Cost Estimation in Aircraft Design Questions and Answers

Answer: A

Correct answer: 8.0 million dollars

Amortised development cost is the RDT&E divided by the number of aircraft:

\[ \frac{2.4 \times 10^9}{300} = 8.0 \times 10^6 = 8.0\ \mathrm{million\ dollars} \]

Every aircraft sold must recover that 8 million on top of its own production cost before the programme contributes anything. Doubling the run to 600 would halve it - which is why manufacturers pursue derivative versions and export sales so hard once the development is paid for.

Answer: B

Correct answer: 0.512

Eight units is three doublings of cumulative output - 1 to 2, 2 to 4, 4 to 8 - and each doubling applies the curve factor:

\[ \frac{C_8}{C_1} = 0.8^3 = 0.512 \]

So the eighth aircraft costs about half the first. The distractor \( 0.800 \) applies the factor once, and \( 0.240 \) applies it too often. The rapid early fall is characteristic: half the total saving of a long programme is realised in the first handful of doublings.

Answer: C

Correct answer: 0.522

Sixteen units is four doublings, so the curve factor is applied four times:

\[ \frac{C_{16}}{C_1} = 0.85^4 = 0.522 \]

Compare this with the previous item: an 80 per cent curve reached \( 0.512 \) in only three doublings, while an 85 per cent curve needs four to reach roughly the same point. A few percentage points on the learning curve slope compound into a large difference over a production run, which is why the assumed slope is one of the most contested numbers in a cost estimate.

Answer: D

Correct answer: 2000 dollars

Divide the annual fixed cost by the block hours flown:

\[ \frac{6\,000\,000}{3000} = 2000\ \mathrm{dollars\ per\ block\ hour} \]

The figure falls as utilisation rises: at 4000 hours the same fixed cost would be 1500 dollars an hour. That is the whole arithmetic behind high-utilisation operating models - the aircraft's fixed charges are unaffected by how much it flies, so every additional hour dilutes them.

Answer: A

Correct answer: 10530 dollars

Multiply the burn rate by the price and the sector length:

\[ 2.6 \times 900 \times 4.5 = 10\,530\ \mathrm{dollars} \]

The distractor \( 2340 \) omits the sector time and \( 4050 \) omits the burn rate. Fuel is typically the largest single direct operating cost and the most volatile, since it moves with the crude price and with exchange rates - which is why airlines hedge it and why a few per cent of fuel burn is worth so much in aircraft selection.

Answer: B

Correct answer: 250 aircraft

Breakeven is the fixed cost divided by the margin each aircraft contributes:

\[ N_{BE} = \frac{3.0 \times 10^9}{12 \times 10^6} = 250\ \mathrm{aircraft} \]

Two hundred and fifty aircraft is a substantial commitment - for a large transport it may represent a decade of production - and until it is reached the programme has consumed cash without returning it. This is why launch orders and the credibility of the market forecast weigh so heavily in the decision to proceed.

Answer: C

Correct answer: 4.0 million dollars

Straight-line depreciation writes off the difference between cost and residual value evenly across the period:

\[ D = \frac{90 - 10}{20} = \frac{80}{20} = 4.0\ \mathrm{million\ dollars\ per\ year} \]

The distractor \( 4.5 \) ignores the residual value and depreciates the full purchase price. Residual value matters a great deal in practice: an aircraft with a strong second-hand market can be depreciated to a higher residual, reducing the annual charge and hence the cost per block hour.

Answer: D

Correct answer: 25.4 million dollars

Discount the future sum back at the given rate:

\[ PV = \frac{50}{(1.07)^{10}} = \frac{50}{1.967} = 25.4\ \mathrm{million\ dollars} \]

At 7 per cent a sum ten years away is worth about half its face value today. This is why discounting matters so much in life cycle cost analysis: an operating cost incurred twenty or thirty years out weighs far less in the decision than a development cost incurred now, and the choice of discount rate can reverse a trade study's conclusion.

Answer: A

The factor is \( 0.92^{0.8} = 0.9354 \), a reduction of 6.5 per cent. The exponent below unity means cost grows a little more slowly than weight, but the leverage a designer has over cost through weight is still substantial.

Answer: B

Correct answer: 20.7 million dollars

Multiply the hourly cost by the annual utilisation:

\[ 2800 \times 7400 = 20\,720\,000 = 20.7\ \mathrm{million\ dollars} \]

The distractors misplace the decimal by a factor of ten either way, which is the usual hazard in figures of this size. Note that this covers direct costs only: the airline's indirect costs - administration, marketing, reservations, ground services - must be added before the aircraft's contribution to the business can be judged.