Question

Toyota is planning a new fuel cell powered car. It will cost $1.9 billion initially and an additional $0.6 billion the year after to build the factory, which can then be linearly depreciated to zero over 20 years, and be sold for $900 million at the end of year 21.

The company also has to put up $80 million to buy components just before operation starts at the beginning of year 2.

For each of the 20 years of operation (years 2 to 21), Toyota expects to sell 1 million cars at a price of $40,000. Labor and components for each car add up to $38,500 per car. After completion at the end of year 1, it also costs $800 million each year to run the factory, independent of the level of production.

Toyota's marginal tax rate is 34% and its cost of capital for this project is 14%.

  Attempt 4/10 for 10 pts.

Part 1

What is the annual depreciation (in $ million)?

Correct ✓

The initial book value of the factory is 1.9 + 0.6 = 2.5 billion.

With linear depreciation over 20 years, the annual depreciation is:
D = 2.5 billion/20 = 125 (million)

  Attempt 3/10 for 10 pts.

Part 2

What is EBIT in each year of operation (in $ million)?

Correct ✓

Revenue = Price * Quantity
= 40,000 * 1
= 40,000 (million)

Costs = Fixed costs + Variable costs
= 800 + 38,500 * 1
= 39,300 (million)

EBIT = Revenue - Costs - Depreciation
= 40,000 - 39,300 - 125
= 575 (million)

  Attempt 1/10 for 10 pts.

Part 3

What is the change in net operating working capital at the end of year 1 (in $ million, as a positive number)?

Correct ✓

The company has to put up $80 million to buy components (inventory) just before operation starts at the beginning of year 2, which is the same as the end of year 1. This amount can be recouped at the end of the project, in year 21.

  Attempt 2/10 for 10 pts.

Part 4

What is the after-tax salvage value (ATSV) of the factory in year 21 (in $ million)?

Correct ✓

The book value will be 0 in year 21.

ATSV = SV - t (SV - BV)
= 900 - 0.34 (900 - 0)
= 594 (million)

  Attempt 5/10 for 12 pts.

Part 5

What is the free cash flow at the end of year 1 (in $ million)?

  Attempt 1/10 for 12 pts.

Part 6

What is the present value of the free cash flow from year 2 to 20 (ignoring the one for year 21 for now) (in $ million)?

  Attempt 1/10 for 10 pts.

Part 7

What is the free cash flow at the end of year 21 (in $ million)?

  Attempt 1/10 for 10 pts.

Part 8

What is the NPV of this project (in $ million)?

Answer 1

A	B	C	D	E	F	G	H	I	J	K	L	M
2
3
4		Initial investment	$2,500	million
5		Depreciation per year	$125	million
6		EBIT from Year 2 to 20	$575	million
7		Change in net operating working in Year 1	($80)	million
8		Change in net operating working in Year 21	$80	million
9		After-tax salvage value	$594	million
10		Tax rate	34%
11		Cost of capital	14%
12		Part 5:
13		Free cash flow needs to be calculated as follows:
14		Free Cash Flow = Operating Cash Flow - Capital Expenditures - Change in working capital
15		Operating Cash Flow = EBIT*(1-Tax Rate)+Depreciation
16
17		Free Cash Flow (in million) in Year 1	= EBIT*(1-Tax Rate)+Depreciation -Capital Expenditure - Change in working capital
18			=$0*(1-34%)+$125-0-80
19			$45.00	=0*(1-D10)+D5-0+D7
20
21		Hence Free Cash Flow (in million) in Year 1	$45.00
22
23		Part 6
24
25		Free Cash Flow (in million) in Year 2 to Year 20	= EBIT*(1-Tax Rate)+Depreciation -Capital Expenditure - Change in working capital
26			=$575*(1-34%)+$125-0-0
27			$504.50	=D6*(1-D10)+D5-0-0
28
29		Hence Free Cash Flow (in million) in Year 2 to Year 20	$504.50
30
31		Present value of Free Cash flow from year 2 to year 20 (in Million)	=$504.50*(P/A,14%,19)*(P/F,14%,1)
32			$2,898.83	=D29*PV(14%,19,-1,0)*(1/(1+D11))
33
34		Hence the Present value of Free Cash flow from year 2 to year 20 (in Million)	$2,898.83
35
36		Part 7:
37
38		Free Cash Flow at Year 21 ( in million)	= EBIT*(1-Tax Rate)+Depreciation -Capital Expenditure - Change in working capital + After Tax Salvage Value
39			=$575*(1-34%)+$125-0+$80+$594
40			$1,178.50
41
42		Hence Free Cash Flow at Year 21 (in million)	$1,178.50
43
44		Part 8:
45
46		NPV of the project (In million)	=Initial investment + PV of FCF in Year 1 + PV of FCF from Year 2 to 20 + PV of FCF in year 21
47			=-$2,500+$45*(P/F,14%,1)+$2898.83+$1,178.50*(P/F,14%,21)
48			$513.52		=-D4+D21*(1/((1+D11)^1))+D34+D42*(1/((1+D11)^21))
49
50		Hence NPV of the project (In million) is	$513.52
51