P16.31.
a.
0 1 2 3 4 5 6 7 8 9 10
6.1446 (Table 6-5 0.3855 (Table 6-4
$(280,000) 10 periods, 10 periods,
258,073 10%) 10%)
11,565
$ (10,362) net present value
b.
Present Value Ratio = ($269,638 present value of inflows / $280,000 investment) = 0.96
c.
Internal rate of return (actual rate of return) is considerably less than the cost of capital of
10% because the net present value is negative and the present value ratio is relatively low.
d.
Payback period = 6.67 years
Total return in years 1-6 ($42,000 annual cash flow * 6 years) …………
$ 280,000
P16.32.
a.
Year
Volume
Contribution Margin
@ $ 4.20 per dozen
Present
Value
2016
3,000 dozen
$12,600
$ 11,666
2017
4,700 dozen
19,740
16,923
2018
7,100 dozen
29,820
23,671
2019
9,400 dozen
39,480
29,018
2020
42,000
28,585
Total present value of inflows ………………………..……………………
$109,863
Investment (machine cost, plus delivery and installation costs) ………..…
Net present value …………………………………..………………………
b.
Profitability index = ($109,863 present value of inflows / $94,000 investment) = 1.17
c.
Because the net present value is positive and the profitability index is rather high, the
IRR is significantly greater than the 8% discount rate used to calculate the NPV.
d.
Year
Cash Flow
Cumulative Cash Flow
1.
2016
$12,600
$ 12,600
2.
2017
19,740
32,340
3.
2018
29,820
62,160
4.
2019
39,480
101,640
5.
2020
42,000
143,640
Chapter 16 Costs for Decision Making
P16.32.
(continued)
d.
The investment of $94,000 will be recovered in the 4th year, after $31,840 of that year’s
P16.33.
a.
Proposal
Investment
Net PV
PV of Inflows
(Investment +
Net PV)
Profitability Index
(PV of Inflows / Outflows)
1
$50,000
$30,000
$80,000
$80,000 / $50,000 = 1.6
2
3
4
Proposal 1 is most desirable because its profitability index is the highest.
P16.34.
a.
Project B:
Initial investment…………………………………………………………
$(100,000)
Present value of net cash return, by year(s):
Years 3-5 = $32,000 * (0.7513 + 0.6830 + 0.6209) ……………………
65,766
Year 6-10 = $20,000 * (6.1446 – 3.7908) …………………………..…
47,076
Net present value…………………………………………………………
$ 12,842
Initial investment…………………………………………………………
$(200,000)
Present value of net cash return, by year(s):
Years 1-5 = $58,000 * 3.7908 …………………………………………
Net present value…………………………………………………………
Project D:
$(200,000)
16,364
29,750
Year 3 = $54,000 * 0.7513 …………………………..…………………
40,570
Year 4 = $72,000 * 0.6830 ………………………..……………………
49,176
Net present value…………………………………………………………
b.
Project
B
C
D
E
Initial investment ……………..……
$100,000
$200,000
$200,000
$400,000
+ Net present value…………………
12,842
19,866
(8,259)
11,501
= PV of inflows….…………………
$112,842
$219,866
$411,501
100,000
200,000
= Profitability index
P16.34.
(continued)
c.
because of its $400,000 initial investment cost.
1. Based on quantitative analysis only, Project C should be invested in because the
$19,866 net present value of this project is expected to exceed the total net present
2. Projects A, B, and C should be invested in—even though this would mean that
3. Projects A, B, C, and E should be invested in—even though this would mean that
only $800,000 has been invested. Project D has a negative net present value.
d.
The analysis above represents only quantitative factors. Management of Scott, Inc.,
should also take a number of qualitative factors into account, such as: 1) the possibility
of estimation errors with respect to net cash return projections, 2) an assessment of
P16.35.
a.
Accounting rate of return =
Investment Average
IncomeNet
=
2 / )## $90,000 ($100,000
# $10,000 – $29,000
= 20%
b.
Investment:
Year 1
Year 2
Year 3
Year 4
Machine
$(80,000)
Working Capital
(20,000)
Cash returns:
Operations
$14,000
$24,000
$29,000
$20,000
Salvage
50,000
Working Capital
Totals
$14,000
$24,000
$29,000
$90,000
PV Factor for 18%
0.7182
0.5158
Present value
$11,865
$17,237
$17,649
$46,422
Sum of present values
Based on this analysis, the investment would not be made because the net present value is
negative, indicating that the ROI on the project is less than the discount rate of 18%.
c.
The net present value analytical approach is the best technique to use because it recognizes
the time value of money.
P16.36.
a.
Accounting rate of return =
Investment Average
IncomeNet
=
2 / )## $82,000 ($100,000
18$– $28,000

= 10.99%
The investment would probably not be made because the indicated ARR of 10.99% is less
b.
The investment would probably not be made because the payback period of 3.57 years is
longer than the desired 3-year payback period.
($100,000 investment / $28,000 cash flows per year) = 3.57 years
c.
Investment:
Year 1
Year 2
Year 3
Year 4
Year 5
Machine
$(100,000)
Cash returns:
Operations
$28,000
$28,000
$28,000
$28,000
$28,000
Salvage
Totals
$(100,000)
$28,000
$28,000
$28,000
$28,000
$38,000
PV Factor for 16%
Present value
$25,001
$22,322
$19,930
$17,794
$21,561
Sum of present
values
The investment probably would be made because the net present value is positive,
indicating that the ROI on the project is more than the cost of capital of 12%.
d.
The net present value analytical approach is the best technique to use because it
recognizes the time value of money.
C16.37.
a.
Notes: All amounts are rounded to the nearest US$1.00 psf = per square foot,
sf = square feet, 1.25 = conversion factor, PV = present value factor (10 years, 12% =
0.3220), PVa = present value of an annuity factor (10 years, 12% = 5.6502).
Initial investment:
US$
US$
Real estate (CI$150 psf * 1,000 sf * 1.25) ………………………
(187,500)
Equipment for health spa ……………………………………
(35,000)
Inventory of cosmetics and skin care products ………………
(8,000)
(230,500)
Annual operating costs:
Cleaning (CI$0.10 psf * 1,000 sf * 12 months * 1.25 * 5.6502 PVa) ..
Utilities (CI$0.40 psf * 1,000 sf * 12 months * 1.25 * 5.6502 PVa) …
(33,901)
Health spa assistant (US$25,000 * 5.6502 PVa)…………………
(141,255)
Advertising (US$3,000 * 5.6502 PVa) …………………………
(16,951)
Maintenance and insurance (US$4,500 * 5.6502 PVa) …………
(25,426)
(226,008)
Annual cash inflows (CI$8,000 * 12 months * 1.25 * 5.6502 PVa)…
Future sale of real estate (CI$300 psf * 1,000 sf * 1.25 * 0.3220 PV)..
b.
Initial investment:
US$
US$
Real estate (CI$150 psf * 2,500 sf * 1.25) ………………………
(468,750)
Equipment for fitness center …………………………………
(50,000)
Equipment for health spa ……………………………………
(35,000)
Inventory of cosmetics and skin care products ………………
(8,000)
(561,750)
Annual operating costs:
Cleaning (CI$0.10 psf * 2,500 sf * 12 months * 1.25 * 5.6502 PVa) ..
(21,188)
Utilities (CI$0.60 psf * 2,500 sf * 12 months * 1.25 * 5.6502 PVa) …
(127,130)
Health spa assistant (US$25,000 * 5.6502 PVa)…………………
(141,255)
Aerobics instructors (2 * US$20,000 * 5.6502 PVa) ……………
(226,008)
Physical trainer (US$30,000 * 5.6502 PVa) ……………………
(169,506)
Advertising (US$3,000 * 5.6502 PVa) …………………………
(16,951)
Maintenance and insurance (US$4,500 * 5.6502 PVa) …………
(25,426)
(727,464)
Annual cash inflows:
Fitness center (CI$300 * 500 members * 1.25 * 5.6502 PVa) ……
Health spa (CI$8,000 * 12 months * 1.25 * 5.6502 PVa) …………
Future sale of real estate (CI$300 psf * 2,500 sf * 1.25 * 0.3220 PV) .
C16.37.
(continued)
c.
Note: Changes from the solution to part b are shown in bold.
Initial investment:
US$
US$
Real estate (CI$150 psf * 2,500 sf * 1.25) ………………………
(468,750)
Equipment for fitness center …………………………………
(50,000)
Equipment for health spa ……………………………………
(35,000)
Inventory of cosmetics and skin care products ………………
(8,000)
(561,750)
Annual operating costs:
Cleaning (CI$0.10 psf * 2,500 sf * 12 months * 1.25 * 5.6502 PVa) ..
(21,188)
Utilities (CI$0.60 psf * 2,500 sf * 12 months * 1.25 * 5.6502 PVa) …
(127,130)
Health spa assistant (US$25,000 * 5.6502 PVa)…………………
(141,255)
Aerobics instructors (2 * US$20,000 * 5.6502 PVa) ……………
(226,008)
Physical trainer (US$30,000 * 5.6502 PVa) ……………………
(169,506)
Advertising (US$3,000 * 5.6502 PVa) …………………………
(16,951)
Maintenance and insurance (US$4,500 * 5.6502 PVa) …………
(25,426)
(727,464)
Annual cash inflows:
Fitness center (CI$300 * 300 members * 1.25 * 5.6502 PVa) ……
635,648
Health spa (CI$6,000 * 12 months * 1.25 * 5.6502 PVa) …………
508,518
1,144,166
Future sale of real estate (CI$200 psf * 2,500 sf * 1.25 * 0.3220 PV)..
201,250
Net present value………………………………………………
$ 56,202
d.
If Jinny initially decides to open the health spa only, she should consider leasing (rather
than purchasing) the 1,000 square foot unit for the following reasons:
By leasing, her initial investment cost would be reduced to only US$43,000 because
Although the nominal value of real estate in Grand Cayman is likely to double over
the next 10 years (from CI$150 to CI$300 per square foot), the present value of the
future selling price of Jinny’s unit (US$120,750) is less than the cost of purchasing it
Chapter 16 Costs for Decision Making
C16.37.
(continued)
e.
Analysis:
1. Without considering the cost of Jinny’s salary, the net present value calculations in
parts a and b adequately support either alternative. The profitability index for each of
these alternatives would be extremely high, calculated as follows:
1,000 sf unit
(see part a)
2,500 sf unit
(see part b)
PV of annual cash inflows …………………………
$678,024
$1,737,437
+ PV of future sale of real estate………………………
120,750
301,875
= PV of net cash inflows………………………………
$572,766
$1,311,848
230,500
561,750
= Profitability index……………………………………
2. One additional line should now be added to the solutions presented for parts a and b.
Without adjusting Jinny’s “reasonably comfortable salary” of CI$4,000 for inflation
over the next 10 years, the following results would occur (changes in bold):
1,000 sf unit
(see part a)
2,500 sf unit
(see part b)
PV of annual cash inflows …………………………
$678,024
$1,737,437
+ PV of future sale of real estate………………………
120,750
301,875
= PV of net cash inflows………………………………
230,500
561,750
= Profitability index……………………………………
operating a small personal service business (i.e., health spa only) with the help of one
personal assistant, Jinny would be taking a low risk, low return strategy. The combined
3. It now becomes clear that the real money to be made is in the full-scale operation.
The combined fitness center / health spa allows Jinny to pay herself a reasonably
4. The analysis above represents only quantitative factors. Jinny should also take a
number of qualitative factors into account, such as: 1) the possibility of estimation errors
with respect to her projections, 2) an assessment of non-financial risks involved with
C16.37.
(continued)
e.
Recommendation:
reputation by operating the health spa—with a target of opening the combined
operation at the end of the initial one-year lease term.
After consulting with Jinny in terms of how she perceives the various risks involved, I
would recommend that she either: 1) consider purchasing the 2,500 square foot unit
C16.38.
a.
Investment…………………………………………………………………
$(150,000)
Investment in working capital……………………………………………
(50,000)
Annual cash inflows, by year:
2016 = $40,000 * 0.8929………………………………………………
35,716
2017 = 50,000 * 0.7972………………………………………………
39,860
2018 = 64,000 * 0.7118………………………………………………
45,555
2019 = 46,000 * 0.6355………………………………………………
29,233
Salvage value = $50,000 * 0.6355..………………………………………
31,775
Release of working capital = $25,000 * 0.6355.…………………………
Net present value…………………………………………………………
b.
Profitability index = ($198,027 present value of inflows / $200,000 outflows) = 0.99
c.
Because the net present value is negative, the IRR will be lower than the cost of
capital.
d.
Payback period = 4.00 years
Initial investment
$(200,000)
Return in year 1 ……………………………………………
$ 40,000
Return in year 2 ……………………………………………
Return in year 3 ……………………………………………
Total return in 3 years ………………………………………
Return required in year 4 ($46,000 / $46,000 = 1.00 year).
Total return in 4.00 years……………………………………
e.
No. The ROI is expected to be lower than the cost of capital.
f.
What are the probabilities of exceeding the annual cash flow estimates? Is the 12%
cost of capital used by Sunset Beach, Inc., a conservative estimate of the firm’s long–
run cost of acquiring funds? If not, what is the firm’s incremental cost of borrowing?