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
2.10
0.0
35.5
35.5
100
37.50
30.00
26.00
3.00
1.93
230.4
220.0
10.4
200
75.00
30.00
52.00
3.00
5.95
460.8
404.5
56.3
Note that the breakeven point can be found algebraically as follows:
NPV = Investment + [(PVA
10/10%
)
×
(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
¥29.00 B
2. Variable Cost
20.11
3. Fixed Cost
3.00
4. Depreciation
3.00
5. Pretax Profit
¥2.89 B
6. Tax
1.01
7. Net Profit
¥1.88
8. Operating Cash Flow
¥4.88
0.01
30
29.99
30
(1.10)
4.88
NPV
10
1
t
t

=

=

=
∑
=
81
V
P
F
t)
(1
V)
(P
)
(PVA
t)
D
(PVA
I
Q
10/10%
10/10%

+

×

×
×
×

=
260,000
375,000
000
3,000,000,
(0.65)
260,000)
(375,000
(6.144567)
461
6,451,795,
,000
30,000,000

+
×

×

=
77,356
26,087
51,269
115,000
000
3,000,000,
459,306
,539
23,548,204
=
+
=
+
=
)
rounding
to
due
difference
(