Discussion
A cost element of \( 50 \) million dollars falls due in \( 10 \) years at a discount rate of \( 7 \) per cent. Its present value is about
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.
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