Question

The table given below shows how, on average, the market value of a Boeing 737 has varied with its age and the cash flow needed in each year to provide a 11% return. (For example, if you bought a 737 for $19.89 million at the start of year 1 and sold it a year later, your total profit would be 18.09 + 3.99 − 19.89 = $2.19 million, 11% of the purchase cost.)

Assume airlines write off their aircraft straight-line over 15 years to a salvage value equal to 25% of the original cost.

Start of Year	Market Value	Cash Flow
1	19.89
2	18.09	3.99
3	16.99	3.09
4	15.88	2.98
5	15.09	2.54
6	14.19	2.56
7	13.56	2.19
8	12.78	2.27
9	12.25	1.94
10	11.56	2.04
11	11.11	1.72
12	10.49	1.84
13	10.11	1.53
14	9.54	1.68
15	9.21	1.38
16	8.69	1.53

a. Calculate economic depreciation, book depreciation, economic return, and book return for each year of the plane’s life. (Leave no cells blank - be certain to enter "0" wherever required. Do not round intermediate calculations. Enter your answers in millions except for percentage values. Round your percentage answers to 1 decimal place and other answers to 2 decimal places.)

b-1. Suppose an airline invested in a fixed number of Boeing 737s each year. Calculate the steady-state book rate of return. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

b-2. Would steady-state book return overstate or understate true return?

• Understate

• Overstate

Answer 1

ANSWER

a)

The tables are completed as below:

	Start of the Year
	1	2	3	4	5	6	7	8
Economic Depreciation		1.80	1.10	1.11	0.79	0.90	0.63	0.78
Book Depreciation		1.00	1.00	1.00	1.00	1.00	1.00	1.00
Economic Return (%)		11.0%	11.0%	11.0%	11.0%	11.0%	11.0%	11.0%
Book Return (%)		15.0%	11.1%	11.1%	9.1%	9.8%	8.0%	9.1%

______

	Start of the Year
	9	10	11	12	13	14	15	16
Economic Depreciation	1.41	1.35	1.27	1.22	1.15	1.11	1.05	1.01
Book Depreciation	0.94	1.04	0.72	0.84	0.53	0.68	0.38	0.53
Economic Return (%)	11.0%	11.0%	11.0%	11.0%	11.0%	11.0%	11.0%	11.0%
Book Return (%)	7.3%	8.7%	6.6%	8.5%	6.0%	8.6%	5.5%	9.0%

______

Notes:

The calculations for the tables above are given

	Start of the Year
	1	2	3	4	5	6	7	8
Market Value	19.89	18.09	16.99	15.88	15.09	14.19	13.56	12.78
Economic Depreciation (A)		1.80	1.10	1.11	0.79	0.90	0.63	0.78
Cash Flow (B)		3.99	3.09	2.98	2.54	2.56	2.19	2.27
Economic Income (B-A)		2.19	1.99	1.87	1.75	1.66	1.56	1.49
Economic Return (%)		11.0%	11.0%	11.0%	11.0%	11.0%	11.0%	11.0%
Book Value	19.89	18.89	17.89	16.89	15.89	14.89	13.89	12.89
Book Depreciation (C) [(19.89 - 25%*19.89)/15]		1.00	1.00	1.00	1.00	1.00	1.00	1.00
Cash Flow (B)		3.99	3.09	2.98	2.54	2.56	2.19	2.27
Book Income (B - C)		2.99	2.09	1.98	1.54	1.56	1.19	1.27
Book Return (%)		15.0%	11.1%	11.1%	9.1%	9.8%	8.0%	9.1%

____

	Start of the Year
	9	10	11	12	13	14	15	16
Market Value	12.25	11.56	11.11	10.49	10.11	9.54	9.21	8.69
Economic Depreciation (A)	0.53	0.69	0.45	0.62	0.38	0.57	0.33	0.52
Cash Flow (B)	1.94	2.04	1.72	1.84	1.53	1.68	1.38	1.53
Economic Income (B-A)	1.41	1.35	1.27	1.22	1.15	1.11	1.05	1.01
Economic Return (%)	11.0%	11.0%	11.0%	11.0%	11.0%	11.0%	11.0%	11.0%
Book Value	11.89	10.89	9.89	8.89	7.89	6.89	5.89	4.89
Book Depreciation (C)	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Cash Flow (B)	1.94	2.04	1.72	1.84	1.53	1.68	1.38	1.53
Book Income (B-C)	0.94	1.04	0.72	0.84	0.53	0.68	0.38	0.53
Book Return (%)	7.3%	8.7%	6.6%	8.5%	6.0%	8.6%	5.5%	9.0%

______

b-1)

The steady-state of book return is calculated

Steady-State of Book Return = Total Book Income/Total Book Value*100

Substituting values in the above formula, we get,

Steady-State of Book Return = (2.99 + 2.09 + 1.98 + 1.54 + 1.56 + 1.19 + 1.27 + .94 + 1.04 + .72 + .84 + .53 + .68 + .38 + .53)/(19.89 + 18.89 + 17.89 + 16.89 + 15.89 + 14.89 + 13.89 + 12.89 + 11.89 + 10.89 + 9.89 + 8.89 + 7.89 + 6.89 + 5.89)*100 = 9.45%

______

b-2)

The steady-state of book return understates the true return. It is because of steady state of book return of 9.45% is less than the true rate of return which is 11%.

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