CHAPTER 12
SOLUTIONS TO PROBLEMS: SET B
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)
$ 47,500
$ 94,500
Project Sarah
Cash Flow
Cumulative Cash Flow
$57,000 ($19,000 + $38,000)
$54,000 ($16,000 + $38,000)
$ 57,000
$111,000
PROBLEM 12-1B (Continued)
(b) Project Mary
Item
Amount
Years
PV Factor
Present
Value
Net annual cash flows
$38,000
1–5
3.60478
$136,982
Project Winnie
Project Sarah
Year
Discount
Factor
Cash
Flow
PV
Cash
Flow
PV
Total
$224,500
46,000
1
2
.89286
.79719
$ 47,500
47,000
$ 42,411
37,468
$ 57,000
54,000
$ 50,893
43,048
(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
The best project is Mary, but even Mary should not be recommended,
because the net present value is negative.
PROBLEM 12-2B
(a)
(1)
Annual
Net Income
(2)
Annual
Cash Inflow
Sales
Expenses
Drivers’ salaries
*$144,000*
43,000
$144,000
43,000
(b) 1. Cash payback period = $90,000 ÷ $59,000 = 1.53 years.
(c) Present value of annual cash inflows ($59,000 X 2.28323*) = $134,711
Capital investment = (90,000)
Net present value = $ 44,711
(d) The computations show that the commuter service is a good
investment for these reasons: (1) annual net income will be $29,000,
PROBLEM 12-3B
(a)
(1) Option A
Cash
Flows
X
11% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
a$32,000a
X
4.23054
=
($135,377)
(2) Profitability index = $96,624/$100,000 = .97
(3) The internal rate of return can be approximated by finding the discount
rate that results in a net present value of approximately zero. This is
accomplished with a 10% discount rate.
Cash
Flows
X
10% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
Les: Capital investment
(1) Option B
Cash
Flows
X
11% Discount
Factor
=
Present
Value
Less: Capital investment
160,000
Present value of net annual cash inflows
b$36,000b
X
4.23054
=
$152,299
(2) Profitability index = $165,130/$160,000 = 1.03
PROBLEM 12-3B (Continued)
(3) Internal rate of return on Option B is 12%, as calculated below:
Cash
Flows
X
12% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
b$36,000b
X
4.11141
=
$148,011
(b) Option A has a lower net present value than Option B, and also a lower
profitability index and internal rate of return. Therefore, Option B is the
Less: Capital investment
PROBLEM 12-4B
(a) The net present value based on the original estimates is as follows:
Cash
Flows
X
10% Discount
Factor
=
Present
Value
Present value of net annual cash inflows
$ 9,600
X
5.33493
=
($ 51,215
(b) The net present value based on the revised estimates is as follows:
Cash
Flows
X
10% Discount
Factor
=
Present
Value
Less: Capital investment
Present value of net annual cash inflows
$14,500*
X
5.33493
=
($77,356)
(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
PROBLEM 12-5B
(a) Using the original 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
a$130,000a
700,000
X
X
7.46944
.10367
=
=
$ 971,027
72,569
1,043,596
(b) Using the revised estimates, the net present value is calculated as
follows:
Cash
Flows
X
12% Discount
Factor
=
Present
Value
Less: Capital investment
Net present value
Present value of net annual cash inflows
b$ 62,000b
X
7.46944
=
$463,105
Net present value
$ 493,596
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
c$130,000c
700,000
X
X
6.25933
.06110
=
=
$813,713
42,770
(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 salvage value
Less: Capital investment
=
Present value of net annual cash inflows
$ 65,000
X
3.35216
=
$217,890
Less: Capital investment