Question

You work for a very large engineering consulting firm. You have been asked to look at the viability of the company purchasing a private jet to fly staff to project sites around the world. A new Gulfstream G450 currently costs $40,000,000. Assume a 15-year service life, a salvage value of $24,000,000, annual costs of $2,500,000/year, and annual benefits of $3,500,000/year (time saved, increased business), a corporate tax rate of 40%, a CCA rate of 25%, and an after-tax MARR of 8% per year, compounded annually.

What is the after-tax net present value of this investment?

Answer 1

CCA rate of 25% is given to us.

Let us find the depreciation that can be offsetted against the earnings per year.

This would be calculated by multipling the CCA rate of 25% to the value of equipment at previous year.

1st year depreciation = 0.25 * 40,000,000 = 10,000,000

Balance at year 1 = 40,000,000 - 10,000,000 = 30,000,000

2nd year depreciation = 0.25 * 30,000,000 = 7,500,000

Balance at year 2 = 30,000,000 - 7,500,000 = 22,500,000 so on and so forth.

Depreciation Table
Year	Depreciation	Balance
0		40,000,000.00
1	10,000,000.00	30,000,000.00
2	7,500,000.00	22,500,000.00
3	5,625,000.00	16,875,000.00
4	4,218,750.00	12,656,250.00
5	3,164,062.50	9,492,187.50
6	2,373,046.88	7,119,140.63
7	1,779,785.16	5,339,355.47
8	1,334,838.87	4,004,516.60
9	1,001,129.15	3,003,387.45
10	750,846.86	2,252,540.59
11	563,135.15	1,689,405.44
12	422,351.36	1,267,054.08
13	316,763.52	950,290.56
14	237,572.64	712,717.92
15	178,179.48	534,538.44

Lets calculate the net cash flows:

Year	Cost of Jet	Salvage value	Annual Cost	Annual Benefit	Cash Flows	Depreciation	Taxable Income	Tax	Net Cash Flows
0	(40,000,000.00)	-			(40,000,000.00)				(40,000,000.00)
1	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	10,000,000.00	(9,000,000.00)	(3,600,000.00)	4,600,000.00
2	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	7,500,000.00	(6,500,000.00)	(2,600,000.00)	3,600,000.00
3	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	5,625,000.00	(4,625,000.00)	(1,850,000.00)	2,850,000.00
4	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	4,218,750.00	(3,218,750.00)	(1,287,500.00)	2,287,500.00
5	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	3,164,062.50	(2,164,062.50)	(865,625.00)	1,865,625.00
6	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	2,373,046.88	(1,373,046.88)	(549,218.75)	1,549,218.75
7	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	1,779,785.16	(779,785.16)	(311,914.06)	1,311,914.06
8	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	1,334,838.87	(334,838.87)	(133,935.55)	1,133,935.55
9	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	1,001,129.15	(1,129.15)	(451.66)	1,000,451.66
10	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	750,846.86	249,153.14	99,661.25	900,338.75
11	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	563,135.15	436,864.85	174,745.94	825,254.06
12	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	422,351.36	577,648.64	231,059.46	768,940.54
13	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	316,763.52	683,236.48	273,294.59	726,705.41
14	-	-	(2,500,000.00)	3,500,000.00	1,000,000.00	237,572.64	762,427.36	304,970.94	695,029.06
15	-	24,000,000.00	(2,500,000.00)	3,500,000.00	25,000,000.00	178,179.48	24,821,820.52	9,928,728.21	15,071,271.79

Cost of Equipment = -40,000,000/-

Salvage Value at 15th year = 24,000,000/-

Annual Cost = 2,500,000

Annual Benefit = 3,500,000

Cash Flows is addition of cost of equipment, salvage value, annual cost and annual benefit year wise.

Depreciation is taken from previous table.

Taxable income = Cash flows - Depreciation

Tax = Taxable income * Tax rate = Taxable income * 40%

Net Cash flows post tax = Cash flows - Tax

We need to find the present value of all the cash flows at MARR of 8%.

Net Present Value = -16,902,484.62

Since the NPV is negative, the investment is not worthwhile.