In our Nodhead example, true depreciation was decelerated. That is not always the case.

For instance, Table 12.6 shows how on average the market value of a Boeing 737 has varied with its age 27 and the cash flow needed in each year to provide a 10% return. (For example, if you bought a 737 for $19.69 million at the start of year 1 and sold it a year later, your total profit would be 17.99  3.67  19.69  $1.97 million , 10% of the purchase cost.)

Many airlines write off their aircraft straight-line over 15 years to a salvage value equal to 20% of the original cost.

a. Calculate economic and book depreciation for each year of the plane’s life.

b. Compare the true and book rates of return in each year.

c. Suppose an airline invested in a fixed number of Boeing 737s each year. Would steadystate book return overstate or understate true return?

27 We are grateful to Mike Staunton for providing us with these estimates.

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◗ TABLE 12.6 Estimated market values of a Boeing 737 in January 1987 as a function of age, plus the cash flows needed to provide a 10% true rate of return (figures in $ millions).

Start of Year Market Value Cash Flow 1 19.69 2 17.99 $3.67 3 16.79 3.00 4 15.78 2.69 5 14.89 2.47 6 14.09 2.29 7 13.36 2.14 8 12.68 2.02 9 12.05 1.90 10 11.46 1.80 11 10.91 1.70 12 10.39 1.61 13 9.91 1.52 14 9.44 1.46 15 9.01 1.37 16 8.59 1.32 AppendixLO1