(4) What is the present value annuity of this amount in (3)?
(5) Given your answer in (4), what does this tell you about the needed price increase if
you are to equal the NPV of $342,266 from expanding? Show this is true by computing the NPV
with the increase in annual net CFA caused by this price increase.
ANSWER (1):
The formula is: NPV = PMT(PVAF
r,n
) – costs = PMT([(1 + r)
n
–
1] / [r(1 + r)
n
]) –
costs
= $102,000([(1.16)
10
– 1] / [0.16(1.16)
10
]) – 0 =
$492,989.20
. This is
$150,732.20
greater
than the $342,266 from the expansion plan. Therefore, although the expansion plan is better than
the status quo, the alternative of increasing the price is even better than expansion. Thus,
raise
price
.
ANSWER (2):
The formula is: NPV = PMT(PVAF
r,n
) – costs = PMT([(1 + r)
n
–
1] / [r(1 + r)
n
]) –
costs = $70,800([(1.16)
10
– 1] / [0.16(1.16)
10
]) – 0 =
$342,192.51
. This is
$73.49
less than the
$342,266 from the expansion plan. Therefore, the expansion plan is better but only slightly.]
ANSWER (3):
An increase of $0.017 generates an increase of $102,000. Since $0.017 divided
by 17 equals $0.001 this implies that $0.001 will generate an increase of $102,000 / 17 =
$6,000
in after-tax revenues.
ANSWER (4):
The formula is: PVA
n
= PMT(PVAF
r,n
) = PMT([(1 + r)
n
–
1] / [r(1 + r)
n
]) =
$6,000([(1.16)
10
– 1] / [0.16(1.16)
10
]) =
$28,999.36
.
ANSWER (5):
With an increase of $28,999.36 in today’s dollars for every $0.001 increase in
price, this tells us that ($342,266 / $28,999.36)(0.001) = $0.011802534 or about
$0.0118
increase
will achieve a NPV of $342,266. To prove this we take $0.011802534 times $10 million and get
$118,025.34. After-taxes, we have: $118.025.34(1 – 0.04) = $70,815.20.Taking the present value
of these cash flows, we have: PVA
n
= PMT(PVAF
r,n
) = PMT([(1 + r)
n
–
1] / [r(1 + r)
n
]) =
$70,815.20([(1.16)
10
– 1] / [0.16(1.16)
10
]) =
$342,266.00 which is the same as the NPV of the
expansion
. It is also the NPV from the price increase since costs are zero.
72.
A new product is being considered by Brooks’ Books, Inc. The after-tax cash flows at
time zero include an outlay for depreciable equipment (I
0
) of $16M (M = million) and $2.2M for
additional net working capital (ΔW). The project is expected to have an 8-year life (n=8), and the
equipment will be depreciated on a straight-line basis to a zero book value (B=0) over 8 years.