b. (See chart on next page.)
Inflows
Outflows
Unit Sales
Revenues Investment
V. Costs
F. Cost
Taxes
PV
PV
NPV
(000’s)
Yrs 110
Yr 0
Yr 110
Yr 110
Yr 110
Inflows
Outflows
0
0.00
30.00
0.00
3.00
3.00
0.0
30.0
30.0
100
37.50
30.00
26.00
3.00
2.75
230.4
225.1
5.3
200
75.00
60.00
52.00
3.00
7.00
460.8
441.0
19.8
Note that the breakeven point can be found algebraically as follows:
NPV = Investment + [PV
×
(t
×
Depreciation)] +
[Quantity
×
(Price  V.Cost)  F.Cost]
×
(1  t)
×
(PVA
10/10%
)
Set NPV equal to zero and solve for Q:
Proof:
1.
Revenue
¥31.8 B
2.
Variable Cost
22.1
3.
Fixed Cost
3.0
4.
Depreciation
3.0
5.
Pretax Profit
¥3.7 B
6.
Tax
1.85
7.
Net Profit
¥1.85
8.
Operating Cash Flow
¥4.85
0.2
30
8
29.
30
(1.10)
4.85
NPV
10
1
t
t

=

=

=
∑
=
91
V
P
F
t)
(1
V)
(P
)
(PVA
t)
D
(PV
I
Q
10/10%

+

×

×
×
×

=
260,000
375,000
000
3,000,000,
(0.5)
260,000)
(375,000
(6.144567)
659
9,216,850,
,000
30,000,000

+
×

×

=
84,910.7
26,087.0
58,823.7
115,000
000
3,000,000,
353,313
,342
20,783,149
=
+
=
+
=
)
rounding
to
due
difference
(