PROBLEM 12-2A
(a)
(1)
Annual
Net Income
(2)
Annual
Cash Inflow
Sales
Expenses
Drivers’ salaries
Out-of-pocket expenses
Depreciation
Total expenses
Net income
Cash inflow
*$108,000*
* 48,000*
* 30,000*
* 25,000*
* 103,000*
*$ 5,000*
$108,000
48,000
30,000
0
78,000
$ 30,000
(b) 1. Cash payback period = $75,000 ÷ $30,000* = 2.50 years.
2.
Annual rate of return
=
$5,000
÷
($75,000 + 0)
=
13.33%.
2
(c) Present value of annual cash inflows ($30,000 X 2.28323*) = $68,497
*3 years at 15%, PV of annuity of 1.
PROBLEM 12-3A
(a)
(1) Option A
Cash
Flows
X
8% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of cost to rebuild
Present value of salvage value
Capital investment
Net present value
a$40,000a
( (50,000)
( 0)
X
X
X
5.20637
.73503
.58349
=
=
=
($208,255)
( (36,752)
( 0)
($171,503)
( (160,000)
($ 11,503)
aNet annual cash flows = $70,000 – $30,000 = $40,000
(2) Profitability index = $171,503/$160,000 = 1.07
(3) The internal rate of return can be approximated by finding the discount
Cash
Flows
X
10% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of cost to rebuild
Present value of salvage value
Capital investment
Net present value
a$40,000a
( (50,000)
( 0)
X
X
X
4.86842
.68301
.51316
=
=
=
($194,737)
( (34,151)
( 0)
($160,586)
(160,000)
($ 586
aNet annual cash flows = $70,000 – $30,000 = $40,000
(1) Option B
Cash
Flows
X
8% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of cost to rebuild
Present value of salvage value
Capital investment
Net present value
b$54,000b
0
8,000
X
X
X
5.20637
.73503
.58349
=
=
=
$281,144
0
4,668
$285,812
(227,000)
$ 58,812
bNet annual cash flows = $80,000 – $26,000 = $54,000
(2) Profitability index = $285,812/$227,000 = 1.26
PROBLEM 12-3A (Continued)
(3) Internal rate of return on Option B is 15%, as calculated below:
Cash
Flows
X
15% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of cost to rebuild
Present value of salvage value
Capital investment
Net present value
b$54,000b
0
8,000
X
X
X
4.16042
.57175
.37594
=
=
=
$224,663
0
3,008
$227,671
(227,000)
$ 671
bNet annual cash flows = $80,000 – $26,000 = $54,000
preferred project.
PROBLEM 12-4A
Cash
Flows
X
9% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of cost of overhaul
Present value of salvage value
Capital investment
Net present value
$ 8,000
( (6,000)
( 12,000)
X
X
X
5.53482
.70843
.50187
=
=
=
($ 44,279
( (4,251)
( 6,022
($ 46,050
(60,000)
($(13,950)
purchased.
(b) The net present value based on the revised estimates is as follows:
Cash
Flows
X
9% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of cost of overhaul
Present value of salvage value
Capital investment
Net present value
$13,500*
( (6,000)*
( 12,000 *
X
X
X
5.53482
.70843
.50187
=
=
=
($74,720)
( (4,251)
( 6,022)
($76,491)
(60,000)
($16,491)
*$8,000 + ($3,000 + $750 + $1,000 + $750)
value and therefore should be purchased.
(c) The present value of the intangible benefits was $30,441 (the increase
in the net present value from a negative $13,950 to a positive $16,491).
Rick’s estimates of the value of these intangible benefits may be overly
net present value.
PROBLEM 12-5A
follows:
Cash
Flows
X
8% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of salvage value
a$ 100,000a
1,500,000
X
X
9.81815
.21455
=
=
$ 981,815
321,825
1,303,640
Capital investment ($300,000 + $600,000)
Net present value
(900,000)
$ 403,640
aNet annual cash flows = $940,000 – $840,000
The positive net present value of the project suggests that it should be
accepted.
(b) Using the revised estimates, the net present value is calculated as
follows:
Cash
Flows
X
8% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of salvage value
Capital investment
Net present value
b$ 50,000b
1,500,000
X
X
9.81815
.21455
=
=
$(490,908)
(321,825)
$(812,733)
(900,000)
$ (87,267)
bNet annual cash flows = $800,000 – $750,000
Under these revised estimates, the project should be rejected. It appears
PROBLEM 12-5A (Continued)
(c) Using the original estimates, but an 11% discount rate, the net present
value is calculated as follows:
Cash
Flows
X
11% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of salvage value
Capital investment
Net present value
c$
100,000c
1,500,000
X
X
7.96333
.12403
=
=
$ 796,333
186,045
$ 982,378
(900,000)
$ 82,378
The positive net present value of the project suggests that it should be
(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 12%.
Cash
Flows
X
12% Discount
Factor
=
Present
Value
Present value of net annual cash flows
Present value of salvage value
Capital investment
Net present value
$ 40,000
1,332,000
X
X
3.60478
.56743
=
=
$144,191
755,817
$900,008
(900,000)
$ 8
PROBLEM 12-1B
(a) Project Mary $140,000 ÷ [($10,000 + $28,000)] = 3.68 years
Project Winnie
Cash Flow
Cumulative Cash Flow
$47,500 ($12,500 + $35,000)
$47,000 ($12,000 + $35,000)
$46,000 ($11,000 + $35,000)
$43,000 ($ 8,000 + $35,000)
$41,000 ($ 6,000 + $35,000)
$ 47,500
$ 94,500
$140,500
$183,500
$224,500
Cash payback period 3.80 years
Project Sarah
Year
Cash Flow
Cumulative Cash Flow
1
2
3
4
5
$57,000 ($19,000 + $38,000)
$54,000 ($16,000 + $38,000)
$52,000 ($14,000 + $38,000)
$47,000 ($ 9,000 + $38,000)
$46,000 ($ 8,000 + $38,000)
$ 57,000
$111,000
$163,000
$210,000
$256,000
Cash payback period 3.57 years
PROBLEM 12-1B (Continued)
(b) Project Mary
Item
Amount
Years
PV Factor
Present
Value
Net annual cash flows
Capital investment
Negative net present
value
$38,000
1–5
3.60478
$136,982
(140,000)
$ (3,018)
Project Winnie
Project Sarah
Year
Discount
Factor
Cash
Flow
PV
Cash
Flow
PV
1
2
3
4
5
Total
.89286
.79719
.71178
.63552
.56743
$ 47,500
47,000
46,000
43,000
41,000
$224,500
$ 42,411
37,468
32,742
27,327
23,265
163,213
(175,000)
$ (11,787)
$ 57,000
54,000
52,000
47,000
46,000
$256,000
$ 50,893
43,048
37,013
29,869
26,102
186,925
(190,000)
$ (3,075)
Capital investment
Positive (negative)
net present value
(c) Project Mary = $10,000 ÷ [($140,000 + $0) ÷ 2] = 14.29%.
(d)
Project
Cash Payback
Net
Present Value
Annual
Rate of Return
Mary
Winnie
Sarah
2
3
1
1
3
2
1
3
2
PROBLEM 12-2B
(a)
(1)
Annual
Net Income
(2)
Annual
Cash Inflow
Sales
Expenses
Drivers’ salaries
Out-of-pocket expenses
Depreciation
Total expenses
Net income
Cash inflow
*$144,000*
43,000
* 42,000**
* 30,000
* 115,000
$ 29,000
$144,000
43,000
42,000
0
85,000
$ 59,000
**$26,000 + $4,000 + $5,300 + $4,500 + $2,200 = $42,000
PROBLEM 12-3B
(a)
(1) Option A
Cash
Flows
X
11% 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
a$32,000a
( (53,000)
( 0)
X
X
X
4.23054
.73119
.53464
=
=
=
($135,377)
( (38,753)
( 0)
( 96,624)
(100,000)
($ (3,376)
aNet annual cash inflows = $56,000 – $24,000 = $32,000
(2) Profitability index = $96,624/$100,000 = .97
accomplished with a 10% discount rate.
Cash
Flows
X
10% 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
a$32,000a
( (53,000)
( 0)
X
X
X
4.35526
.75132
.56447
=
=
=
($139,368)
( (39,820)
( 0)
( 99,548)
(100,000)
$ (452)
aNet annual cash inflows = $56,000 – $24,000 = $32,000
(1) Option B
Cash
Flows
X
11% 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
4.23054
.73119
.53464
=
=
=
$152,299
0
12,831
165,130
(160,000)
$ 5,130
bNet annual cash inflows = $60,000 – $24,000 = $36,000