38. Expected Return. Dr. Kevin Lenahan & Associates is a local optometrist considering two alternative
capital budgeting projects. Project A is an investment of $800,000 in a new office addition to showcase an
expanded selection of designer frames and contact lenses. Project B is an investment of $750,000 to upgrade
existing testing facilities. Relevant annual cash flow data for the two projects over their expected seven-year
lives are as follows:
Project A
Project B
Pr.
Cash Flow
Pr.
Cash Flow
0.50
$ 0
0.045
$ 0
0.50
500,000
0.910
200,000
0.045
400,000
A.
Calculate the expected value, standard deviation, and coefficient of variation of cash flows for each project.
B.
Calculate the risk-adjusted NPV for each project, using a 20% cost of capital for the more risky project and 15% for the less risky one.
Which project is preferred using the NPV criterion?
C.
Calculate the PI for each project, and rank them according to their PIs.
D.
Calculate the IRR for each project, and rank them according to their IRRs.
E.
Compare your answers to parts B, C, and D, and discuss any differences.
A.
Project A
= $150,000(PVIFA, n = 5, i = X%) – $450,000 = 0
IRR criterion.
despite being riskier, project B has an IRR that is no greater than the less risky project A.
39. Incremental Analysis. Cunningham’s Drug Store, a medium-sized drug store located in Milwaukee,
Wisconsin, is owned and operated by Richard Cunningham. Cunningham’s sells pharmaceuticals, cosmetics,
toiletries, magazines, and various novelties. Cunningham’s most recent annual net income statement is as
follows:
Sales revenue
$2,000,000
Total costs
Cost of goods sold
$1,250,000
Wages and salaries
100,000
Rent
120,000
Depreciation
100,000
Utilities
40,000
Miscellaneous
40,000
Total
1,650,000
Net profit before tax
$ 350,000
Cunningham’s sales and expenses have remained relatively constant in the past few years and are expected to continue unchanged in the near future.
To increase sales, Cunningham is considering using some floor space for a small soda fountain. Cunningham would operate the soda fountain for an
initial five-year period, and then reevaluate its profitability. The soda fountain requires an incremental investment of $25,000 to lease furniture,
equipment, utensils, and so on. This is the only capital investment required during the initial five-year period. At the end of that time, additional
capital would be required to continue operating the soda fountain and no capital would be recovered if it were dropped. The soda fountain is expected
to have sales of $125,000 and food and materials expenses of $30,000 per year. The soda fountain is also expected to increase wage and salary
expenses by 8% and utility expenses by 5%. Because the soda fountain will reduce the floor space available for display of other merchandise, sales of
nonsoda fountain items are expected to decline by 10%.
A.
Calculate net incremental cash flows for the soda fountain.
B.
Assume that Cunningham has the capital necessary to install the soda fountain and places a 12% before-tax opportunity cost on those
funds. Should the soda fountain be installed? Why or why not?
A.
The relevant annual cash flows from the proposed soda fountain are:
Incremental revenue:
$125,000
Increment cost:
Food and materials
$30,000
Wages and salaries ($100,000 ´ 0.08)
8,000
Utilities ($40,000 ´ 0.05)
2,000
Opportunity Cost: Profit contribution lost on regular
sales = 0.1($2,000,000 – $1,250,000)
75,000
Total incremental cost
115,000
Net incremental annual cash flow
$ 10,000
Incremental investment
$ 25,000
Therefore, 18% < IRRB < 20% (or exactly 18.58%).
40. Incremental Analysis. Warren Buffet is a medium-sized restaurant located in Omaha, Nebraska. Warren
Buffet currently offers elegant dining to luncheon and dining customers. The restaurant’s most recent annual net
income statement is as follows:
Sales revenue:
$5,000,000
Total costs:
Cost of goods sold
$1,500,000
Wages and salaries
2,500,000
Rent
180,000
Depreciation
250,000
Utilities
75,000
Miscellaneous
20,000
Total
4,525,000
Net profit before tax
$ 475,000
Luncheon and dining customer sales and expenses have remained relatively constant in the past few years and are expected to continue unchanged in
the near future. To increase sales, Warren Buffet is considering offering a new Sunday buffet brunch service. Warren Buffet would offer Sunday
brunch for an initial two-year period, and then reevaluate its profitability. Offering a Sunday brunch would require an initial outlay of $10,000 to
cover new buffet equipment and utensils. This is the only capital investment required during the initial two-year period. At the end of that time,
additional capital would be required to continue operation, and no capital would be recovered if the buffet were dropped. Buffet sales of $300,000 are
anticipated, and the share of revenues devoted to cost of goods sold expenses are expected to represent the same as previously. Wage and salary
expenses are expected to increase by 8% and utility expenses by 5%. No other incremental costs are expected.
A.
Calculate net incremental cash flows for the Sunday buffet.
B.
Assume that Warren Buffet’s has the necessary capital and places a 20% before-tax opportunity cost on those funds. Should the buffet
service be offered? Why or why not?
A.
The relevant annual cash flows from the proposed soda fountain are:
Incremental revenue:
$300,000
Increment cost:
Food and materials ($300,000 ´ 0.3)
$ 90,000
Wages and salaries ($2,500,000 ´ 0.08)
200,000
Utilities ($75,000 ´ 0.05)
3,750
Total incremental cost
293,750
Net incremental annual cash flow
$ 6,250
Incremental investment
$ 10,000
NPV
= (Incremental annual cash flow)(PVIFA, n = 5, i = 12%) – $25,000
= $10,000(3.6048) – $25,000
= $11,048
project.
41. Incremental Analysis. Grey’s Anatomy, Ltd., is contemplating opening a new retail outlet in a suburban
shopping mall. Projections for an initial 10-year period for the potential outlet are:
Sales revenue:
$2,000,000
Total costs:
Advertising
$500,000
Cost of goods sold
750,000
Wages and salaries
350,000
Rent
75,000
Depreciation
25,000
Utilities
75,000
Miscellaneous
25,000
Total
1,800,000
Projected Net profit before tax
$ 200,000
A.
Calculate the NPV for the proposed outlet assuming that an initial investment of $750,000 is required and the cost of capital is k=20%.
B.
Given the proposed outlet’s projected net profit before tax, calculate the maximum initial investment that could be justified when
k=20%.
A.
The NPV for the proposed outlet is calculated as follows:
NPV
= (Incremental annual cash flow)(PVIFA, n = 10, i = 20%)
– $750,000
= $200,000(4.1925) – $750,000
= $88,500
NPV
= (Incremental annual cash flow)(PVIFA, n = 2, i = 20%) – $10,000
= $6,250(1.5278) – $10,000
= $451.25 (a loss)
42. Cash Flow Analysis. The Gulf States Press, Inc., is analyzing the potential profitability of three printing
jobs put up for bid by the State Department of Transportation:
Job A
Job B
Job C
Projected winning bid (per unit)
$7.00
$9.00
$11.00
Direct cost per unit
$6.00
$6.00
$8.00
Annual unit sales volume
1,000,000
500,000
550,000
Annual distribution costs
$120,000
$90,000
$75,000
Investment required to produce annual
volume
$5,000,000
$4,500,000
$4,000,000
Assume that: (1) The company’s marginal state plus federal tax rate is 40%, (2) each job is expected to have a ten-year life, (3) the firm uses
straight-line depreciation, (4) the average cost of capital is 10%, (5) the jobs have the same risks as the firm’s other business, and (6) the company has
already spent $100,000 on developing the preceding data. This $100,000 has been capitalized and will be amortized over the life of the job chosen, if
any.
A.
What is the expected net cash flow each year? (Hint: Cash flow equals net profit after taxes plus depreciation and amortization charges.)
B.
What is the net present value of each job? On which job, if any, should Gulf States bid?
C.
Suppose that Gulf States’ primary business is quite cyclical, improving and declining with the economy, which Job B is expected to be
counter cyclical. Might this have any bearing on your decision?
Job A
Job B
Job C
Projected winning bid (per unit)
$7.00
$9.00
$11.00
Deduct direct cost per unit
– 6.00
– 6.00
– 8.00
Profit contribution per unit
$1.00
$3.00
$3.00
Times annual unit sales volume
´ 1,000,000
´ 500,000
´ 550,000
Profit contribution per year
$1,000,000
$1,500,000
$1,650,000
Deduct annual distribution costs
– 120,000
– 90,000
– 75,000
Cash flow before amortization, depreciation
and taxes
$880,000
$1,410,000
$1,575,000
Deduct amortization charges
– 10,000
– 10,000
– 10,000
Cash flow before depreciation and taxes
$870,000
$1,400,000
$1,565,000
Deduct depreciation
– $500,000
– $450,000
– $400,000
Cash flow before taxes
$370,000
$950,000
$1,165,000
Deduct taxes
– 148,000
– 380,000
– 466,000
Cash flow
$222,000
$570,000
$699,000
Add back depreciation plus amortization
510,000
460,000
410,000
Net annual cash flow
$732,000
$1,030,000
$1,109,000
Investment required to produce annual
volume
$5,000,000
$4,500,000
$4,000,000
Job cost development
$100,000
Job life (years)
Tax rate
40%
B.
The NPV calculations are:
43. Cash Flow Analysis. The Printing Press, Inc., (PPI) is analyzing the potential profitability of three printing
jobs put up for bid by a national textbook publisher:
Job A
Job B
Job C
Projected winning bid (per unit)
$25.00
$35.00
$50.00
Direct cost per unit
$5.00
$15.00
$10.00
Annual unit sales volume
10,000
20,000
7,500
Annual distribution costs
$150,000
$200,000
$50,000
Investment required to produce annual
volume
$500,000
$400,000
$250,000
Assume that: (1) The company’s marginal city-plus-state-plus-federal tax rate is 35%, (2) each job is expected to have a five-year life, (3) the firm
uses straight-line depreciation, (4) the average cost of capital is 15%, (5) the jobs have the same risks as the firm’s other business, and (6) the
company has already spent $10,000 on developing the preceding data. This $10,000 has been capitalized and will be amortized over the life of the
job chosen, if any.
A.
What is the expected net cash flow each year? (Hint: Cash flow equals net profit after taxes plus depreciation and amortization charges.)
B.
What is the net present value of each job? On which job, if any, should PPI bid?
C.
Suppose that PPI’s primary business is quite cyclical, improving and declining with the economy, which job B is expected to be counter
cyclical. Might this have any bearing on your decision?
Job A
Job B
Job C
Net annual cash flow
$732,000
$1,030,000
$1,109,000
Times PVIFA
´ 6.1446
´ 6.1446
´ 6.1446
Present value of annual net cash flows
$4,497,847
$6,328,938
$6,814,362
Deduct initial investment cost
– 5,000,000
– 4,500,000
– 4,000,000
Net present value (NPV)
-$502,153
$1,828,938
$2,814,361
Relevant discount rate
10%
Job life (years)
44. Cash Flow Analysis. Biometric Devices, Inc., is analyzing the potential profitability of three potential new
testing devices:
Product X
Product Y
Product Z
Projected market price (per unit)
$100.00
$250.00
$300.00
Direct cost per unit
$25.00
$50.00
$75.00
Annual unit sales volume
12,000
15,000
5,000
Annual selling expenses
$150,000
$250,000
$125,000
Investment required to produce annual
volume
$1,200,000
$900,000
$750,000
Job A
Job B
Job C
Projected winning bid (per unit)
$25.00
$35.00
$50.00
Deduct direct cost per unit
– 5.00
– 15.00
– 10.00
Profit contribution per unit
$20.00
$20.00
$40.00
Times annual unit sales volume
´ 10,000
´ 20,000
´ 7,500
Profit contribution per year
$200,000
$400,000
$300,000
Deduct annual distribution costs
– 150,000
– 200,000
– 50,000
Cash flow before amortization, depreciation
and taxes
$50,000
$200,000
$250,000
Deduct amortization charges
– 2,000
– 2,000
– 2,000
Cash flow before depreciation and taxes
$48,000
$198,000
$248,000
Deduct depreciation
– 100,000
– 80,000
– 50,000
Cash flow before taxes
-$52,000
$118,000
$198,000
Deduct taxes
– (18,200)
– 41,300
– 69,300
Cash flow
-$33,800
$76,700
$128,700
Add back depreciation plus amortization
102,000
82,000
52,000
Net annual cash flow
$68,200
$158,700
$180,700
Investment required to produce annual
volume
$500,000
$400,000
$250,000
Job cost development
$10,000
Job life (years)
5
Tax rate
35%
The NPV calculations are:
Net annual cash flow
$68,200
$158,700
$180,700
Times PVIFA
´ 3.3522
´ 3.3522
´ 3.3522
Present value of annual net cash flows
$228,620
$531,994
$605,742
Deduct initial investment cost
– 500,000
– 400,000
– 250,000
Net present value (NPV)
-$271,380
$131,994
$355,742
Relevant discount rate
15%
Job life (years)
5