PROBLEM 12-3B (Continued)
Cash
Flows
X
12% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
Present value of cost to rebuild
Present value of salvage value
Capital investment
Net present value
b$36,000b
0
24,000
X
X
X
4.11141
.71178
.50663
=
=
=
$148,011
0
12,159
160,170
(160,000)
$ 170
bNet annual cash inflows = $60,000 – $24,000 = $36,000
PROBLEM 12-4B
Cash
Flows
X
10% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
Present value of cost of overhaul
Present value of salvage value
Capital investment
Net present value
$ 9,600
( (7,000)
16,000
X
X
X
5.33493
.68301
.46651
=
=
=
($ 51,215
( (4,781)
( 7,464
(53,898
(65,000)
($(11,102)
Based on its negative net present value, the tow truck should not be
purchased.
(b) The net present value based on the revised estimates is as follows:
Cash
Flows
X
10% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
Present value of cost of overhaul
Present value of salvage value
Capital investment
Net present value
$14,500*
(7,000)*
16,000 *
X
X
X
5.33493
.68301
.46651
=
=
=
($77,356)
( (4,781)
( 7,464)
(80,039)
(65,000)
($15,039)
*$9,600 + ($2,600 + $600 + $1,200 + $500)
value and therefore should be purchased.
(c) The present value of the intangible benefits was $26,141 (the increase
in the net present value from a negative $11,102 to a positive $15,039).
Brad’s estimates of the value of these intangible benefits may be
positive net present value.
PROBLEM 12-5B
follows:
Cash
Flows
X
12% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
Present value of salvage value
a$130,000a
700,000
X
X
7.46944
.10367
=
=
$ 971,027
72,569
1,043,596
Capital investment ($200,000 + $350,000)
Net present value
(550,000)
$ 493,596
aNet annual cash inflows = $700,000 – $570,000
The positive net present value of the project suggests that it should be
accepted.
(b) Using the revised estimates, the net present value is calculated as
follows:
Cash
Flows
X
12% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
Present value of salvage value
Capital investment
Net present value
b$ 62,000b
700,000
X
X
7.46944
.10367
=
=
$463,105
72,569
535,674
(550,000)
$ (14,326)
bNet annual cash inflows = $570,000 – $508,000
Under these revised estimates, the project should be rejected. It
appears that many of the camp’s costs are fixed; thus, when the
number of campers declines, cash inflows decline, but cash outflows
don’t decline proportionately.
PROBLEM 12-5B (Continued)
(c) Using the original estimates, but a 15% discount rate, the net present
value is calculated as follows:
Cash
Flows
X
15% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
Present value of salvage value
Capital investment
Net present value
c$130,000c
700,000
X
X
6.25933
.06110
=
=
$813,713
42,770
856,483
(550,000)
$306,483
cNet annual cash inflows = $700,000 – $570,000
The positive net present value of the project suggests that it should be
accepted; however, it is not nearly as profitable using a 15% discount
rate.
(d) The internal rate of return can be determined by calculating the discount
rate that results in a net present value of approximately zero. In this
case the internal rate of return was approximately 15%.
Cash
Flows
X
15% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
Present value of salvage value
Capital investment
Net present value
$ 65,000
668,000
X
X
3.35216
.49718
=
=
$217,890
332,116
550,006
(550,000)
$ 6
The project had a high internal rate of return, even though the business
itself was not generating much cash flows, because the property
increased significantly in value during the 5-year period.
BYP 12-1 DECISION-MAKING AT CURRENT DESIGNS
(a) Average investment = ($256,000 + 0) ÷ 2 = $128,000
(b) Net annual cash flow = $15,200 + $32,000 = $47,200
(c)
Event
Time
Period
Cash
Flows
9% Discount
Factor
Present
Value
Net annual cash flow
1-8
$ 47,200
5.53482
$ 261,244
Oven purchase
0
(256,000)
1.00000
(256,000)
Net present value
$ 5,244
(d)
Event
Time
Period
Cash
Flows
15% Discount
Factor
Present
Value
Net annual cash flow
1-8
$ 47,200
4.48732
$ 211,802
Oven purchase
0
(256,000)
1.00000
(256,000)
Net present value
$ (44,198)
Do not accept the proposal
BYP 12-2 DECISION-MAKING ACROSS THE ORGANIZATION
Purchase
New Machine
Sales
Costs and expenses
Cost of goods sold
Selling expenses
Administrative expenses
Depreciation
Loss on disposal of machine
Total costs and expenses
Net income
$3,500,000
704,000
448,000
130,000
40,000
(2)
(3)
(4)
(5)
(6)
$5,000,000
4,822,000
$ 178,000
(1)
(1) 10,000 X $100 X 4 years = $4,000,000 X 125% = $5,000,000
(2) $5,000,000 X (100% – 30%) = $3,500,000
(a) Annual rate of return = 68.5%; ($178,000 ÷ 4) ÷ [($130,000 + $0) ÷ 2]
(c)
Net present value =
Amount
Factor
Present
Value
Net annual cash flows
Capital investment
Net present value
$ 87,000
$130,000
*
2.85498
1.00000
$248,383
(130,000)
$118,383
*($178,000 + $130,000 + $40,000) ÷ 4
BYP 12-3 MANAGERIAL ANALYSIS
Cash
Flows
X
11% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of salvage value
Capital investment
Net present value
$ 460,000a
2,000,000
X
X
7.19087
.20900
=
=
($3,307,800)
( 418,000)
(3,725,800
(4,000,000)
($ (274,200)
(b) Using the revised estimates, the net present value is calculated as
follows:
Cash
Flows
X
11% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of salvage value
Capital investment
Net present value
b$ 720,000b
2,000,000
X
X
7.19087
.20900
=
=
$5,177,426
418,000
5,595,426
(4,000,000)
$1,595,426
bNet annual cash flows = $4,200,000 – $3,480,000