−$490,065	$8,932,915	0.90
σ B  = 25 %	$14,857,467	−$910,146	$5,050,779	0.70
σ B  = 75 %	$51,500,818	−$2,788,717	$6,233,006	0.68
α B  = 1.2	$20,808,112	−$3,404,459	$2,415,589	0.71
α B  = 1.8	$25,484,084	−$1,043,981	$7,770,022	0.68
L = 2.5 years	$25,710,863	−$1,607,823	$6,229,019	0.60
L = 3.5 years	$23,577,541	−$1,895,917	$5,846,831	0.76
rf = 5 %	$24,445,123	−$1,906,979	$6,324,958	0.68
rf = 9 %	$24,848,362	−$2,267,019	$4,723,778	0.70
$\bar{I}$ = 10 million	$25,419,897	−$2,470,750	$5,291,738	0.65
$\bar{I}$ = 15 million	$23,192,150	−$2,279,636	$5,166,807	0.62
g = 1.2	$13,424,309	−$4,150,840	$1,312,199	0.80
g = 1.8	$34,940,379	−$890,426	$8,957,987	0.63
α I  = 0.05	$23,803,475	−2,041,563	$5,361,201	0.66
α I  = 0.15	$22,520,575	−1,881,505	$5,569,076	0.71

Appendix 4: Numerical solution procedure

An important problem in option pricing theory is the valuation and optimal exercise of derivatives with American-style exercise features. In the management of IT investment risk, these types of real options also can be found. When more than one factor affects the value of the option, valuation and optimal exercise of an American option is an especially challenging problem. The Longstaff–Schwartz [46] provides a simple, yet powerful simulation approach to approximating the value of American options. The method is readily applied when the option value depends on multiple factors. Simulation also allows state variables to follow general stochastic processes, such as a jump diffusion process [53].

At the final exercise date, the optimal exercise strategy for an American-style option is to exercise it if it is in the money. Prior to the final date, however, the optimal strategy is to compare the immediate exercise value with the expected cash flows from continuing, and then exercise if immediate exercise is more valuable. Thus, the key to optimally exercising an American option is identifying the conditional expected value of continuation. A central part of the Longstaff–Schwartz method is the approximation of a set of conditional expectation functions, so it is appropriate to use the cross-sectional information in the simulated paths to identify the conditional expectation functions.

We solved the model by applying a variant of the Longstaff–Schwartz method to approximate the value of all future benefit flows at each date, given the current value of the two governing state variables, I and B. This involved first simulating 100,000 sample paths for the two state variables. We regressed the subsequent project benefit flows from continuation on a set of functions of the values of the relevant state variables. The fitted values of this regression are efficient unbiased estimates of the conditional expectation function. The regression coefficients are used to approximate the expected value of continuation. We also used another procedure to compare the exercise value and continuation value at each date to determine the optimal stopping rule. The optimal stopping rule estimated by the conditional expectation regressions from one set of paths should lead to out-of-sample values that closely approximate the in-sample values for the investment option [71].

Then we compared the value of the technology investment project for the case where there is no possibility of a jump, λ = 0, and when a jump may occur with the probability of λ = 0.05. When λ increases, the conditional variance of the future benefit flows increases. We adjusted the parameter values of the means and variances for the two cases to give a more meaningful comparison. Because of the martingale restriction implied by the risk-neutral framework, the means for the two cases will be the same.