Airframe Acquisition Cost Model Selection

Aircraft manufacturers will have well-developed models for predicting the cost of a new project and setting a list price for the aircraft. However, these acquisition cost models, and more ad-vanced modern models, have not been made available for public use. The publicly available parametric models rely on older data to develop trends, and will therefore introduce a large measure of uncertainty into the cost prediction. This is especially true for a novel concep-tual aircraft with an entry into service more than 30 years after the year in which many of the available models were released. In order to reduce the estimate uncertainty, it was important to select cost models which include factors that may be used to adjust for novel aircraft con-cepts. Two publicly available models were selected with this form of support (models detailed in Appendix E):

• RAND Corporation (Resetar et al., 1991 [173] updated by Younossi et al., 2001 [174])

• Roskam, 1990 [158]

The RAND Corporation cost models divide the aircraft cost into a number of groups covering the aircraft development program. It should be noted that the RAND model database consists predominantly of military aircraft, including fighter aircraft. However, Hess and Romanoff note that breaking the database up to cover only transport aircraft does not benefit the cost prediction models [162]. Resetar et al’s models were used to provide the parametric cost functions, which consist of the the following groups:

• Development program cost, Cdevelopment

– Non-recurring engineering hours – Non-recurring tooling hours – Development support cost – Flight test cost

• Manufacturing cost, Cmanufacture

– Recurring engineering hours – Recurring tooling hours – Recurring labour hours

– Recurring manufacturing material cost – Recurring QA hours

The cost of the development program is classified as a non-recurring cost and is spread out over a first lot of aircraft. The manufacturing cost applies to each aircraft and would continue after the development program cost had been paid off following the sale of the first lot. Resetar et al. provide cost functions for the aircraft development program and manufacturing process, including material weight factors to adjust for the use of advanced materials [173]. The more re-cent models provided by Younossi et al. add more up to date cost factors which may be used to extrapolate the change in the cost of manufacturing with various material types over time [174].

The RAND corporation models also include a learning curve correction for manufacturing cost

0%

25%

50%

75%

100%

0 200 400 600 800 1000

Percentage of First Unit Cost

Unit Number

90%

85%

80%

-0.152 -0.234 -0.322

a b

Figure 6.7: Example learning curves for the manufacturing cost of an airframe

that accounts for the fact that the cost of production reduces as more aircraft are manufactured (Figure 6.7):

X_n= aX_n−1= X₁n^b (6.8)

Where a is the learning slope, b is the learning exponent, X1 is the manufacturing cost of the first item, and X_nis the manufacturing cost of the n^thitem.

The cost per aircraft is the total of the cost estimate for the development program and manufacture of the first lot of aircraft, divided by the number of aircraft in the first lot:

X = Cdevelopment+ Cmanufacture

N_aircraft (6.9)

The cost is created for a fixed first lot of N_aircraft. As the actual manufacturing cost for a single aircraft is a function of the learning curve, the value of X incorporates the average manufactur-ing cost of aircraft in the first lot. It is assumed that the development program will be paid off after the first lot is sold. The price X therefore represents the ‘break even’ cost for the aircraft, i.e. the sale price for which costs are exactly covered. As the development program is a finite cost, the manufacturer will begin to make a profit on the aircraft once the development program is paid off after the sale of the first lot of aircraft. The manufacturing learning curve means that aircraft manufacturing costs reduce as more aircraft is produced. However, it may be expected that not all of these savings will be passed on to the customer. Instead, the lower manufacturing cost can be used to provide a profit for the manufacturer. It may therefore be assumed that the sale price X would remain unchanged after the sale of the first lot of aircraft.

Roskam’s models follow a similar cost estimation procedure to the RAND Corporation mod-els. Although no material cost factors are presented, the models do include aircraft ‘difficulty’

factors which may be used to adjust for novel or new aircraft. Roskam’s cost model breaks the aircraft cost into a similar set of components to the RAND Corporation methods. Aircraft cost is again estimated based on a set of parametric cost functions for the development program and the aircraft manufacturing cost. Roskam also notes that the unit price of an aircraft will include a margin to allow for a profit to be made on the aircraft. By neglecting the profit term of the aircraft cost estimate, the break even aircraft price may be estimated. Roskam’s cost functions consist of the following groups:

6. Acquisition Cost Estimation

• Finance cost, with rate r_finance

• Development program cost, Cdevelopment

– Airframe engineering and design

Roskam’s models include a financing cost term which accounts for the cost of funding the manufacturing and development program for the aircraft. Roskam suggests a value of 10%

of manufacturing and development cost for the aircraft is suitable for the finance rate [158].

Roskam’s parametric cost functions estimate the manufacturing cost for a single aircraft, unlike the relationships developed by the RAND corporation which include a learning factor and esti-mate the cumulative cost for an aircraft lot. The development cost must therefore be distributed as a cost per aircraft by dividing by the total number of aircraft. The concept of a first lot of air-craft may be introduced here to define the total number of airair-craft after which the development program is paid off. The break even acquisition price can finally be calculated as the sum of the development and manufacturing costs, multiplied by the financing cost:

X = Cdevelopment

Naircraft

+ Cmanufacture



(1 + r_finance) (6.10)

The cost estimates produced by both models link to the number of aircraft sold in the first lot.

The more aircraft in the first lot, the smaller the percentage contribution of the development program to the total cost, as it is distributed over a larger number of aircraft. A larger number of aircraft sold in the first lot therefore leads to a lower cost per aircraft. The RAND corpora-tion models also include a learning curve for manufacturing cost. The manufacturing cost per unit therefore decreases as more aircraft are produced. In both cases, it is assumed that the development program is paid off following the sale of the first lot of aircraft. Sales beyond the first lot of aircraft are assumed to make a profit, as the development program has been paid off (assuming the acquisition price has not changed). The first lot has been used here as a target number of initial sales for the aircraft to break even and is used to establish a list price for the aircraft. In both cases, cost estimates must be scaled to the current value of money using the rate of inflation between the dollar year of the model and the current year.

Acquisition Cost Model Modifications

Both the Roskam and RAND Corporation models include factors that are useful in predicting the cost of a novel aircraft. As both models break costs down into similar groups, it is possible to combine elements from each to cover factors not covered by one or another of the models.

The RAND corporation model provides materials cost weighting factors which are especially useful for a modern aircraft with increasingly high composite material use. The Roskam mod-els include a program difficulty factor, and also covers the cost of financing the development program and the cost of aircraft interiors. These elements were combined in each cost model to create two modified cost models which could then subsequently be used to create two cost predictions for the aircraft.

R² = 0.8135

0 5 10 15 20 25

0 100 200 300 400 500 600

Cost (US$mil)

Maximum Thrust (kN) (a) Thrust

R² = 0.8098

0 5 10 15 20 25

0 2 4 6 8 10

Cost (US$mil)

Weight (tonnes)

(b) Engine Weight Figure 6.8: Engine price correlation with thrust and weight

By combing aspects from each model, the aim is to cover perceived gaps in each of the models. In combination, the models offer the following features:

• Program finance cost

• Development program cost

• Manufacturing cost

• Scale factors for advanced materials in manufacture

• Program difficulty scale factor for development and manufacturing cost

• Cost of aircraft interiors