Case Solutions
Corporate Finance
Ross, Westerfield, Jaffe, and Jordan
12th edition
01/02/2019
Prepared by:
Brad Jordan
University of Kentucky
Joe Smolira
Belmont University
CHAPTER 2
CASH FLOWS AT WARF COMPUTERS
The operating cash flow for the company is: (NOTE: All numbers are in thousands of dollars)
OCF = EBIT + Depreciation – Current taxes
OCF = $2,665 + 298 – 559
OCF = $2,404
To calculate the cash flow from assets, we need to find the capital spending and change in net
working capital. The capital spending for the year was:
Capital spending
Ending net fixed assets
– Beginning net fixed assets
+ Depreciation
Net capital spending
$4,322
3,356
298
$1,264
And the change in net working capital was:
Change in net working capital
Ending NWC
– Beginning NWC
Change in NWC
$1,361
1,097
$264
So, the cash flow from assets was:
Cash flow from assets
Operating cash flow
– Net capital spending
– Change in NWC
Cash flow from assets
$2,404
1,264
264
$876
The cash flow to creditors was:
Cash flow to creditors
Interest paid
– Net New Borrowing
Cash flow to Creditors
$164
36
$128
C-2 CASE SOLUTIONS
The cash flow to stockholders was:
Cash flow to stockholders
Dividends paid
– Net new equity raised
Cash flow to Stockholders
$688
– 60
$748
The accounting cash flow statement of cash flows for the year was:
Statement of Cash Flows
Operations
Net income
Depreciation
Deferred taxes
Changes in assets and liabilities
Accounts receivable
Inventories
Accounts payable
Accrued expenses
Other
Total cash flow from operations
$1,876
298
66
–57
26
41
–185
–16
$2,049
Investing activities
Acquisition of fixed assets
Sale of fixed assets
Total cash flow from investing activities
–$1,778
514
–$1,264
Financing activities
Retirement of debt
Proceeds of long-term debt
Dividends
Repurchase of stock
Proceeds from new stock issues
Total cash flow from financing activities
–$238
274
–688
–79
19
–$712
Change in cash (on balance sheet)
$73
C-3 CASE SOLUTIONS
Answers to questions
1. The firm had positive earnings in an accounting sense (NI > 0) and had positive cash flow from
operations and a positive cash flow from assets. The firm invested $264 in new net working capital
and $1,264 in new fixed assets. The firm was able to return $748 to its stockholders and $128 to
creditors.
2. The financial cash flows present a more accurate picture of the company since it accurately reflects
interest cash flows as a financing decision rather than an operating decision.
3. The expansion plans look like they are probably a good idea. The company was able to return a
significant amount of cash to its shareholders during the year, but a better use of these cash flows may
have been to retain them for the expansion. This decision will be discussed in more detail later in the
book.
CHAPTER 3
RATIOS AND FINANCIAL PLANNING AT
EAST COAST YACHTS
1.
The calculations for the ratios listed are:
Current ratio = $17,406,200/$22,754,600
Current ratio = .76 times
Quick ratio = ($17,406,200 – 7,290,100)/$22,754,600
Quick ratio = .44 times
Total asset turnover = $231,900,000/$129,035,500
Total asset turnover = 1.80 times
Inventory turnover = $170,157,000/$7,290,100
Inventory turnover = 23.34 times
Receivables turnover = $231,900,000/$6,501,900
Receivables turnover = 35.67 times
Total debt ratio = ($129,035,500 – 66,180,900)/$129,035,500
Total debt ratio = .49 times
Debt-equity ratio = ($22,754,600 + 40,100,000)/$66,180,900
Debt-equity ratio = .95 times
Equity multiplier = $129,035,500/$66,180,900
Equity multiplier = 1.95 times
Interest coverage = $26,464,900/$4,170,100
Interest coverage = 6.35 times
Profit margin = $17,612,892/$231,900,000
Profit margin = .0760, or 7.60%
Return on assets = $17,612,892/$129,035,500
Return on assets = .1365, or 13.65%
Return on equity = $17,612,892/$66,180,900
Return on equity = .2661, or 26.61%
CHAPTER 3 CASE C-5
2.
Regarding the liquidity ratios, East Coast Yachts’ current ratio is below the median industry ratio.
This implies the company has less liquidity than the industry in general. However, the current ratio
is above the lower quartile, so there are companies in the industry with lower liquidity than East
Coast Yachts. The company may have more predictable cash flows, or more access to short-term
borrowing.
The turnover ratios are all higher than the industry median; in fact, all three turnover ratios are
above the upper quartile. This may mean that East Coast Yachts is more efficient than the industry
in using its assets to generate sales.
The financial leverage ratios are all below the industry median but above the lower quartile. East
Coast Yachts generally has less debt than comparable companies but is still within the normal
range.
The profit margin for the company is about the same as the industry median, the ROA is slightly
higher than the industry median, and the ROE is well above the industry median. East Coast Yachts
seems to be performing well in the profitability area.
Overall, East Coast Yachts’ performance seems good, although the liquidity ratios indicate that a
closer look may be needed in this area.
C-6 CASE SOLUTIONS
Below is a list of possible reasons it may be good or bad that each ratio is higher or lower than the
industry. Note that the list is not exhaustive, but merely one possible explanation for each ratio.
Ratio
Current ratio
Quick ratio
Total asset turnover
Inventory turnover
Receivables turnover
Good
Better at managing current
accounts.
Better at managing current
accounts.
Better at utilizing assets.
Better at inventory management,
possibly due to better procedures.
Better at collecting receivables.
Total debt ratio
Less debt than industry median
means the company is less likely
to experience credit problems.
Debt-equity ratio
Less debt than industry median
means the company is less likely
to experience credit problems.
Equity multiplier
Less debt than industry median
means the company is less likely
to experience credit problems.
Interest coverage
Less debt than industry median
means the company is less likely
to experience credit problems.
Profit margin
The PM is slightly above the
industry median, so it is
performing better than many
peers.
Company is performing above
many of its peers.
Company is performing above
many of its peers.
ROA
ROE
Bad
May be having liquidity problems.
May be having liquidity problems.
Assets may be older and
depreciated, requiring extensive
investment soon.
Could be experiencing inventory
shortages.
May have credit terms that are too
strict. Decreasing receivables
turnover may increase sales.
Increasing the amount of debt can
increase shareholder returns.
Especially notice that it will
increase ROE.
Increasing the amount of debt can
increase shareholder returns.
Especially notice that it will
increase ROE.
Increasing the amount of debt can
increase shareholder returns.
Especially notice that it will
increase ROE.
Increasing the amount of debt can
increase shareholder returns.
Especially notice that it will
increase ROE.
May be able to better control
costs.
Assets may be old and depreciated
relative to industry.
Profit margin and EM could still
be increased, which would further
increase ROE.
If you created an Inventory/Current liabilities ratio, East Coast Yachts would have a ratio that is
lower than the industry median. The current ratio is below the industry median, while the quick
ratio is above the industry median. This implies that East Coast Yachts has less inventory to current
liabilities than the industry median. Because the cash ratio is lower than the industry median, East
Coast Yachts has less inventory than the industry median, but more accounts receivable.
CHAPTER 3 CASE C-7
3.
To calculate the sustainable growth rate, we first need to find the ROE and the retention ratio, so:
ROE = Net income/Total equity
ROE = $17,612,892/$66,180,900
ROE = .2661, or 26.61%
b = Addition to RE/Net income
b = $9,687,892/$17,612,892
b = .55, or 55%
So, the sustainable growth rate is:
Sustainable growth rate = (ROE × b)/[1 – (ROE × b)]
Sustainable growth rate = [.2661(.55)]/[1 – .2661(.55)]
Sustainable growth rate = .1715, or 17.15%
The sustainable growth rate is the growth rate the company can achieve with no external financing
while maintaining a constant debt-equity ratio.
At the sustainable growth rate, the pro forma statements next year will be:
Income statement
Sales
COGS
Other expenses
Depreciation
EBIT
Interest
Taxable income
Taxes (21%)
Net income
Dividends
Add to RE
$271,668,145
199,336,941
32,463,348
7,566,900
$32,300,957
4,170,100
$28,130,857
5,907,480
$22,223,377
$9,999,508
12,223,868
C-8 CASE SOLUTIONS
Balance sheet
Assets
Current Assets
Cash
Accounts rec.
Inventory
Total CA
$4,233,993
7,616,900
8,540,267
$20,391,160
Liabilities & Equity
Current Liabilities
Accounts Payable
$8,174,294
Notes Payable
18,482,454
Total CL
$26,656,749
Long-term debt
$40,100,000
$6,140,000
72,264,768
$78,404,768
Fixed assets
Net PP&E
$130,772,423
Shareholder Equity
Common stock
Retained earnings
Total Equity
Total Assets
$151,163,583
Total L&E
So, the EFN is:
EFN = Total assets – Total liabilities and equity
EFN = $151,163,583 – 145,161,517
EFN = $6,002,066
The ratios with these pro forma statements are:
Current ratio = $20,391,160/$26,656,749
Current ratio = .76 times
Quick ratio = ($20,391,160 – 8,540,267)/$26,656,749
Quick ratio = .44 times
Total asset turnover = $271,668,145/$151,163,583
Total asset turnover = 1.80 times
Inventory turnover = $199,336,941/$8,540,267
Inventory turnover = 23.34 times
Receivables turnover = $271,668,145/$7,616,900
Receivables turnover = 35.67 times
Total debt ratio = ($151,163,583 – 78,404,768)/$151,163,583
Total debt ratio = .48 times
Debt-equity ratio = ($26,656,749 + 40,100,000)/$78,404,768
Debt-equity ratio = .85 times
$145,161,517
CHAPTER 3 CASE C-9
Equity multiplier = $151,163,583/$78,404,768
Equity multiplier = 1.93 times
Interest coverage = $32,300,957/$4,170,100
Interest coverage = 7.75 times
Profit margin = $22,223,377/$271,668,145
Profit margin = .0818, or 8.18%
Return on assets = $22,223,377/$151,163,583
Return on assets = .1470, or 14.70%
Return on equity = $22,223,377/$78,404,768
Return on equity = .2834, or 28.34%
The only ratios that changed are the debt ratio, the interest coverage ratio, profit margin, return on
assets, and return on equity. The debt ratio changes because long-term debt is assumed to remain
fixed in the pro forma statements. The other ratios change slightly because interest and depreciation
are also assumed to remain constant.
4.
Pro forma financial statements for next year at a 20 percent growth rate are:
Income statement
Sales
COGS
Other expenses
Depreciation
EBIT
Interest
Taxable income
Taxes (21%)
Net income
Dividends
Add to RE
$278,280,000
204,188,400
33,253,440
7,566,900
$33,271,260
4,170,100
$29,101,160
6,111,244
$22,989,916
$10,344,416
12,645,500
C-10 CASE SOLUTIONS
Balance sheet
Assets
Current Assets
Cash
Accounts rec.
Inventory
Total CA
$4,337,040
7,802,280
8,748,120
$20,887,440
Liabilities & Equity
Current Liabilities
Accounts Payable
$8,373,240
Notes Payable
18,932,280
Total CL
$27,305,520
Long-term debt
$40,100,000
$6,140,000
72,686,400
$78,826,400
Fixed assets
Net PP&E
$133,955,160
Shareholder Equity
Common stock
Retained earnings
Total Equity
Total Assets
$154,842,600
Total L&E
$146,231,920
So, the EFN is:
EFN = Total assets – Total liabilities and equity
EFN = $154,842,600 – 146,231,920
EFN = $8,610,680
5.
Now we are assuming the company can only build in amounts of $30 million. We will assume that
the company will go ahead with the fixed asset acquisition. In this case, the pro forma financial
statement calculation will change slightly. To estimate the new depreciation charge, we will find the
current depreciation as a percentage of fixed assets, then apply this percentage to the new fixed
assets. The depreciation as a percentage of assets this year was:
Depreciation percentage = $7,566,900/$111,629,300
Depreciation percentage = .0678, or 6.78%
The new level of fixed assets with the $30 million purchase will be:
New fixed assets = $111,629,300 + 30,000,000 = $141,629,300
So, the pro forma depreciation as a percentage of sales will be:
Pro forma depreciation = .0678($141,629,300)
Pro forma depreciation = $9,600,479
CHAPTER 3 CASE C-11
We will use this amount in the pro forma income statement. So, the pro forma income statement will
be:
Income statement
Sales
COGS
Other expenses
Depreciation
EBIT
Interest
Taxable income
Taxes (21%)
Net income
$278,280,000
204,188,400
33,253,440
9,600,479
$31,237,681
4,170,100
$27,067,581
5,684,192
$21,383,389
Dividends
Add to RE
$9,621,552
11,761,837
The pro forma balance sheet will remain the same except for the fixed asset and equity accounts. The
fixed asset account will increase by $30 million, rather than the growth rate of sales.
Balance sheet
Assets
Current Assets
Cash
Accounts rec.
Inventory
Total CA
$4,337,040
7,802,280
8,748,120
$20,887,440
Liabilities & Equity
Current Liabilities
Accounts Payable
$8,373,240
Notes Payable
18,932,280
Total CL
$27,305,520
Long-term debt
$40,100,000
$6,140,000
71,802,737
$77,942,737
Fixed assets
Net PP&E
$141,629,300
Shareholder Equity
Common stock
Retained earnings
Total Equity
Total Assets
$162,516,740
Total L&E
$145,348,257
So, the EFN is:
EFN = Total assets – Total liabilities and equity
EFN = $162,516,740 – 145,348,257
EFN = $17,168,483
Since the fixed assets have increased at a faster percentage than sales, the capacity utilization for
next year will decrease.
CHAPTER 4
THE MBA DECISION
1.
Age is obviously an important factor. The younger an individual is, the more time there is for the
(hopefully) increased salary to offset the cost of the decision to return to school for an MBA. The
cost includes both the explicit costs such as tuition, as well as the opportunity cost of the lost salary.
2.
Perhaps the most important nonquantifiable factors would be whether he is married and if he has any
children. With a spouse and/or children, he may be less inclined to return for an MBA since his
family may be less amenable to the time and money constraints imposed by classes. Other factors
would include his willingness and desire to pursue an MBA, job satisfaction, and how important the
prestige of a job is to him, regardless of the salary.
3.
He has three choices: remain at his current job, pursue a Wilton MBA, or pursue a Mt. Perry MBA.
In this analysis, room and board costs are irrelevant since presumably they will be the same whether
he attends college or keeps his current job. We need to find the aftertax value of each, so:
Remain at current job:
Aftertax salary = $65,000(1 – .26)
Aftertax salary = $48,100
His salary will grow at 3 percent per year, so the present value of his aftertax salary is:
PV = C{[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}
PV = $48,100{[1/(.047 – .03)] – [1/(.047 – .03)] × [(1 + .03)/(1 + .047)] 40}
PV = $1,359,409.93
Wilton MBA:
Costs:
The direct costs will occur today and in one year, and include tuition, books and supplies, health
insurance, and the room and board increase. The total direct costs are:
PV of direct expenses = ($70,000 + 3,000 + 3,000 + 2,000)
+ ($70,000 + 3,000 + 3,000 + 2,000)/1.047
PV of direct expenses = $152,498.57
CHAPTER 4 CASE C-13
The financial benefits are the bonus to be paid in two years and the future salary.
PV of aftertax bonus paid in 2 years = $20,000(1 – .31)/1.0472
PV of aftertax bonus paid in 2 years = $12,588.84
Aftertax salary = $110,000(1 – .31)
Aftertax salary = $75,900
His salary will grow at 4 percent per year. We must also remember that he will now only work for 38
years, so the present value of his aftertax salary is:
PV = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}
PV = $75,900{[1/(.047 – .04)] – [1/(.047 – .04)] × [(1 + .04)/(1 + .047)] 38}
PV = $2,439,811.44
Since the first salary payment will be received three years from today, we need to discount this for
two years to find the value today, which will be:
PV = $2,439,811.44/1.0472
PV = $2,225,680.91
So, the total value of a Wilton MBA is:
Value = –$152,498.57 + 12,588.84 + 2,225,680.91
Value = $2,085,771.18
Mount Perry MBA:
The direct costs will occur today and include tuition, books and supplies, health insurance, and the
room and board increase. The total direct costs are:
Total direct costs = $85,000 + 4,500 + 3,000 + 2,000
Total direct costs = $94,500
Note, this is also the PV of the direct costs since they are all paid today.
The financial benefits are the bonus to be paid in one year and the future salary.
PV of aftertax bonus paid in 1 year = $18,000(1 – .29)/1.047
PV of aftertax bonus paid in 1 year = $12,206.30
His aftertax salary at his new job will be:
Aftertax salary = $92,000(1 – .29)
Aftertax salary = $65,320
C-14 CASE SOLUTIONS
His salary will grow at 3.5 percent per year. We must also remember that he will now only work for
39 years, so the present value of his aftertax salary is:
PV = C{[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}
PV = $65,320{[1/(.047 – .035)] – [1/(.047 – .035)] × [(1 + .035)/(1 + .047)] 39}
PV = $1,971,027.37
Since the first salary payment will be received two years from today, we need to discount this for one
year to find the value today, which will be:
PV = $1,971,027.37/1.047
PV = $1,882,547.63
So, the total value of a Mount Perry MBA is:
Value = –$94,500 + 12,206.30 + 1,882,547.63
Value = $1,800,253.93
4.
He is somewhat correct. Calculating the future value of each decision will result in the option with
the highest present value having the highest future value. Thus, a future value analysis will result in
the same decision. However, his statement that a future value analysis is the correct method is wrong
since a present value analysis will give the correct answer as well.
5.
To find the salary offer he would need to make the Wilton MBA as financially attractive as the as the
current job, we need to take the PV of his current job, add the costs of attending Wilton, and the PV
of the bonus on an aftertax basis. Note, this assumes that the signing bonus is constant. So, the
necessary PV to make the Wilton MBA the same as his current job will be:
PV = $1,359,409.93 + 152,498.57 – 12,588.84
PV = $1,499,319.66
This PV will make his current job exactly equal to the Wilton MBA on a financial basis. Since the
salary will not start for three years, we need to find the value in two years so that it is the present
value of a growing annuity. So:
Value in 2 years = $1,499,319.66(1.0472)
Value in 2 years = $1,643,567.70
Since his salary will still be a growing annuity, the aftertax salary needed is:
PV = C{[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t}
$1,643,567.70 = C{[1/(.047 – .04)] – [1/(.047 – .04)] × [(1 + .04)/(1 + .047)]38}
C = $51,129.68
This is the aftertax salary. So, the pretax salary must be:
Pretax salary = $51,129.68/(1 – .31)
Pretax salary = $74,100.99
6.
The cost (interest rate) of the decision depends on the riskiness of the use of the funds, not the source
of the funds. Therefore, whether he can pay cash or must borrow is irrelevant. This is an important
CHAPTER 4 CASE C-15
concept which will be discussed further when we discuss capital budgeting and the cost of capital in
later chapters.
CHAPTER 5
BULLOCK GOLD MINING
1.
An example spreadsheet is:
CHAPTER 4 CASE C-17
2.
Since the NPV of the mine is positive, the company should open the mine. We should note, it may be
advantageous to delay the mine opening because of real options, a topic covered in more detail in a
later chapter.
3.
There are many possible variations on the VBA code to calculate the payback period. Below is a
VBA program from http://www.vbaexpress.com/kb/getarticle.php?kb_id=252.
Function PAYBACK(invest, finflow)
Dim x As Double, v As Double
Dim c As Integer, i As Integer
x = Abs(invest)
i=1
c = finflow.Count
Do
x=x-v
v = finflow.Cells(i).Value
If x = v Then
PAYBACK = i
Exit Function
ElseIf x < v Then
P=i-1
Z = x/v
PAYBACK = P + Z
Exit Function
End If
i=i+1
Loop Until i > c
PAYBACK = "no payback"
End Function
CHAPTER 6, Case #1
BETHESDA MINING
To analyze this project, we must calculate the incremental cash flows generated by the project. Since
net working capital is built up ahead of sales, the initial cash flow depends in part on this cash
outflow. So, we will begin by calculating sales. Each year, the company will sell 500,000 tons under
contract, and the rest on the spot market. The total sales revenue is the price per ton under contract
times 500,000 tons, plus the spot market sales times the spot market price. The sales per year will be:
Year 1
$43,000,000
9,240,000
$52,240,000
Contract
Spot
Total
Year 2
$43,000,000
13,860,000
$56,860,000
Year 3
$43,000,000
17,710,000
$60,710,000
Year 4
$43,000,000
6,930,000
$49,930,000
The current aftertax value of the land is an opportunity cost. The initial outlay for net working
capital is the required net working capital percentage times Year 1 sales, or:
Initial net working capital = .05($52,240,000) = $2,612,000
So, the cash flow today is:
Equipment
Land
NWC
Total
–$95,000,000
–6,500,000
–2,612,000
–$104,112,000
Now we can calculate the OCF each year. The OCF is:
Sales
VC
FC
Dep.
EBT
Tax
NI
+ Dep.
OCF
Year 1
Year 2
Year 3
Year 4
$52,240,000 $56,860,000 $60,710,000 $49,930,000
19,220,000 21,080,000 22,630,000 18,290,000
4,100,000
4,100,000
4,100,000
4,100,000
13,575,500 23,265,500 16,615,500
11,865,500
$15,344,500 $8,414,500 $17,364,500 $15,674,500
3,836,125
2,103,625
4,341,125
3,918,625
$11,508,375 $6,310,875 $13,023,375 $11,755,875
13,575,500 23,265,500 16,615,500
11,865,500
$25,083,875 $29,576,375 $29,638,875 $23,621,375
Year 5
Year 6
$2,700,000
–$2,700,000
–675,000
–$2,025,000
0
–$2,025,000
–1,500,000
$1,500,000
0
$1,500,000
CHAPTER 6 CASE #1 C-19
Years 5 and 6 are of particular interest. Year 5 has an expense of $2.7 million to reclaim the land, and
it is the only expense for the year. Taxes that year are a credit, an assumption given in the case. In
Year 6, the charitable donation is irrelevant since it is required for the company to donate the land in
order to receive the necessary permits. However, the donation of the land does mean that the
company will receive a tax credit on the donation of the land, so this tax credit is relevant.
Next, we need to calculate the net working capital cash flow each year. NWC is 5 percent of next
year’s sales, so the NWC requirement each year is:
Beg. NWC
End NWC
NWC CF
Year 1
$2,612,000
2,843,000
–$231,000
Year 2
$2,843,000
3,035,500
–$192,500
Year 3
$3,035,500
2,496,500
$539,000
Year 4
$2,496,500
$2,496,500
The last cash flow we need to account for is the salvage value. The fact that the company is keeping
the equipment for another project is irrelevant. The aftertax salvage value of the equipment should
be used as the cost of equipment for the new project. In other words, the equipment could be sold
after this project. Keeping the equipment is an opportunity cost associated with that project. The
book value of the equipment is the original cost, minus the accumulated depreciation, or:
Book value of equipment = $95,000,000 – 13,575,500 – 23,265,500 – 16,615,500 – 11,865,500
Book value of equipment = $29,678,000
Since the market value of the equipment is $57 million, the equipment is sold at a gain to book
value, so the sale will incur the taxes of:
Taxes on sale of equipment = ($29,678,000 – 57,000,000)(.25)
Taxes on sale of equipment = –$6,830,500
And the aftertax salvage value of the equipment is:
Aftertax salvage value = $57,000,000 – 6,830,500
Aftertax salvage value = $50,169,500
C-20 CASE SOLUTIONS
So, the net cash flows each year, including the operating cash flow, net working capital, and aftertax
salvage value, are:
Time
0
1
2
3
4
5
6
Cash flow
–$104,112,000
24,852,875
29,383,875
30,177,875
76,287,375
–2,025,000
1,500,000
So, the capital budgeting analysis for the project is:
Payback period = 3 + $19,697,375/$76,287,375
Payback period = 3.26 years
PI = ($24,852,875/1.12 + $29,383,875/1.122 + $30,177,875/1.123 + $76,287,375/1.124
– $2,025,000/1.125 + $1,500,000/1.126)/$104,112,000
Profitability index = 1.1064
The NPV is:
NPV = –$104,112,000 + $24,852,875/1.12 + $29,383,875/1.122 + $30,177,875/1.123
+ $76,287,375/1.124 – $2,025,000/1.125 + $1,500,000/1.126
NPV = $11,075,640.82
The equation for IRR is:
0 = –$104,112,000 + $24,852,875/(1 + IRR) + $29,383,875/(1 + IRR)2 + $30,177,875/(1 + IRR)3
+ $76,287,375/(1 + IRR)4 – $2,025,000/(1 + IRR)5 + $1,500,000/(1 + IRR)6
Using a spreadsheet or financial calculator, the IRR for the project is:
IRR = 16.11%
Note, although the sign changes of the cash flows indicate up to three IRRs, a glance at the NPV
profile shows only one real IRR.
In the final analysis, the company should accept the project since the NPV is positive.
CHAPTER 6, Case #2
GOODWEEK TIRES, INC.
The cash flow to start the project is the $160 million equipment cost and the $9 million required for
net working capital, yielding a total cash outflow today of $169 million. The research and
development costs and the marketing test are sunk costs.
We can calculate the future cash flows on a nominal basis or a real basis. Since the depreciation is
given in nominal values, we will calculate the cash flows in nominal terms. The same solution can be
found using real cash flows. Since the price and variable costs increase by 1 percent, and the
inflation rate is 3.25 percent, the nominal growth in both variables is:
(1 + R) = (1 + r)(1 + h)
R = [(1.01)(1.0325)] – 1
R = .0428, or 4.28%
To analyze this project, we must calculate the incremental cash flows generated by the project. We
will calculate the real cash flows, although using nominal cash flows will result in the same NPV.
The sales of new automobiles will grow by 2.5 percent per year, and there are four tires per car.
Since the company expects to capture 11 percent of the market, the number of tires sold in the OEM
market will be:
Automobiles sold
Tires for automobiles sold
SuperTread tires sold
Year 1
6,200,000
24,800,000
2,728,000
Year 2
6,355,000
25,420,000
2,796,200
Year 3
6,513,875
26,055,500
2,866,105
Year 4
6,676,722
26,706,888
2,937,758
The number of tires sold in the replacement market will grow at 2 percent per year, and Goodweek
will capture 8 percent of the market. So, the number of tires sold in the replacement market will be:
Total tires sold in market
SuperTread tires sold
Year 1
32,000,000
2,560,000
Year 2
32,640,000
2,611,200
Year 3
33,292,800
2,663,424
Year 4
33,958,656
2,716,692
The tires will be sold in each market at a different price. The price will increase each year at the rate
calculated earlier, so the price each year will be:
OEM
Replacement
Year 1
$41.00
$62.00
Year 2
$42.76
$64.66
Year 3
$44.59
$67.42
Year 4
$46.50
$70.31
C-22 CASE SOLUTIONS
Multiplying the number of tires sold in each market by the respective price in that market, the
revenue each year will be:
OEM market
Replacement market
Total
Year 1
$111,848,000
158,720,000
$270,568,000
Year 2
$119,553,838
168,827,528
$288,381,366
Year 3
$127,790,574
179,578,718
$307,369,292
Year 4
$136,594,786
191,014,560
$327,609,346
Now we can calculate the incremental cash flows each year. We will calculate the nominal cash
flows. Doing so, we find:
Revenue
Variable costs
Mkt. and general costs
Depreciation
EBT
Tax
Net income
OCF
Year 1
$270,568,000
153,352,000
43,000,000
22,864,000
$51,352,000
11,810,960
$39,541,040
$62,405,040
Year 2
$288,381,366
163,530,185
44,397,500
39,184,000
$41,269,680
9,492,026
$31,777,654
$70,961,654
Year 3
$307,369,292
163,915,828
45,840,419
27,984,000
$69,629,045
16,014,680
$53,614,365
$81,598,365
Year 4
$327,609,346
167,627,528
47,330,232
19,984,000
$92,667,586
21,313,545
$71,354,041
$91,338,041
Net working capital is a percentage of sales, so the net working capital requirements will change
every year. The net working capital cash flows will be:
Beginning
Ending
NWC cash flow
Year 1
$9,000,000
40,585,200
–$31,585,200
Year 2
$40,585,200
43,257,205
–$2,672,005
Year 3
$43,257,205
46,105,394
–$2,848,189
Year 4
$46,105,394
$46,105,394
The book value of the equipment is the original cost minus the accumulated depreciation. The book
value of equipment each year will be:
Book value of equipment
Year 1
$137,136,000
Year 2
$97,952,000
Year 3
$69,968,000
Year 4
$49,984,000
Since the market value of the equipment is $54 million, the equipment is sold at a gain to book
value, so the sale will incur taxes of:
Taxes on sale of equipment = ($49,984,000 – 65,000,000)(.23) = –$3,453,680
And the aftertax salvage value of the equipment is:
Aftertax salvage value = $65,000,000 – 3,453,680
Aftertax salvage value = $61,546,320
CHAPTER 6 CASE #2 C-23
So, the net cash flows each year, including the operating cash flow, net working capital, and aftertax
salvage value, are:
Time
0
1
2
3
4
Cash flow
–$169,000,000
30,819,840
68,289,649
78,750,176
198,989,755
So, the payback period for the project is:
Payback period = 2 + $69,890,511/$78,750,176
Payback period = 2.89 years
The discounted cash flows are:
Time
0
1
2
3
4
Discounted cash flow
–$169,000,000
27,177,989
53,104,188
54,002,314
120,331,270
Discounted payback period = 3 + $34,715,509/$120,331,270
Discounted payback period = 3.29 years
The required return for the project is in nominal terms, so the profitability index is:
Profitability index = ($30,819,840/1.134 + $68,289,649/1.1342 + $78,750,176/1.1343 +
$198,989,755/1.1344)/$169,000,000
Profitability index = 1.507
The equation for IRR is:
0 = –$169,000,000 + $30,819,840/(1 + IRR) + $68,289,649/(1 + IRR)2 + $78,750,176/(1 + IRR)3
+ $198,989,755/(1 + IRR)4
Using a spreadsheet or financial calculator, the IRR for the project is:
IRR = 30.17%
NPV = –$169,000,000 + $30,819,840/1.134 + $68,289,649/1.1342 + $78,750,176/1.1343
+ $198,989,755/1.1344
NPV = $85,615,760.49
In the final analysis, the company should accept the project since the NPV is positive.
CHAPTER 7
BUNYAN LUMBER, LLC
The company is faced with the option of when to harvest the lumber. Whatever harvest cycle the
company chooses, it will follow that cycle in perpetuity. Since the forest was planted 20 years ago,
the options available in the case are 40-, 45-, 50-, and 55-year harvest cycles. No matter what harvest
cycle the company chooses, it will always thin the timber 20 years after harvests and replants. The
cash flows will grow at the inflation rate, so we can use the real or nominal cash flows. In this case,
it is simpler to use real cash flows, although nominal cash flows would yield the same result. So, the
real required return on the project is:
(1 + R) = (1 + r)(1 + h)
1.10 = (1 + r)(1.037)
r = .0608, or 6.08%
The conservation funds are expected to grow at a slower rate than inflation, so the real return for the
conservation fund will be:
(1 + R) = (1 + r)(1 + h)
1.10 = (1 + r)(1.032)
r = .0659, or 6.59%
The company will thin the forest today regardless of the harvest schedule, so this first thinning is not
an incremental cash flow, but future thinning is part of the analysis since the thinning schedule is
determined by the harvest schedule. The cash flow from the thinning process is:
Cash flow from thinning = Acres thinned × Cash flow per acre
Cash flow from thinning = 5,000($1,200)
Cash flow from thinning = $6,000,000
The real cost of the conservation fund is constant, but the expense will be tax deductible, so the
aftertax cost of the conservation fund will be:
Aftertax conservation fund cost = (1 – .21)($500,000)
Aftertax conservation fund cost = $395,000
For each analysis, the revenue and costs are:
Revenue = [∑ (% of grade)(harvest per acre)(value of board grade)](acres harvested)(1 – defect rate)
Tractor cost = (Cost MBF)(MBF per acre)(acres)
Road cost = (Cost MBF)(MBF per acre)(acres)
Sale preparation and administration = (Cost MBF)(MBF acre)(acres)
Excavator piling, broadcast burning, site preparation, and planting costs are the cost of each per acre
times the number of acres. These costs are the same no matter what the harvest schedule since they
are based on acres, not MBF.
CHAPTER 7 C-25
Now we can calculate the cash flow for each harvest schedule. One important note is that no
depreciation is given in the case. Since the harvest time is likely to be short, the assumption is that
no depreciation is attributable to the harvest. This implies that operating cash flow is equal to net
income. Now we can calculate the NPV of each harvest schedule. The NPV of each harvest schedule
is the NPV of the first harvest, the NPV of the thinning, the NPV of all future harvests, minus the
present value of the conservation fund costs.
40-year harvest schedule:
Revenue
Tractor cost
Road
Sale preparation & admin
Excavator piling
Broadcast burning
Site preparation
Planting costs
EBIT
Taxes
Net income (OCF)
$44,139,565
10,947,500
3,775,000
1,359,000
775,000
1,525,000
750,000
1,150,000
$23,858,065
5,010,194
$18,847,871
The PV of the first harvest in 20 years is:
PVFirst = $18,847,871(1 + .0608)20
PVFirst = $5,794,070
Thinning will also occur on a 40-year schedule, with the next thinning 40 years from today. The
effective 40-year interest rate for the project is:
40-year project interest rate = [(1 + .0608)40] – 1
40-year project interest rate = 958.17%
We also need the 40-year interest rate for the conservation fund, which will be:
40-year conservation interest rate = [(1 + .0659) 40] – 1
40-year conservation interest rate = 1,183.87%
Since we have the cash flows from each thinning, and the next thinning will occur in 40 years, we
can find the present value of future thinnings on this schedule, which will be:
PVThinning = $6,000,000/9.5817
PVThinning = $626,190.97
C-26 CASE SOLUTIONS
The operating cash flow from each harvest on the 40-year schedule is $18,847,871, so the present
value of the cash flows from the harvests are:
PVHarvest = [($18,847,871/9.5817)]/(1 + .0608)20
PVHarvest = $604,699.04
Now we can find the present value of the conservation fund deposits. The present value of these
deposits is at Year 20 is:
PVConservation = –$395,000 – $395,000/11.8387
PVConservation = –$428,365.28
And the value today is:
PVConservation = –$428,365.28/(1 + .0659)20
PVConservation = –$119,551.36
So, the NPV of a 40-year harvest schedule is:
NPV = $5,794,070 + 626,190.97 + 604,699.04 – 119,551.36
NPV = $6,905,408.59
45-year harvest schedule:
Revenue
Tractor cost
Road
Sale preparation & admin
Excavator piling
Broadcast burning
Site preparation
Planting costs
EBIT
Taxes
Net income (OCF)
$51,209,940
12,615,000
4,350,000
1,566,000
775,000
1,525,000
750,000
1,150,000
$28,478,940
5,980,577
$22,498,363
The PV of the first harvest in 25 years is:
PVFirst = $22,498,363/(1 + .0608)25
PVFirst = $5,149,946
Thinning will also occur on a 45-year schedule, with the next thinning 45 years from today. The
effective 45-year interest rate for the project is:
45-year project interest rate = [(1 + .0608)45] – 1
45-year project interest rate = 1,321.11%
CHAPTER 7 C-27
We also need the 45-year interest rate for the conservation fund, which will be:
45-year conservation interest rate = [(1 + .0659) 45] – 1
45-year conservation interest rate = 1,666.38%
Since we have the cash flows from each thinning, and the next thinning will occur in 45 years, we
can find the present value of future thinnings on this schedule, which will be:
PVThinning = $6,000,000/13.2111
PVThinning = $454,164.56
The operating cash flow from each harvest on the 45-year schedule is $22,498,363, so the present
value of the cash flows from the harvests are:
PVHarvest = [($22,498,363/13.21111)]/(1 + .0608)25
PVHarvest = $389,820.51
Now we can find the present value of the conservation fund deposits. The present value of these
deposits at Year 25 is:
PVConservation = –$395,000 – $395,000/16.6638
PVConservation = –$418,704.06
And the value today is:
PVConservation = –$418,704.06/(1 + .0659)25
PVConservation = –$84,934.18
So, the NPV of a 45-year harvest schedule is:
NPV = $5,149,946 + 454,164.56 + 389,820.51 – 84,934.18
NPV = $5,908,997.10
50-year harvest schedule:
Revenue
Tractor cost
Road
Sale preparation & admin
Excavator piling
Broadcast burning
Site preparation
Planting costs
EBIT
Taxes
Net income (OCF)
$53,659,515
13,195,000
4,550,000
1,638,000
775,000
1,525,000
750,000
1,150,000
$30,076,515
6,316,068
$23,760,447
C-28 CASE SOLUTIONS
The PV of the first harvest in 30 years is:
PVFirst = $23,760,447/(1 + .0608)30
PVFirst = $4,049,830
Thinning will also occur on a 50-year schedule, with the next thinning 50 years from today. The
effective 50-year interest rate for the project is:
50-year project interest rate = [(1 + .0608)50] – 1
50-year project interest rate = 1,808.52%
We also need the 50-year interest rate for the conservation fund, which will be:
50-year conservation interest rate = [(1 + .0659) 50] – 1
50-year conservation interest rate = 2,330.24%
Since we have the cash flows from each thinning, and the next thinning will occur in 50 years, we
can find the present value of future thinnings on this schedule, which will be:
PVThinning = $6,000,000/18.0852
PVThinning = $331,763.21
The operating cash flow from each harvest on the 50-year schedule is $23,760,447, so the present
value of the cash flows from the harvests are:
PVHarvest = [($23,760,447/18.0852]/(1 + .0608)30
PVHarvest = $223,930.74
Now we can find the present value of the conservation fund deposits. The present value of these
deposits at Year 30 is:
PVConservation = –$395,000 – $395,000/23.3024
PVConservation = –$411,951.03
And the value today is:
PVConservation = –$411,951.03/(1 + .0659)30
PVConservation = –$60,737.37
So, the NPV of a 50-year harvest schedule is:
NPV = $4,049,830 + 331,763.21 + 223,930.74 – 60,737.37
NPV = $4,544,786.10
CHAPTER 7 C-29
55-year harvest schedule:
Revenue
Tractor cost
Road
Sale preparation & admin
Excavator piling
Broadcast burning
Site preparation
Planting costs
EBIT
Taxes
Net income (OCF)
$55,808,629
13,702,500
4,725,000
1,701,000
775,000
1,525,000
750,000
1,150,000
$31,480,129
6,610,827
$24,869,302
The PV of the first harvest in 35 years is:
PVFirst = $24,869,302/(1 + .0608)35
PVFirst = $3,156,284
Thinning will also occur on a 55-year schedule, with the next thinning 55 years from today. The
effective 55-year interest rate for the project is:
55-year project interest rate = [(1 + .0608)55] – 1
55-year project interest rate = 2,463.10%
We also need the 55-year interest rate for the conservation fund, which will be:
55-year conservation interest rate = [(1 + .0659) 55] – 1
55-year conservation interest rate = 3,243.60%
Since we have the cash flows from each thinning, and the next thinning will occur in 55 years, we
can find the present value of future thinnings on this schedule, which will be:
PVThinning = $6,000,000/24.6310
PVThinning = $243,595.16
The operating cash flow from each harvest on the 55-year schedule is $24,869,302, so the present
value of the cash flows from the harvests are:
PVHarvest = [($24,869,302/24.6310]/(1 + .0608)35
PVHarvest = $128,142.59
Now we can find the present value of the conservation fund deposits. The present value of these
deposits is at Year 35 is:
PVConservation = –$395,000 – $395,000/32.4360
PVConservation = –$407,177.83
C-30 CASE SOLUTIONS
And the value today is:
PVConservation = –$407,177.83/(1 + .0659)35
PVConservation = –$43,634.45
So, the NPV of a 55-year harvest schedule is:
NPV = $3,156,284 + 243,595.16 + 128,142.59 – 43,634.45
NPV = $3,484,387.37
The company should use a 40-year harvest schedule since it has the highest NPV. Notice that when
the NPV began to decline, it continued declining. This is expected since the growth in the trees
increases at a decreasing rate. So, once we reach a point where the increased growth cannot
overcome the increased effects of compounding, harvesting should take place. There is no point
further in the future which will provide a higher NPV.
CHAPTER 8
FINANCING EAST COAST YACHT’S
EXPANSION PLANS WITH A BOND ISSUE
1.
A rule of thumb with bond provisions is to determine who the provisions benefit. If the company
benefits, the bond will have a higher coupon rate. If the bondholders benefit, the bond will have a
lower coupon rate.
a.
A bond with collateral will have a lower coupon rate. Bondholders have the claim on the collateral,
even in bankruptcy. Collateral provides an asset that bondholders can claim, which lowers their
risk in default. The downside of collateral is that the company generally cannot sell the asset used
as collateral, and they will generally have to keep the asset in good working order.
b.
The more senior the bond is, the lower the coupon rate. Senior bonds get full payment in
bankruptcy proceedings before subordinated bonds receive any payment. A potential problem may
arise in that the bond covenant may restrict the company from issuing any future bonds senior to
the current bonds.
c.
A sinking fund will reduce the coupon rate because it is a partial guarantee to bondholders. The
problem with a sinking fund is that the company must make the interim payments into a sinking
fund or face default. This means the company must be able to generate these cash flows.
d.
A provision with specific call dates and prices would increase the coupon rate. The call provision
would only be used when it is to the company’s advantage, thus the bondholders’ disadvantage.
The downside is the higher coupon rate. The company benefits by being able to refinance at a
lower rate if interest rates fall significantly, that is, enough to offset the call provision cost.
e.
A deferred call would reduce the coupon rate relative to a call provision without a deferred call.
The bond will still have a higher rate relative to a plain vanilla bond. The deferred call means that
the company cannot call the bond for a specified period. This offers the bondholders protection for
this period. The disadvantage of a deferred call is that the company cannot call the bond during the
call protection period. Interest rates could potentially fall to the point where it would be beneficial
for the company to call the bond, yet the company is unable to do so.
f.
A make-whole call provision should lower the coupon rate in comparison to a call provision with
specific dates since the make-whole call repays the bondholder the present value of the future cash
flows. However, a make-whole call provision should not affect the coupon rate in comparison to a
plain vanilla bond. Since the bondholders are made whole, they should be indifferent between a
plain vanilla bond and a make-whole bond. If a bond with a make-whole provision is called,
bondholders receive the market value of the bond, which they can reinvest in another bond with
similar characteristics. If we compare this to a bond with a specific call price, investors rarely
receive the full market value of the future cash flows.
g.
A positive covenant would reduce the coupon rate. The presence of positive covenants protects
bondholders by forcing the company to undertake actions that benefit bondholders. Examples of
C-32 CASE SOLUTIONS
positive covenants would be: the company must maintain audited financial statements; the
company must maintain a minimum specified level of working capital or a minimum specified
current ratio; the company must maintain any collateral in good working order. The negative side
of positive covenants is that the company is restricted in its actions. The positive covenant may
force the company into actions in the future that it would rather not undertake.
2.
h.
A negative covenant would reduce the coupon rate. The presence of negative covenants protects
bondholders from actions by the company that would harm the bondholders. Remember, the goal
of a corporation is to maximize shareholder wealth. This says nothing about bondholders.
Examples of negative covenants would be: the company cannot increase dividends, or, at least, it
cannot increase them beyond a specified level; the company cannot issue new bonds senior to the
current bond issue; the company cannot sell any collateral. The downside of negative covenants is
the restriction of the company’s actions.
i.
Even though the company is not public, a conversion feature would likely lower the coupon rate.
The conversion feature would permit bondholders to benefit if the company does well and also
goes public. The downside is that the company may be selling equity at a discounted price.
j.
The downside of a floating rate coupon is that if interest rates rise, the company pays a higher
interest rate. However, if interest rates fall, the company pays a lower interest rate.
Since the coupon bonds will have a coupon rate equal to the YTM, they will sell at par. So, the number
of coupon bonds to sell will be: (NOTE: The text has a typo. The coupon rate on the coupon bonds
should be 7.5 percent.)
Coupon bonds to sell = $50,000,000/$1,000 = 50,000
The price of the 20-year, zero coupon bond when it is issued will be:
Zero coupon price = $1,000/1.037540 = $229.34
So, the number of zero coupon bonds the company will need to sell is:
Zero coupon bonds to sell = $50,000,000/$229.34 = 218,016
3.
At maturity, the principal payment for the coupon bonds will be:
Coupon bond principal payment at maturity = 50,000($1,000) = $50,000,000
The principal payment for the zero coupon bonds at maturity will be:
Zero coupon bond payment at maturity = 218,016($1,000) = $218,016,000
CHAPTER 8 C-33
4.
One of the main considerations is timing of the cash flows. The annual coupon payment on the coupon
bonds will be:
Annual coupon bond payments = 50,000($1,000)(.075) = $3,750,000
Since the interest payments are tax deductible, the aftertax cash flow from the interest payments will be:
Aftertax coupon payments = $3,750,000(1 – .21) = $2,962,500
Even though interest payments are not actually made each year, the implied interest on the zero coupon
bonds is tax deductible. The value of the zero coupon bonds next year will be:
Value of zero in one year = $1,000/1.037538 = $246.86
So, the growth on the zero coupon bond was:
Zero coupon growth = $246.86 – 229.34 = $17.52
This increase in value is tax deductible, so it reduces taxes even though there is no cash flow for interest
payments. So, there is a positive cash flow created next year in the amount of:
Zero cash flow = 218,016($17.52)(.21) = $802,157.54
This cash flow will increase each year since the value of the zero coupon bond will increase by a greater
dollar amount each year.
5.
If the Treasury rate is 4.80 percent, the make-whole call price in seven years is:
P = $37.50({1 – [1/(1 + .026)]26}/.026) + $1,000[1/(1 + .026)26]
P = $1,215.38
And, if the Treasury rate is 8.20 percent, the make-whole call price in seven years is:
P = $37.50({1 – [1/(1 + .043)]26}/.043) + $1,000[1/(1 + .043)26]
P = $914.90
6.
The investor is not necessarily made completely whole with the make-whole call provision but is made
close to whole. Assume a company issues a bond with a make-whole call of the Treasury rate plus .5
percent. Further assume this is the correct average spread for the company’s bond over the life of the
bond. Although the spread is correct on average, it is not correct at every specific time. The spread over
the Treasury rate varies over the life of the bond and is higher when the bond has a longer time to
maturity. To see this, consider, at the extreme that the spread for any bond above the Treasury yield at
maturity is zero. So, if the bond is called early in its life, the spread above the Treasury is likely to be
too low. This means the investor is more than made whole. If the bond is called late in its life, the spread
is too high. This means the interest rate used to calculate the present value of the cash flows is too high,
which results in a lower present value. Thus, the bondholder is made less than whole. In practical terms,
this difference is likely to be small, and it will almost always result in a higher price paid to the
bondholder when compared to a traditional call feature.
C-34 CASE SOLUTIONS
7.
There is no definitive answer to which type of bond the company should issue. If the intermediate cash
flows for the coupon payments will be difficult, a zero coupon bond is likely to be the best solution.
However, the zero coupon bond will require a larger payment at maturity.
As for the type of call provision, a make-whole call provision is generally better for bondholders,
therefore the coupon rate of the bond will likely be lower to be able to sell the bond at par value. Again,
there is a tradeoff.
CHAPTER 9
STOCK VALUATION AT RAGAN ENGINES
1.
The total dividends paid by the company were $640,000. Since there are 300,000 shares outstanding, the
total earnings for the company were:
Total earnings = 300,000($5.35) = $1,605,000
This means the payout ratio was:
Payout ratio = $640,000/$1,605,000 = .3988, or 39.88%
So, the retention ratio was:
Retention ratio = 1 – .3988 = .6012, or 60.12%
Using the retention ratio, the company’s growth rate is:
g = ROE × b = .21(.6012) = .1263, or 12.63%
Now we can value the company using the entire dividend payment. The total value of the company’s
equity under these assumptions is:
Total equity value = D1/(R – g)
Total equity value = $640,000(1.1263)/(.18 – .1263)
Total equity value = $13,413,286.96
So, the value per share is:
Value per share = $13,413,286.96/300,000
Value per share = $44.71
2.
Since Nautilus Marine Engines had a write-off which affected its earnings per share, we need to
recalculate the industry EPS. So, the industry EPS is:
Industry EPS = ($1.19 + 1.26 + 2.07)/3 = $1.51
Using this industry EPS, the industry payout ratio is:
Industry payout ratio = $.44/$1.51 = .2898, or 28.98%
C-36 CASE SOLUTIONS
So, the industry retention ratio is
Industry retention ratio = 1 – .2898 = .7102, or 71.02%
This means the industry growth rate is:
Industry g = .11(.7102) = .0781, or 7.81%
The company will continue to grow at its current pace for five years before slowing to the industry
growth rate. So, the total dividends for each of the next six years will be:
D1 = $640,000.00(1.1263) = $720,807.48
D2 = $720,807.48(1.1263) = $811,817.84
D3 = $811,817.84(1.1263) = $914,319.33
D4 = $914,319.33(1.1263) = $1,029,762.82
D5 = $1,029,762.82(1.1263) = $1,159,782.41
D6 = $1,159,782.41(1.0781) = $1,250,384.00
The total value of the stock in Year 5 with the industry required return will be:
Stock value in Year 5 = $1,250,384.00/(.15 – .0781) = $17,395,308.29
This means the total value of the stock today is:
Value of stock today = $720,807.48/1.15 + $811,817.84/1.152 + $914,319.33/1.153 +
$1,029,762.82/1.154 + ($1,159,782.41 + 17,395,308.29)/1.155
Value of stock today = $11,655,749.48
And the value per share of the stock today is:
Value per share = $11,655,749.48/300,000
Value per share = $38.85
3.
Using the revised industry EPS, the industry PE ratio is:
Industry PE = $18.08/$1.51 = 12.00
Using the original stock price assumption, Ragan’s PE ratio is:
Ragan PE (original assumptions) = $44.71/$5.35 = 8.36
Using the revised assumptions, Ragan’s PE = $38.85/$5.35 = 7.26
Obviously, Ragan’s PE is lower than the industry average. Given that the growth rate for the company is
higher than the industry, this is unexpected. The reason is that the company pays out a higher dividend
than the industry.
CHAPTER 9 CASE C-37
4.
Here, we must make an assumption. We have two estimates of the required return. Since we are assuming
the growth rate follows the growth rate assumption in Question 2, we will use the industry average
required return assumed in that question as well. As a cash cow, the total earnings of the company which
would be paid out as a dividend are:
Total earnings = 2(150,000 shares)($5.35)
Total earnings = $1,605,000
So, the value of Ragan as a cash cow is:
Cash cow value = $1,605,000/.15 = $10,700,000
The total stock value with growth from Question 2 is $11,655,749.48, so the percentage of the value of
the company not attributable to growth opportunities is:
Percentage of value not attributable to growth opportunities = $10,700,000/$11,655,749.48 = .9180
So, the percentage of the company’s value attributable to growth opportunities is:
Percentage of value attributable to growth opportunities = 1 – .9180 = .0820, or 8.20%
5.
Again, we will assume the results in Question 2 are correct. The growth rate of the company we
calculated in this question was the industry growth rate of 7.81 percent. Since the growth rate is:
g = ROE × b
If we assume the payout ratio remains constant, the ROE is:
.0781 = ROE(.6012)
ROE = .1299, or 12.99%
6.
The most obvious solution is to retain more of the company’s earnings and invest in profitable
opportunities. This strategy will not work if the return on the company’s investment is lower than the
required return on the company’s stock.
CHAPTER 10
A JOB AT EAST COAST YACHTS
1.
The biggest advantage the mutual funds have is instant diversification. The mutual funds have
multiple assets in the portfolio.
2.
Both the APR and EAR are infinite. The match is instantaneous, so the number of periods in a year is
infinite.
3.
The advantage of the actively managed fund is the possibility of outperforming the market, which
the fund has done on average over the past ten years. The major disadvantage is the likelihood of
underperforming the market. In general, most mutual funds do not outperform the market for an
extended period of time and finding the funds that will outperform the market in the future
beforehand is a daunting task. One factor that makes outperforming the market even more difficult is
the management fee charged by the fund.
4.
The returns are the most volatile for the small cap fund because the stocks in this fund are the
riskiest. This does not imply the fund is bad, just that the risk is higher and, therefore, the expected
return is higher. You would want to invest in this fund if your risk tolerance is such that you are
willing to take on the additional risk in expectation of a higher return.
The higher expenses of the fund are expected. In general, small cap funds have higher expenses, in
large part due to the greater cost of running the fund, including researching smaller stocks.
5.
The Sharpe ratio for each of the mutual funds and the company stocks are:
Bledsoe S&P 500 Index Fund = (11.04% – 3.2)/18.45% = .4249
Bledsoe Small-Cap Fund = (16.14% – 3.2)/29.18% = .4435
Bledsoe Large Company Stock Fund = (12.15% – 3.2)/24.43% = .3664
Bledsoe Bond Fund = (6.93% – 3.2)/9.96% = .3745
East Coast Yachts Stock = (16% – 3.2)/58% = .2207
The Sharpe ratio is most applicable for a diversified portfolio and is least applicable for the company
stock.
CHAPTER 10 CASE C-39
6.
This is a very open-ended question. The asset allocation depends on the risk tolerance of the
individual. However, most students will be young, so in this case, the portfolio allocation should be
more heavily weighted toward stocks.
In any case, there should be little, if any, money allocated to the company stock. The principle of
diversification indicates that an individual should hold a diversified portfolio. Investing heavily in
company stock does not create a diversified portfolio. This is especially true since income comes
from the company as well. If times get bad for the company, employees face layoffs, or reduced
work hours. So, not only does the investment perform poorly, but income may be reduced as well.
We only must look at employees of Enron or WorldCom to see the potential for problems with
investing in company stock. At most, 5 to 10 percent of the portfolio should be allocated to company
stock.
Age is a determinant in the decision. Older individuals should be less heavily weighted toward
stocks. A commonly used rule of thumb is that an individual should invest 100 minus their age in
stocks. Unfortunately, this rule of thumb tends to result in an underinvestment in stocks.
CHAPTER 11
A JOB AT EAST COAST YACHTS,
PART 2
1.
There should be little, if any, money allocated to the company stock. The principle of diversification
indicates that an individual should hold a diversified portfolio. Investing heavily in company stock
does not create a diversified portfolio. This is especially true since income also comes from the
company. If times get bad for the company, employees face layoffs, or reduced work hours. So, not
only does the investment perform poorly, but income may be reduced as well. We only have to look
at employees of Enron or WorldCom to see the potential for problems with investing in company
stock. At most, 5 to 10 percent of the portfolio should be allocated to company stock.
2.
This is not the portfolio with the least risk. By adding stocks, a riskier asset, the overall risk of the
portfolio will decline. This will be demonstrated in the next questions.
3.
We can use the equations for the expected return of the portfolio, and the portfolio standard
deviation, that is:
E(RP) = XEE(RE) + XDE(RD)
P = (X
2
E

2
E
+X
2
D

2
D
+ 2XEXDEDD,E)1/2
Using these equations and equity portfolio weights from zero to 100 percent at intervals of 10
percent, we get the following portfolio expected returns and standard deviations:
Weight of stock fund
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Portfolio E(R)
6.93%
7.45%
7.97%
8.50%
9.02%
9.54%
10.06%
10.58%
11.11%
11.63%
12.15%
Portfolio standard
deviation
9.9600%
9.6380%
9.9520%
10.8468%
12.1952%
13.8656%
15.7559%
17.7961%
19.9403%
22.1583%
24.4300%
CHAPTER 11 CASE C-41
The graph of the opportunity set of feasible portfolios will look like the following:
Investment Opportunity Set
10%
9%
Portfolio Expected Return
8%
7%
6%
5%
4%
3%
2%
1%
0%
8%
10%
12%
14%
16%
18%
20%
22%
24%
26%
Portfolio Standard Deviation
4.
Now we can use Solver to maximize this expression by changing the weight of the equity input cell.
The constraint is that the standard deviation of the portfolio is equal to the standard deviation of the
bond fund. Using Solver, the weight of the large cap stock fund and bond fund in this portfolio is:
XE = .2013
XD = .7987
So, the expected return and standard deviation of this portfolio are:
E(R) = .2013(.1215) + .7987(.0693)
E(R) = .0798, or 7.98%
 = [.20132(.2443)2 + .79872(.0996)2 + 2(.2013)(.7987)(.2443)(.0996)(.15)]1/2
 = .0996, or 9.96%
This is the exact same standard deviation as the bond fund, but the expected return is about one-half
percent higher.
C-42 CASE SOLUTIONS
5.
To find the weights of each asset in the minimum variance portfolio, we begin with the equation for
the variance of the portfolio. Using S to represent the large company fund and B to represent the
bond fund, the variance of a portfolio of two assets equals:

2
P
=X
2
S

2
S
+X
2
B

2
B
+ 2XSXBS,B
Since the weights of the assets must sum to one, we can write the variance of the portfolio as:

2
P
=X
2
S

2
S
+ (1 – XS)2
2
B
+ 2XS(1 – XS)SBS,B
To find the minimum for any function, we find the derivative and set the derivative equal to zero.
Finding the derivative of the variance function, setting the derivative equal to zero, and solving for
the weight of the stock fund, we find:
dσp2/dXS = 2XS
2
S
– 2(1 – XS )σB2 + 2σSσB S,B – 4XSσSσBS,B = 0
Solve for XS to get:
XS = (
2
B
– SBS,B)/(
2
S
+
2
B
– 2SBS,B)
Using this expression, we find the weight of the stock fund, must be:
XS = [.09962 – (.2443)(.0996)(.15)]/[.24432 + .09962 – 2(.2443)(.0996)(.15)]
XS = .1006
This implies the weight of the bond fund is:
XB = 1 – XS
XB = 1 – .1006
XB = .8994
The expected return of this portfolio is:
E(R) = .1006(.1215) + .8994(.0693)
E(R) = .07455, or 7.46%
The variance of the portfolio is:



2
P
2
P
2
P
=X
2
S

2
S
+X
2
B

2
B
+ 2XSXBSBS,B
= (.10062)(.24432) + (.89942)(.09962) + 2(.1006)(.8994)(.2443)(.0996)(.15)
= .009289
And the standard deviation is:
 = .0092891/2
CHAPTER 11 CASE C-43
 = .0964, or 9.64%
With these returns and variances, the minimum variance portfolio is important because no investor
would ever hold a portfolio with a greater weight in bonds. If an investor increases the weight of
bonds in the portfolio, the risk of the portfolio increases and the expected return decreases. The
result is illustrated in Question 4.
6.
We can find the Sharpe optimal portfolio by using Solver. To use Solver, we input the Sharpe ratio in
a cell. The Sharpe ratio is:
Sharpe ratio =
E (R )− Rf
σP
We also need to recognize that the weight of debt in the portfolio is one minus the weight of equity.
Substituting the equations for the expected return of the portfolio and the standard deviation of the
portfolio, we get:
Sharpe ratio =
X E E( R E )+(1 −X E ) E( R D )− Rf
2 2
2 2
( X E σ E +(1 −X E ) σ D+ 2 X E (1− X E )σ E σ D
1/2
ρE,D )
Now we can use Solver to maximize this expression by changing the weight of equity input cell.
Doing so, we find the weight of equity in the Sharpe optimal portfolio is 28.35 percent.
This question can also be solved directly. The goal is to maximize the Sharpe ratio, so we can use the
expression for the Sharpe ratio, set the derivative equal to zero, and solve for the weight of equity (or
debt). Doing so, the resulting expression for the weight of equity in the Sharpe optimal portfolio is:
[ E( R E )− R f ]σ 2D−[ E (R D )− R f ]σ E σ D ρE,D
XE =
[ E (R E )− R f ]σ 2D +[ E ( R D )− R f ]σ 2E−[ E( R )E − R f + E( R )D − R f ]σ E σ D ρE,D
Using this equation, we find the weight of equity in the Sharpe optimal portfolio is:
XE =
[.1215  .032].0996 2  [.0693  .0320](.2443)(.0996)(.15)
[.1215  .0320].09642  [.1215  .032].24432  [.1215  .0320  .0693  .0320](.2443)(.0996)(.15)
XE = .2835
and the weight of debt is:
XD = 1 – .2835
XD = .7165
C-44 CASE SOLUTIONS
So, the expected return and standard deviation of the Sharpe optimal portfolio is:
E(R) = .2835(.1215) + .7165(.0693)
E(R) = .0841, or 8.41%
 = [.28352(.2443)2 + .71652(.0996)2 + 2(.2835)(.2443)(.7165)(.0996)(.15)]1/2
 = .1066, or 10.66%
The Sharpe ratio of the Sharpe optimal portfolio is:
.0841  .0320
.1066
Sharpe ratio =
Sharpe ratio = .4885
The Sharpe optimal portfolio is the best risky portfolio for all investors because it delivers a greater
reward-to-risk ratio than any other portfolio. If a line is drawn from the risk-free rate to the Sharpe
optimal portfolio, it shows the best combination of portfolios available to any investor. Investors can
change the level of risk by altering the percentage of their investment in the risk-free asset and the
Sharpe optimal portfolio. This line is the Security Market Line.
CHAPTER 12
THE FAMA-FRENCH MULTI-FACTOR
MODEL AND MUTUAL FUND RETURNS
NOTE: The example below shows the results for returns between October 2010 and September
2015. The actual answer to the case will change based on current market conditions.
1.
For a large-company stock fund, we would expect the beta for the market risk premium to be near
one since large company returns account for a large part of the total market return on a market-value
basis. We would expect the betas for the SMB and HML risk factors to be low, and possibly
negative, since large company stock returns are not highly related to small company stock returns
and large company stocks tend to be more oriented toward value stocks.
2.
Fidelity Magellan:
Regression Statistics
0.97626239
Multiple R
4
0.95308826
R Square
1
Adjusted R
0.95057513
Square
3
0.00871456
Standard Error
3
Observations
60
ANOVA
df
Regression
Residual
Total
Intercept
Mkt-RF
SMB
HML
3
56
59
SS
0.08640
0.00425
0.09066
Coefficients
-0.00216
1.08816
0.06291
-0.13206
Standard
Error
0.00120
0.03546
0.05736
0.06311
MS
0.02880
0.00008
F
379.24369
t Stat
-1.79745
30.69090
1.09670
-2.09264
P-value
0.07766
0.00000
0.27747
0.04092
Significanc
eF
3.6948E-37
C-46 CASE SOLUTIONS
Fidelity Low-Priced Stock Fund:
Regression Statistics
Multiple R
0.97094
R Square
0.94273
Adjusted R
Square
0.93967
Standard Error
0.00868
Observations
60.00000
ANOVA
Regression
Residual
Total
Intercept
Mkt-RF
SMB
HML
df
3.00000
56.00000
59.00000
SS
0.06939
0.00422
0.07361
Coefficient
s
0.00065
0.95742
0.11224
0.09351
Standard
Error
0.00119
0.03530
0.05711
0.06283
MS
0.02313
0.00008
F
307.29301
t Stat
0.54383
27.12394
1.96550
1.48837
P-value
0.58871
0.00000
0.05432
0.14226
Significanc
eF
0.00000
Baron Small Cap Fund:
Regression Statistics
Multiple R
0.96584
R Square
0.93284
Adjusted R Square
0.92924
Standard Error
0.01147
Observations
60.00000
ANOVA
Regression
Residual
Total
Intercept
Mkt-RF
SMB
HML
df
3.00000
56.00000
59.00000
SS
0.10239
0.00737
0.10976
Coefficient
s
-0.00147
1.01454
0.58630
-0.12235
Standard
Error
0.00158
0.04668
0.07552
0.08308
MS
0.03413
0.00013
F
259.28367
Significance
F
0.00000
t Stat
-0.92967
21.73473
7.76379
-1.47266
P-value
0.35653
0.00000
0.00000
0.14644
Lower 95%
-0.00463
0.92103
0.43502
-0.28878
CHAPTER 12 CASE C-47
3.
This answer will depend on the returns used by the students.
4.
If the market is efficient, all assets should have an alpha of zero. In this case, none of the three funds
has a statistically significant positive alpha at the 5 percent level, so the evidence provided here
against market efficiency is limited.
5.
Once adjusting for risk, we cannot say any of these three funds performed better since all three
alphas are not significantly different from zero at the 5 percent level of confidence, although the
alpha for the Fidelity Magellan Fund is significantly negative at the 10 percent level, so it may have
had the worst performance given its level of risk.
CHAPTER 13
COST OF CAPITAL FOR SWAN MOTORS
NOTE: The example below shows the results during November 2015. The actual answer to the case
will change based on current market conditions.
1.
The book value of the company’s liabilities and equity can be found from a number of sources. We
went to www.sec.gov and found Tesla’s Form 10-Q, dated September 30, 2015. Tesla’s Form 10-Q
showed the following:
CHAPTER 13 CASE C-49
The book value of equity is $1,315 million on the balance sheet. However, for a more current book
value, we multiplied the number of shares outstanding by the book value per share on Yahoo!
Finance. For the book value of debt, we used the following note in the 10-Q:
In the notes, the company issued $800 million of 2019 bonds, then issued another $120 million. For
the 2021 bond, the company initially issued $1.2 billion, then issued another $180 million. The total
numbers do not match the balance sheet debt, but we will use these numbers nonetheless. It is likely
that the company has repurchased some of the outstanding debt, but any repurchase is not noted in
the 10-Q.
2.
We need various pieces of information to estimate the cost of equity. We can use the dividend growth
model or the CAPM, so we will attempt to use both. The following information is necessary for our
calculations. We gathered all the information from finance.yahoo.com. The screen shots below show
this information.
Market price = $232.36
Market capitalization = $30.16 billion
Shares outstanding = 129.80 million
Most recent dividend = $0
Beta = 1.40
3-month Treasury bill rate = .06%
C-50 CASE SOLUTIONS
CHAPTER 13 CASE C-51
Tesla has never paid a dividend, so we cannot use the dividend growth model to estimate the cost of
equity. We do have the information to estimate the cost of equity with the CAPM. Using the market
risk premium of 7 percent from the textbook, we get:
RE = Rf + [E(RM) – Rf]
RE = .0006 + 1.40(.07)
RE = .0986, or 9.86%
3.
Below are the top 10 competitors in the automobile industry by market capitalization at the time:
Company
Beta
Ford
General Motors
Honda
Toyota
Fiat Chrysler
Volkswagen
DaimlerChrysler
.97
1.44
.74
.54
.49
1.97
1.55
Industry Average
1.10
We should make an important note here: All of the competitors listed may not be direct
competitors. First, since Tesla manufactures only electric cars, it could be in an entirely different
industry by itself. Additionally, Tesla primarily sells only in the United States, so it is largely
immune from the currency risk faced by many of the above auto companies. Finally, since several
of the companies listed are based overseas and only have ADRs listed on U.S. exchanges, they
may not be comparable. In this case, we have chosen to use all the companies listed.
C-52 CASE SOLUTIONS
Using the industry average beta, the cost of equity is:
RE = Rf + [E(RM) – Rf]
RE = .0006 + 1.10(.07)
RE = 7.76%
Because Tesla’s beta is so different from the industry beta, a decision must be made as to the correct
cost of equity. We will use the cost of equity using Tesla’s beta.
4.
To get the yield to maturity on Tesla’s bonds, we went to finramarkets.morningstar.com/BondCenter/. We gathered the following information:
Tesla has a convertible bond that matures on 06/01/2018. Because the convertible feature is so deep
in the money, the bond is priced near the conversion value, resulting in a very large negative yield to
maturity. We have chosen to ignore this bond in our analysis.
If you click on the link for each bond, the website provides information concerning the bond,
including the face amount of the issue. So, the weighted average cost of debt for Tesla using both the
book value and the market value is:
3/1/2019
3/1/2021
Total
Book value
(millions)
$920
1,380
$2,300
Percent
of total
.40
.60
1.00
Quoted
price
94.347
92.625
Market
value
(millions)
$867.992
1,278.225
$2,146.22
Percent
of total
.40
.60
1.00
Yield to
Maturity
2.028%
2.754%
Book
values
.81%
1.65%
2.46%
Market
values
.82%
1.64%
2.46%
It is irrelevant whether we use book or market values to calculate the cost of debt for Tesla. The
weighted average cost of debt using book value weights is 2.46 percent and using market value
weights we get 2.46 percent.
5.
Using book value weights, the total value of Tesla is:
V = $2,300,000,000 + $1,322,662,000
V = $3,622,662,000
So, the WACC based on book value weights is:
WACC = RE(E/V) + RD(D/V)(1 – TC)
WACC = (.0986)($1,322.662/$3,622.662) + (.0246)($2,300/$3,622.662)(1 – .21)
WACC = .0484, or 4.84%
CHAPTER 13 CASE C-53
Using the market value weights, the total value of Tesla is:
V = $2,146,217,400 + $30,160,328,000
V = $32,306,545,400
So, the WACC based on market value weights is:
WACC = RE(E/V) + RD(D/V)(1 – TC)
WACC = (.0986)($30,160,328,000/$32,306,545,400)
+ (.0246)($3,622,662,000/$32,306,545,400)(1 – .21)
WACC = .0942, or 9.42%
The cost of capital for Tesla using book value weights and market value weights is dramatically
different since Tesla has a market-to-book ratio of about 22.7.
6.
The biggest potential problem with SMI using Tesla’s cost of capital is that SMI operates stores that
generate the company’s sales. Tesla generates sales almost exclusively from its internet site. This
could potentially be a risk factor that affects the cost of capital. Another factor that could affect the
cost of capital is Tesla’s access to capital since it is a public company, while Swan Motors is private.
CHAPTER 14
YOUR 401(k) ACCOUNT AT EAST COAST
YACHTS
1.
Before the fact, you would expect that mutual fund managers would be able to outperform the
market. This is due, in part, to the Darwinian nature of the business. Good performing fund
managers are richly rewarded, and poor performing fund managers are fired, often very quickly. In
reality, we should expect that less than 50 percent of all equity mutual funds would outperform the
market. This does not depend on the level of market efficiency. Consider the following question:
What percentage of investors will outperform the market in a given year? Answer: Fifty percent.
While there could be one poor investor who takes all of the losses in a given year, in general, to get
the market average, we would expect one-half of investors would outperform the market, and onehalf would underperform the market. After all, the market average return must be the average return
of all investors’ average returns. This is true if we consider the weighted average return, that is, the
average return of investors weighted by the dollar amount of the investment. We would expect more
than 50 percent of mutual funds would underperform the market because of the expenses charged by
the mutual funds. Consider the large-cap stock fund, with an expense ratio of 1.50 percent. The fund
must exceed the market return by 1.50 percent before fees to achieve a return after fees equal to the
market return. Whether the market is efficient or inefficient is irrelevant unless mutual funds
managers are the best investors in the market, and all other investors, including private money
managers, pension fund managers, individuals, etc. are the worst investors in the market.
We should also consider that mutual funds managers may be able to outperform the market before
expenses. Whether they can outperform the market on an after-expense basis becomes a question of
whether mutual fund managers can extract economic rents from the stock market. The evidence
tends to support the idea that they cannot. In general, research has found that mutual fund managers
underperform the market after expenses by the average expense ratio. This means that mutual funds
tend to have the market average return before expenses, so they do not appear to be able to
outperform the market.
2.
The results in the graph tend to support the idea of market efficiency. Consider the case of the
Fidelity Magellan Fund, one of the largest actively managed equity mutual funds at the time this was
written. The total assets of the fund at the time this was written was about $22.4 billion. So, the
question is this: What would Fidelity pay for one year to increase the return of the Magellan Fund by
.01 percent? If we multiply the fund assets by .01 percent, we get: $22,400,000,000(.0001) =
$2,240,000. So, if Fidelity can increase the return of this one fund by only .01 percent per year, it
should be willing to pay up to $2.24 million for that year. Given the amount mutual fund companies
would be willing to spend for research, and the Darwinian nature of the industry, we would expect
that mutual fund managers should be able to outperform the market. While there have been notable
exceptions, such as Peter Lynch’s tenure at Magellan, as a whole, mutual fund managers do not seem
to be able to outperform the market. As a result, if the “best” and definitely “best-financed” investors
cannot outperform the market, the results support the concept of market efficiency.
CHAPTER 14 CASE C-55
3.
Given that the evidence presented tends to support market efficiency, you should invest in the S&P
500 index fund. However, this is not the entire answer. By investing the entire equity portion of your
account in the S&P 500 index, your portfolio is not diversified since the S&P 500 index includes
only large-cap stocks. Therefore, part of your equity investment should probably be in the small cap
fund for diversification purposes. Note that a small cap index fund may be the best option, but there
is no small cap index fund available in the 401k account.
CHAPTER 16
STEPHENSON REAL ESTATE
RECAPITALIZATION
1.
If Stephenson wishes to maximize the overall value of the firm, it should use debt to finance the $49
million purchase. Since interest payments are tax deductible, debt in the firm’s capital structure will
decrease the firm’s taxable income, creating a tax shield that will increase the overall value of the
firm.
2.
Since Stephenson is an all-equity firm with 12 million shares of common stock outstanding, worth
$53.80 per share, the market value of the firm is:
Market value of equity = $53.80(12,000,000)
Market value of equity = $645,600,000
So, the market value balance sheet before the land purchase is:
Assets
Total assets
3.
a.
Market value balance sheet
$645,600,000
Equity
$645,600,000
Debt & Equity
$645,600,000
$645,600,000
As a result of the purchase, the firm’s pre-tax earnings will increase by $11.5 million per year
in perpetuity. These earnings are taxed at a rate of 21 percent. Therefore, after taxes, the
purchase increases the annual expected earnings of the firm by:
Earnings increase = $11,500,000(1 – .21)
Earnings increase = $9,085,000
Since Stephenson is an all-equity firm, the appropriate discount rate is the firm’s unlevered cost
of equity, so the NPV of the purchase is:
NPV = –$49,000,000 + ($9,085,000/.105)
NPV = $37,523,810
CHAPTER 16 C-57
b.
After the announcement, the value of Stephenson will increase by $37,523,810, the net present
value of the purchase. Under the efficient-market hypothesis, the market value of the firm’s
equity will immediately rise to reflect the NPV of the project. Therefore, the market value of
Stephenson’s equity after the announcement will be:
Equity value = $645,600,000 + 37,523,810
Equity value = $683,123,810
Old assets
NPV of project
Total assets
Market value balance sheet
$645,600,000
37,523,810
Equity
$683,123,810
Debt & Equity
$683,123,810
$683,123,810
Since the market value of the firm’s equity is $683,123,810 and the firm has 12 million shares
of common stock outstanding, Stephenson’s stock price after the announcement will be:
New share price = $683,123,810/12,000,000
New share price = $56.93
Since Stephenson must raise $49 million to finance the purchase and the firm’s stock is worth
$56.93 per share, Stephenson must issue:
Shares to issue = $49,000,000/$56.93
Shares to issue = 860,752
c.
Stephenson will receive $49 million in cash as a result of the equity issue. This will increase the
firm’s assets and equity by $49 million. So, the new market value balance sheet after the stock
issue will be:
Cash
Old assets
NPV of project
Total assets
Market value balance sheet
$ 49,000,000
645,600,000
37,523,810
Equity
$732,123,810
Debt & Equity
$732,123,810
$732,123,810
The stock price will remain unchanged. To show this, Stephenson will now have:
Total shares outstanding = 12,000,000 + 860,752
Total shares outstanding = 12,860,752
So, the share price is:
Share price = $732,123,810/12,860,752
Share price = $56.93
C-58 CASE SOLUTIONS
d.
The project will generate $11.5 million of additional annual pretax earnings forever. These
earnings will be taxed at a rate of 21 percent. Therefore, after taxes, the project increases the
annual earnings of the firm by $6.9 million. So, the aftertax present value of the earnings
increase is:
PVProject = $9,085,000/.105
PVProject = $86,523,810
So, the market value balance sheet of the company will be:
Old assets
PV of project
Total assets
4.
a.
Market value balance sheet
$645,600,000
86,523,810
Equity
$732,123,810
Debt & Equity
$732,123,810
$732,123,810
Modigliani-Miller Proposition I states that in a world with corporate taxes:
VL = VU + tCB
As was shown in Question 3, Stephenson will be worth $732,123,810 if it finances the purchase
with equity. If it were to finance the initial outlay of the project with debt, the firm would have
$49 million worth of 7 percent debt outstanding. So, the value of the company if it financed
with debt is:
VL = $732,123,810 + .21($49,000,000)
VL = $742,413,810
b.
After the announcement, the value of Stephenson will immediately rise by the present value of
the project. Since the market value of the firm’s debt is $49 million and the value of the firm is
$742,413,810, we can calculate the market value of Stephenson’s equity. Stephenson’s marketvalue balance sheet after the debt issue will be:
Value unlevered
Tax shield
Total assets
Market value balance sheet
$732,123,810
Debt
10,290,000
Equity
$742,413,810
Debt & Equity
$ 49,000,000
693,413,810
$742,413,810
Since the market value of Stephenson’s equity is $693,413,810 and the firm has 12 million
shares of common stock outstanding, Stephenson’s stock price after the debt issue will be:
Stock price = $693,413,810/12,000,000
Stock price = $57.78
5.
If Stephenson uses equity to finance the project, the firm’s stock price will remain at $56.93 per
share. If the firm uses debt to finance the project, the firm’s stock price will rise to $57.78 per share.
Therefore, debt financing maximizes the per share stock price of the firm’s equity.
CHAPTER 17
McKENZIE CORPORATION’S CAPITAL
BUDGETING
1.
We assume the $5,400,000 is spent immediately so we can ignore time value of money
considerations. If we include the time value of money, the numerical solutions will change slightly,
but the analysis will remain the same. The expected value of the company in one year without
expansion is:
V = .30($22,000,000) + .50($31,000,000) + .20($48,000,000)
V = $31,700,000
And the expected value of the company in one year with expansion is:
V = .30($29,000,000) + .50($37,000,000) + .20($54,000,000)
V = $38,000,000
The company’s stockholders appear to be better off with expansion since the expected NPV of the
project is positive. The difference in the expected value of the company with and without expansion
is $6,300,000. If the required investment is $5,400,000, the expansion creates a positive increase in
expected value for current shareholders. However, as further analysis will show, stockholders are
actually worse off.
2.
The value of the company’s debt with low economic growth is the value of the company because the
company value is less than the face value of the debt. In both other economic states, the value of the
debt is the face value of the debt. So, the expected value of debt in one year without expansion is:
VD = .30($22,000,000) + .50($26,000,000) + .20($26,000,000)
VD = $24,800,000
And the value of the company’s debt in one year with expansion is:
VD = .30($26,000,000) + .50($26,000,000) + .20($26,000,000)
VD = $26,000,000
C-60 CASE SOLUTIONS
3.
The value of the company’s equity with low economic growth is zero both with and without
expansion since the company value will be less than the face value of the debt. The value of equity
with normal growth or high growth is the value of the company minus the $26,000,000 face value of
debt. So, the expected value of the equity without expansion is:
VE = .30($0) + .50($5,000,000) + .20($22,000,000)
VE = $6,900,000
And the value of equity with expansion is:
VE = .30($3,000,000) + .50($11,000,000) + .20($28,000,000)
VE = $12,000,000
The value expected for bondholders from the expansion is the difference in the expected value of
debt. So, with expansion, the company’s bondholders gain:
Bondholder gain = $26,000,000 – 24,800,000
Bondholder gain = $1,200,000
And the value expected for stockholders is:
Stockholder gain = $12,000,000 – 6,900,000
Stockholder gain = $5,100,000
The stockholder value increases by $5,100,000, but the expansion was funded entirely by equity, so
the expected NPV of expansion for stockholders is actually:
Stockholder NPV = –$5,400,000 + 5,100,000
Stockholder NPV = –$300,000
4.
Assuming bondholders are fully informed, and they act rationally, they will expect the stockholders
to act in their best interest and not expand, so the price of the bonds will not change. If the expansion
is announced, the price of the bonds will increase.
5.
If they don’t expand, nothing will happen since this assumption is already priced into the bond. If the
company announces the expansion, they signal they are willing to sacrifice for the bondholders, so
the company will receive a lower interest rate in the future.
6.
It is a stronger signal that stockholders are not acting in their best interest if the expansion is
financed with cash on hand. If the company issues new equity, the expected loss in stock value is
shared proportionally by the new investors, so the current stockholders will not bear the entire loss in
stock value alone. By expanding with cash on hand, current stockholders are bearing the entire
expected loss in stock value.
CHAPTER 18
THE LEVERAGED BUYOUT OF CHEEK
PRODUCTS, INC.
In this leveraged buyout, the debt level of the company changes through time. Since the debt level
changes through time, the APV method is appropriate for evaluating the LBO. The steps we must
undertake are:
Step 1: Calculating the present value of unlevered cash flows for the first five years.
Step 2: Calculating the present value of the unlevered cash flows beyond the first five years.
Step 3: Calculating the present value of interest tax shields for the first five years.
Step 4: Calculating the present value of interest tax shields beyond the first five years.
Step 1: Calculating the present value of unlevered cash flows for the first five years.
The income statement presented does not include interest, so it is the projected unlevered cash flows of
the company. To find the cash flows each year, we find the operating cash flow by adding depreciation
back to net income. Next, we subtract any capital expenditures, subtract or add changes in net working
capital, and add the asset sales. So, the unlevered cash flows each year will be:
Sales
Costs
Dep
EBT
Tax
Net income
Capital expenditures
Change in NWC
Asset sales
Unlevered cash flows
2019
$3,024.00
804.00
534.00
$1,686.00
354.06
$1,331.94
2020
$3,391.00
1,055.00
568.00
$1,768.00
371.28
$1,396.72
2021
$3,654.00
1,110.00
591.00
$1,953.00
410.13
$1,542.87
2022
$3,740.00
1,200.00
620.00
$1,920.00
403.20
$1,516.80
2023
$3,893.00
1,264.00
633.00
$1,996.00
419.16
$1,576.84
$307
–134
1,560
$266
–205
1,131
$334
111
$339
105
$334
119
$3,252.94
$3,034.72
$1,688.87
$1,692.80
$1,756.84
Since these are unlevered cash flows, we need to discount at the unlevered cost of equity. Because the
company currently has no debt, the required return on assets is equal to the cost of equity. So, using this
discount rate, we find the present value of the unlevered cash flows for the next five years will be:
PV = $3,252.94/1.14 + $3,034.72/1.142 + $1,688.87/1.143 + $1,692.80/1.144 + $1,756.84/1.145
PV = $8,243.23
C-62 CASE SOLUTIONS
Step 2: Calculating the present value of the unlevered cash flows beyond the first five years.
The assumption given is that the cash flows will grow at 3.5 percent into perpetuity. Again, we discount
these cash flows at the unlevered return on equity. So, the value of these cash flows in Year 5 will be:
Unlevered CF value in Year 5 = [$1,756.84(1 + .035)]/(.14 – .035)
Unlevered CF value in Year 5 = $17,317.42
The value today of this terminal value is:
PV = $17,317.42/1.145
PV = $8,994.13
Step 3: Calculating the present value of interest tax shields for the first five years.
The interest tax shield each year is the interest paid times the tax rate. To find the present value of the
interest tax shield, we need to discount these at the pretax cost of debt, so the present value of the interest
tax shield for the first five years is:
PV = ($2,120)(.21)/1.125 + ($2,045)(.21)/1.1252 + ($2,851)(.21)/1.1253 + ($2,779)(.21)/1.1254
+ ($2,875)(.21)/1.1255
PV = $1,854.92
Step 4: Calculating the present value of interest tax shields beyond the first five years.
Finally, we must calculate the value of tax shields associated with debt used to finance the operations of
the company after the first five years. The assumption given in the case is that debt will be reduced and
maintained at 25 percent of the value of the firm from that date forward. Under this assumption, it is
appropriate to use the WACC method to calculate a terminal value for the firm at the target capital
structure. This, in turn, can be decomposed into an all-equity value and a value from tax shields. Note that
we need to use the interest rate on the debt beyond Year 5 in these calculations. If the capital structure
changes after the first five years, the levered cost of equity can be found with Modigliani-Miller
Proposition II with corporate taxes:
RS = R0 + (B/S)(R0 – RB)(1 – TC)
RS = .14 + (.25)(.14 – .08)(1 – .21)
RS = .1519, or 15.19%
Now, we can calculate the WACC for the company beyond Year 5. The WACC at this point will be:
RWACC = [B/(B + S)](1 – TC)RB + [S/(B + S)]RS
RWACC = [.25](1 – .21)(.08) + [1/1.25](.1519)
RWACC = .1373, or 13.73%
We can use the WACC to calculate the terminal value of the levered company, which will be:
VL = [$1,756.84(1 + .035)]/(.1373 – .035)
VL = $17,777.96
CHAPTER 18 CASE C-63
Using Modigliani-Miller’s valuation of a levered firm:
VL = VU + TCB
we can value the interest tax shield as:
$17,777.96 = $17,317.42 + Interest tax shield
Interest tax shield = $460.53
This is the value of the interest tax shield beyond Year 5. Discounting this at the cost of debt over the first
five years, we find the value today is:1
PV = $460.53/1.1255
PV = $255.56
We have valued all future cash flows of the company. The value of the unlevered cash flows today is:
Value of unlevered CF = $8,243.23 + 8,994.13
Value of unlevered CF = $17,237.36
And the value of the interest tax shield today is:
Value of interest tax shield = $1,854.92 + 255.56
Value of interest tax shield = $2,110.48
So, the total value of the company today is:
Value of company today = $17,237.36 + 2,110.48
Value of company today = $19,347.84
So, the most the group should offer per share is:
Price = $19,347.84/385
Price = $50.25
1 A good argument can be made that since post-2019 debt levels are proportional to firm value, the tax
shields are as risky as the firm and should be discounted at the rate R0.
CHAPTER 19
ELECTRONIC TIMING, INC.
1.
The value of the company will decline by the amount of the dividend. Ignoring taxes, shareholder
wealth will not be affected because the stock price will drop by the amount of the dividend payment.
2.
The value of the company could increase or decrease. If the company is over-levered, paying off
debt can lower the interest rate on debt, and decrease financial distress costs. If there are no financial
distress costs, capital structure theory argues that increasing debt can increase the value of the
company because of the interest tax shield.
3.
The PE ratio will fall and the ROA and ROE will increase, but the changes are irrelevant.
4.
A regular dividend payment is something the company should probably not undertake. A company
rarely begins regular dividend payments that anticipates will not be sustainable Cessation of
dividend payments is viewed by the market as a negative signal.
5.
The implication is that the company should not retain earnings unless the ROE of the new project is
greater than the shareholders required return on equity. This is an intuitive result. Shareholders want
the company to retain earnings for future growth if the earnings will earn a greater return than
shareholders require. If the return on the retained earnings is lower than shareholders’ required
return, the company is lowering shareholder value.
6.
The decision does depend on the organizational form of the company. Money paid to shareholders of
a corporation are dividends, and currently taxed at the lower dividend tax rate. Money paid to the
owners of an LLC is considered income and is taxed at the applicable personal income tax rate.
CHAPTER 20
EAST COAST YACHTS GOES PUBLIC
1.
The main difference in the costs is the reduced possibility of underpricing in a Dutch auction. As to
which is better, we don’t know. In theory, the Dutch auction should be better since it should
eliminate underpricing. However, as Google shows, underpricing can still exist in a Dutch auction.
Whether the underpricing is as severe in a Dutch auction as it would be in a traditional underwritten
offer is unknown.
2.
There is no way to calculate the optimum size of the IPO, so whether Dan is correct or Larissa is
correct will only be told in time. The disadvantages of raising the extra cash in the IPO include the
agency costs of excess cash. The extra cash may encourage management to act carelessly. The extra
cash will also earn a small return unless invested in income producing assets. At best, cash and shortterm investments are a zero NPV investment. The advantages of the increased IPO size include the
increased liquidity for the company, and the lower probability that the company will have to go back
to the primary market in the near future. The increased size will also reduce the costs of the IPO as a
percentage of funds raised, although this may not be a large advantage.
3.
The underwriter fee is 7 percent of the amount raised, or:
Underwriter fee = $90,000,000(.07)
Underwriter fee = $6,300,000
Since the company must currently provide audited financial statements due to the bond covenants,
the audit costs are not incremental costs and should not be included in the calculation of the fees. So,
the sum of the other fees is:
Total other fees = $2,200,000 + 15,000 + 20,000 + 100,000 + 8,500 + 525,000 + 75,000
Total other fees = $2,943,500
This means the total fees are:
Total fees = $6,300,000 + 2,943,500
Total fees = $9,243,500
The net amount raised is the IPO offer size minus the underwriter fee, or:
Net amount raised = $90,000,000 – 6,300,000
Net amount raised = $83,700,000
So, the fees as a percentage of the net amount to the company are:
Fee percentage = $9,243,500/$83,700,000
Fee percentage = .1104, or 11.04%
C-66 CASE SOLUTIONS
4.
Because of legal repercussions, you should not provide specific advice on which option the
employees should choose. There are advantages and disadvantages to each. If the employee tenders
the stock to be sold in the IPO, the employee will lose out on any underpricing. This could be a
significant cost. However, if the employee retains the stock, he/she must hold the stock for the
lockup period, typically 180 days. Additionally, during the lockup period, the employee is legally
prohibited from hedging the price risk of the stock with any derivatives. And heavy selling by
insiders is considered a negative signal by the market. Another risk in not selling in the IPO is that
after the lockup period expires, the employees may be considered insiders, subject to SEC
restrictions on selling stock.
CHAPTER 21
THE DECISION TO LEASE OR BUY AT
WARF COMPUTERS
1.
The decision to buy or lease is made by looking at the incremental cash flows. The incremental cash
flows from leasing the machine are the security deposit, the lease payments, the tax savings on the
lease, the lost depreciation tax shield, the saved purchase price of the machine, and the lost salvage
value. The salvage value of the equipment in four years will be:
Aftertax salvage value = $780,000 – $780,000(.21)
Aftertax salvage value = $616,200
This is an opportunity cost to Warf Computers since, if the company leases the equipment, it will not
be able to sell the equipment in four years. The lease payments are due at the beginning of each year,
so the incremental cash flows are:
Saved purchase
Lost salvage value
Lost dep. tax shield
Security deposit
Lease payment
Tax on lease payment
Cash flow from leasing
Year 0
$6,100,000
–400,000
–1,480,000
310,800
$4,530,800
Year 1
Year 2
Year 3
–$426,957
–$569,405
–$189,716
–1,480,000
310,800
–$1,596,157
–1,480,000
310,800
–$1,738,605
–1,480,000
310,800
–$1,358,916
The aftertax cost of debt is:
Aftertax cost of debt = .09(1 – .21)
Aftertax cost of debt = .0711, or 7.11%
And the NAL of the lease is:
NAL = $4,530,800 – $1,596,157/1.0711 – $1,738,605/1.07112 – $1,358,916/1.07113
– $311,122/1.07114
NAL = $182,902.93
The company should lease the equipment.
Year 4
–$616,200
–94,922
400,000
–$311,122
C-68 CASE SOLUTIONS
2.
The book value of the equipment in Year 2 will be:
Book value = $6,100,000 – $6,100,000(.3333 + .4445)
Book value = $1,355,420
So, the aftertax salvage value in Year 2 will be:
Aftertax salvage value = $3,200,000 + ($1,355,420 – 3,200,000)(.21)
Aftertax salvage value = $2,812,638
So, the NAL of the lease under the new terms would be:
Saved purchase
Lost salvage value
Lost dep. tax shield
Lease payment
Tax on lease payment
Cash flow from leasing
Year 0
$6,100,000
–1,875,000
393,750
$4,618,750
Year 1
–$426,957
–1,875,000
393,750
–$1,908,207
Year 2
–$2,812,638
–569,405
–$3,382,043
So, the NAL of the lease under these terms is:
NAL = $4,618,750 – $1,908,207/1.0711 – $3,382,043/1.07112
NAL = –$110,732.59
The NAL of the lease is negative under these terms, so it appears the terms are less favorable for the
lessee. However, the lease will likely be classified as an operating lease. The lease is now for two
years, which is less than 75 percent of the equipment’s life. Using the company’s cost of debt, the
present value of the lease payments is:
PV of lease payments = $1,875,000 + $1,875,000/1.09
PV of lease payments = $3,595,183.49
This is less than 90 percent of the price of the equipment. If the lease contract does transfer
ownership to the lessee at the end of the contact, or allow for a purchase at a bargain price, the FAS
13 conditions for a capital lease are not met. As such, the reason for suggesting the revised lease
terms is unethical on Nick’s part. Also, notice that the question also states that if the lease is renewed
in two years, the lessor will allow for the increased lease payments made over the first two years.
This is also an indication that the revision is likely for less than ethical reasons.
CHAPTER 21 CASE C-69
3.
4.
a.
The inclusion of a right to purchase the equipment will have no effect on the value of the lease.
If the company does not purchase the equipment, it can go on the market and purchase identical
equipment at the same price.
b.
The right to purchase the equipment at a fixed price will increase the value of the lease. If the
company can purchase the equipment at the end of the lease at below market value, it will save
money, or at a minimum, can purchase the equipment at the fixed price and resell it in the open
market. This is a real option, therefore it has value to the lessee. It is a call option on the
equipment. As such, it must have a value until it expires or is exercised. It is also important to
note that this would likely make the lease contract a capitalized lease.
c.
The right to purchase the equipment at a bargain price is also a real option for the lessee and
will increase the value of the lease. It is a call option, and therefore will have value until it
expires or is exercised. This contract condition will ensure the lease is classified as a capitalized
lease.
The cancellation option is also a real option. The cancellation option is a put option on the
equipment. It will increase the value of the lease since the lessee will only exercise the option when
it is to the lessee’s advantage.
CHAPTER 22
CLISSOLD INDUSTRIES OPTIONS
1.
Since the Black-Scholes model uses the standard deviation of the underlying asset, and there is only
one underlying asset no matter how many strike prices are available, we would only expect to see
one implied standard deviation.
2.
To find the implied volatility for an option, you can set up a spreadsheet to calculate the option price.
The Solver function in Excel will allow you to input the desired price and will solve for the desired
unknown variable. We did this (the spreadsheet is available), and the implied standard deviation for
each of the options is:
Strike Price
$50
55
60
65
3.
Option Price
$12.78
10.14
7.99
5.81
Implied Standard Deviation
75.04%
70.96
68.21
63.22
There are two possible explanations. The first is model misspecification. Although the Black-Scholes
option pricing model is widely acclaimed, it is possible that the model specifications are incorrect.
One potential variable that is incorrectly specified is the assumption of constant volatility. In fact, the
volatility of the underlying stock is itself volatile, and will increase or decrease over time. The
Black-Scholes model may also ignore important variables. For example, Fisher Black describes
trades he, Myron Scholes, Robert Merton, and others made when the model was first developed
(Black, Fisher, 1989, “How we came up with the option pricing formula,” The Journal of Portfolio
Management, Winter, 4-8.) As in any potential arbitrage opportunity, they purchased underpriced
assets, in this case warrants on National General stock. Unfortunately, soon after they took this
position, American Financial announced a tender offer for National General, which sharply reduced
the value of the warrants. The market had already priced the potential tender offer into the warrant
price, while this variable was not accounted for in the Black-Scholes model.
A second possible explanation is liquidity. At- or near-the-money options tend to be more liquid than
deep in-the-money or deep out-of-the-money options. Since options that are not near the money are
less liquid, the price should carry a liquidity premium.
4.
The VIX is a benchmark for stock market volatility. The VIX is based on option prices, which reflect
investors' consensus view of future expected stock market volatility. During periods of market
turmoil, both option prices and the VIX tend to rise. When the market is calmer, investor fear, option
prices, and the VIX decline.
5.
The VIX uses eight different S&P 100 Index (OEX) option series to represent the implied volatility
of a hypothetical OEX option with exactly 30 days to expiration.
CHAPTER 23
EXOTIC CUISINES’ EMPLOYEE STOCK
OPTIONS
1.
We can use the Black-Scholes equation to value the employee stock options. We need to use the riskfree rate that is the same maturity as the options. So, assuming expiration in three years, the value of
the stock options per share of stock is:
d1 = [ln($27.15/$40) + (.038 + .602/2)  3]/(.60 
d2 = .2564 – (.60 
√3
√3
) = .2564
) = –.7828
N(d1) = .6012
N(d2) = .2169
Putting these values into the Black-Scholes model, we find the option value is:
C = $27.15(.6012) – ($40e–.038(3))(.2169)
C = $8.58
Assuming expiration in 10 years, the value of the stock options per share of stock is:
d1 = [ln($27.15/$40) + (.044 + .602/2)  10]/(.60 
d2 = .9764 – (.60 
√ 10
√ 10
) = .9764
) = –.9210
N(d1) = .8356
N(d2) = .1785
Putting these values into the Black-Scholes model, we find the option value is:
C = $27.15(.8356) – ($40e–.044(10))(.1785)
C = $18.09
2.
Whether you should exercise the options in three years depends on several factors. A primary factor
is how long you plan to stay with the company. If you are planning to leave next week, you should
exercise the options. A second factor is how the option exercise will affect your taxes.
3.
The fact that the employee stock options are not traded decreases the value of the options. A basic
way to understand this is to realize that an option always has value since, ignoring the premium, it
C-72 CASE SOLUTIONS
can never lose money. The right to sell an option also must have value. If the right to sell is removed,
it decreases the price of the option.
4.
The rationale for employee stock options is to reduce agency costs by better aligning employee and
shareholder interests. Vesting requires employees to work at a company for a specified time, which
means the employee actions are part of the company’s performance. Vesting is also a “golden
handcuff”. The employee is less likely to leave the company if in-the-money employee stock options
will vest soon.
5.
The evaluation of the argument for or against repricing is open-ended. There are valid reasons on
both sides of the discussion.
Repricing increases the value of the employee stock option. Consider an extreme: A company
announces the employee stock options will be worth a minimum of $10 at expiration. Since all
values less than $10 are no longer possible, the value of the option increases.
6.
Employee stock options increase in value if the stock price increases; however, the stock price can
increase because of a general market increase. Consider a company of average risk in a bull market
that has a large return for several years. The company’s stock should closely mirror the market
return, even though most of the stock price increase is due to the general market increase. Similarly,
if the market falls, the company’s stock will likely fall as well, even if the company is doing well.
A better method of valuing employee stock options might be to reward employees for company
performance in excess of the market performance, adjusted for the company’s level of risk.
CHAPTER 24
S&S AIR’S CONVERTIBLE BOND
1.
Chris is suggesting a conversion price of $45 because it means the stock price will have to increase
before the bondholders can benefit from the conversion. Even though the company is not publicly
traded, the conversion price is important. First, the company may go public in the future. The case
does not discuss whether the company has plans to go public, and if so, how soon it might go public.
If the company does go public, the bondholders will have an active market for the stock if they
convert. Second, even if the company does not go public, the bondholders could potentially have an
equity interest in the company. This equity interest can be sold to the original owners, or someone
else. The potential problem with private equity is that the market is not as liquid as the market for a
public company. This illiquidity lowers the value of the stock.
We can use the PE ratio to estimate the current stock price. Doing so, we get:
P/E = Price/EPS
17.50 = Price/$1.75
Price = $30.63
2.
The floor value is the maximum of the conversion value and the intrinsic value. The conversion
value of the bond is given as $680.56. The intrinsic value of the bond is:
Intrinsic value = $25(PVIFA4%,20) + $1000(PVIF4%,20)
Intrinsic value = $703.11
So, the floor value of the bond is $703.11. This means that if the company offered bonds with the
same coupon rate and no conversion feature, they would be able to sell them for $703.11.
3.
The conversion ratio of the bonds is:
Conversion ratio = $1,000/$45 = 22.22
So, each bond can be converted to 22.22 shares of stock.
4.
The conversion premium is the increase in stock price necessary to make the conversion option
possible. Since the stock is currently selling for $30.63, and the conversion price is $45, the
conversion premium of the bond is:
Conversion premium = ($45 – 30.63)/$30.63
Conversion premium = .4694 or 46.94%
C-74 CASE SOLUTIONS
5.
The option value of a convertible bond is defined as the difference between the market value of the
bond and the maximum of its straight value and conversion value. Since the bond is sold at par
value, the option value is:
Option value = Market value – Max[Straight value, Conversion value]
Option value = $1,000 – Max[$703.11, $680.56]
Option value = $1,000 – 703.11
Option value = $296.89
6.
Todd’s argument is wrong because it ignores the fact that if the company does well, bondholders will
be allowed to participate in the company’s success. If the stock price rises to $50, bondholders are
effectively allowed to purchase stock at the conversion price of $45.
7.
Mark’s argument is incorrect because the company is issuing debt with a lower coupon rate than they
would have been able to otherwise. If the company does poorly, it will receive the benefit of a lower
coupon rate.
8.
Reconciling the two arguments requires that we remember our central goal: to increase the wealth of
the existing shareholders. Thus, with 20/20 hindsight, we see that issuing convertible bonds will turn
out to be worse than issuing straight bonds and better than issuing common stock if the company
prospers. The reason is that the prosperity must be shared with bondholders after they convert.
In contrast, if a company does poorly, issuing convertible bonds will turn out to be better than
issuing straight bonds and worse than issuing common stock. The reason is that the firm will have
benefited from the lower coupon payments on the convertible bonds.
Both arguments have a grain of truth; we just need to combine them. Ultimately, which option is
better for the company will only be known in the future and will depend on the performance of the
company. The table below illustrates this point.
Convertible bonds
issued instead of
straight bonds
Convertible bonds
issued instead of
common stock
9.
If the company does poorly
Low stock price and no
conversion
Cheap financing because
coupon rate is lower (good
outcome).
Expensive financing because
firm could have issued
common stock at high prices
(bad outcome).
If the company prospers
High stock price and
conversion
Expensive financing because
bonds are converted, which
dilutes existing equity (bad
outcome).
Cheap financing because firm
issues stock at high prices
when bonds are converted
(good outcome).
The call provision allows the company to redeem the bonds at the company’s discretion. If the
company’s stock appears to be poised to rise, the company can call the outstanding bonds. It could
be possible that the bondholders would benefit from converting the bonds at that point, but it would
eliminate the potential future gains to the bondholders.
CHAPTER 25
WILLIAMSON MORTGAGE, INC.
1.
Jerry’s mortgage payments form a 25-year annuity with monthly payments, discounted at the longterm interest rate of 5.5 percent. We can solve for the payment amount so that the present value of
the annuity equals $500,000, the amount of principal that he plans to borrow. The monthly mortgage
payment will be:
$500,000 = C(PVIFA5.5%/12,300)
C = $3,070.44
2.
The most significant risk that she faces is interest rate risk. If the current market rate of interest rises
between today and the date the mortgage is sold, the fair value of the mortgage will decrease, and
Max will only be willing to purchase the mortgage for a price less than $500,000. If this is the case,
she will not be able to loan Jerry the full $500,000 promised.
3.
Treasury bond prices have an inverse relationship with interest rates. As interest rates rise, Treasury
bonds become less valuable; as interest rates fall, Treasury bonds become more valuable. Since
Jennifer will be hurt when interest rates rise, she is also hurt when Treasury bonds decrease in value.
To protect herself from decreases in the price of Treasury bonds, she should take a short position in
Treasury bond futures to hedge this interest rate risk. Since three-month Treasury bond futures
contracts are available and each contract is for $100,000 of Treasury bonds, she would take a short
position in five 3-month Treasury bond futures contracts to hedge her $500,000 exposure to changes
in the market interest rate over the next three months
4.
a.
If the market interest rate is 6.2 percent on the date that Jennifer meets with the Max, the fair
value of the mortgage is the present value of an annuity that makes monthly payments of
$3,070.44 for 25 years, discounted at 6.2 percent, or:
Mortgage value = $3,070.44(PVIFA6.2%/12,300)
Mortgage value = $467,639.54
b.
5.
An increase in the interest rate will cause the value of the T-bond futures contracts to decrease.
The long position will lose, and the short position will gain. Since Jennifer is short in the
futures, the futures gain will offset the loss in value of the mortgage.
a. If the market interest rate is 4.6 percent on the date that Jennifer meets with Max, the fair value of
the mortgage is the present value of an annuity that makes monthly payments of $3,070.44 for
25 years, discounted at 4.6 percent, or:
Mortgage value = $3,070.44(PVIFA4.6%/12,300)
Mortgage value = $546,804.59
C-76 CASE SOLUTIONS
b.
6.
An increase in the interest rate will cause the value of the Treasury bond futures contracts to
increase. The long position will gain, and the short position will lose. Since Jennifer is short in
the futures, the futures loss will be offset by the gain in value of the mortgage.
The biggest risk is that the hedge is not a perfect hedge. If interest rates change, the fact that
Treasury bond interest is semiannual, while the mortgage payments are monthly, may affect the
relative value of the two. Additionally, while a change in one of the interest rates will likely coincide
with a change in the other interest rate, the change does not have to be the same. For example, the
Treasury rate could increase 20 basis points, and the mortgage rates could increase by 40 basis
points. The fact that this is not a perfect hedge means that the gain/loss from the futures contracts
may not exactly offset the loss/gain in the mortgage. We would expect, especially given the shortterm nature of the hedge, that the loss in one instrument would be similar to the gain in the other
instrument.
CHAPTER 26
KEAFER MANUFACTURING WORKING
CAPITAL MANAGEMENT
1.
The cash flow each quarter will consist of the sales collection, minus the suppliers paid, expenses,
dividends, interest, and capital outlays. The cash flows for each quarter will be:
Collections from previous quarter
Collections from current quarter
sales
Payments to suppliers for
previous quarter
Payments to suppliers for current
quarter
Expenses
Dividends and interest
Outlay
Net cash flow
Beginning cash balance
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus –deficit
Cash Flow
Q1
Q2
$607,500.00
$753,768.00
Q3
$780,444.00
Q4
$769,500.00
436,392.00
451,836.00
445,500.00
420,948.00
–350,436.00
–362,838.00
–357,750.00
–338,034.00
–253,302.00
–297,540.00
–185,000.00
–249,750.00
–308,070.00
–185,000.00
–264,215.52
–287,010.00
–185,000.00
–$42,386.00
$99,946.00
–235,986.00
–303,750.00
–185,000.00
–390,000.00
–$246,542.00
Cash Balance
Q1
Q2
$210,000.00
$167,614.00
–42,386.00
99,946.00
$167,614.00
$267,560.00
135,000.00
135,000.00
$32,614.00
$132,560.00
Q3
$267,560.00
–246,542.00
$21,018.00
135,000.00
–$113,982.00
Q4
$21,018.00
116,188.48
$137,206.48
135,000.00
$2,206.48
$116,188.48
C-78 CASE SOLUTIONS
The short-term financial plan looks like this:
Target cash balance
Net cash inflow
New short-term investments
Income on short-term investments
Short-term investments sold
New short-term borrowing
Interest on short-term borrowing
Short-term borrowing repaid
Ending cash balance
Minimum cash balance
Cumulative surplus –deficit
Beginning short-term investments
Ending short-term investments
Beginning short-term debt
Ending short-term debt
Short-term Financial Plan
$135,000.00
$135,000.00
–42,386.00
99,946.00
0
–100,321.00
375.00
375.00
42,011.00
0
0
0
0
0
0
0
$135,000.00
$135,000.00
–135,000.00
–135,000.00
$0
$0
$75,000.00
75,000.00
0
$0
$75,000.00
175,321.00
0
$0
$135,000.00
–246,542.00
0
876.61
175,321.00
70,344.40
0
0
$135,000.00
–135,000.00
$0
$135,000.00
116,188.48
–44,999.95
0
0
0
–844.13
–70,344.40
$135,000.00
–135,000.00
$0
$175,321.00
0
0
$70,344.40
$0
44,999.95
70,344.40
$0
The interest calculations for each quarter and the net cash cost are:
Q1:
Q2:
Q3:
Q4:
Excess funds at start of quarter of
Excess funds at start of quarter of
Excess funds at start of quarter of
Shortage of funds at start of quarter of
Net cash cost
Q1
Q2
Q3
Q4
Cash generated by short-term financing
$75,000.00
$75,000.00
$175,321.00
$70,344.40
$375.00
375.00
876.61
–844.13
$782.47
earns
earns
earns
costs
$375.00
$375.00
$876.61
$844.13
in income.
in income.
in income.
in interest.
CHAPTER 26 CASE C-79
2.
If Keafer reduces its target cash balance to $90,000, the cash flows each quarter will remain the
same, so they will not be repeated here. The cash balance and short-term financial plan will be:
Cash Balance
Q1
Q2
$210,000.00
$167,614.00
–42,386.00
99,946.00
$167,614.00
$267,560.00
90,000.00
90,000.00
$77,614.00
$177,560.00
Q3
$267,560.00
–246,542.00
$21,018.00
90,000.00
–$68,982.00
Q4
$21,018.00
116,188.48
$137,206.48
90,000.00
$47,206.48
Short-term Financial Plan
$90,000.00
$90,000.00
–42,386.00
99,946.00
0
–100,546.00
600.00
600.00
41,786.00
0
0
0
0
0
0
0
$90,000.00
$90,000.00
–90,000.00
–90,000.00
$0
$0
$90,000.00
–246,542.00
0
1,102.73
220,546.00
24,893.27
0
0
$90,000.00
–90,000.00
$0
$90,000.00
116,188.48
–90,996.49
0
0
0
–298.72
–24,893.27
$90,000.00
–90,000.00
$0
$220,546.00
0
0
$24,893.27
$0
90,996.49
24,893.27
$0
Beginning cash balance
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus –deficit
Target cash balance
Net cash inflow
New short-term investments
Income on short-term investments
Short-term investments sold
New short-term borrowing
Interest on short-term borrowing
Short-term borrowing repaid
Ending cash balance
Minimum cash balance
Cumulative surplus –deficit
Beginning short-term investments
Ending short-term investments
Beginning short-term debt
Ending short-term debt
Q1:
Q2:
Q3:
Q4:
Excess funds at start of quarter of
Excess funds at start of quarter of
Excess funds at start of quarter of
Shortage of funds at start of quarter of
Net cash cost
Q1
Q2
Q3
Q4
Cash generated by short-term financing
$120,000.00
120,000.00
0
$0
$120,000.00
220,546.00
0
$0
$120,000.00
$120,000.00
$220,546.00
$24,893.27
$600.00
600.00
1,102.73
–298.72
$2,004.01
earns
earns
earns
costs
$600.00
$600.00
$1,102.73
$298.72
in income.
in income.
in income.
in interest.
C-80 CASE SOLUTIONS
3.
If the sales growth rate is 11 percent, the cash flows for each quarter will be:
Collections from previous quarter
Collections from current quarter
sales
Payments to suppliers for
previous quarter
Payments to suppliers for current
quarter
Expenses
Dividends and interest
Outlay
Net cash flow
Beginning cash balance
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus –deficit
Cash Flow
Q1
Q2
$607,500.00
$774,706.00
Q3
$802,123.00
Q4
$790,875.00
448,514.00
464,387.00
457,875.00
432,641.00
–360,170.33
–372,916.83
–367,687.50
–347,423.83
–260,338.17
–305,805.00
–185,000.00
–256,687.50
–316,627.50
–185,000.00
–279,098.03
–294,982.50
–185,000.00
–$55,299.50
$107,861.17
–242,541.17
–312,187.50
–185,000.00
–390,000.00
–$237,418.17
Cash Balance
Q1
Q2
$210,000.00
$154,700.50
–55,299.50
107,861.17
$154,700.50
$262,561.67
135,000.00
135,000.00
$19,700.50
$127,561.67
Q3
$262,561.67
–237,418.17
$25,143.50
135,000.00
–$109,856.50
Q4
$25,143.50
117,011.64
$142,155.14
135,000.00
$7,155.14
$135,000.00
–237,418.17
0
916.18
183,236.17
53,265.82
0
0
$135,000.00
–135,000.00
$0
$135,000.00
117,011.64
–63,106.63
0
0
0
–639.19
–53,265.82
$135,000.00
–135,000.00
$0
$183,236.17
0
0
$53,265.82
$0
63,106.63
53,265.82
$0
$117,011.64
The short-term financial plan looks like this:
Target cash balance
Net cash inflow
New short-term investments
Income on short-term investments
Short-term investments sold
New short-term borrowing
Interest on short-term borrowing
Short-term borrowing repaid
Ending cash balance
Minimum cash balance
Cumulative surplus –deficit
Beginning short-term investments
Ending short-term investments
Beginning short-term debt
Ending short-term debt
Short-term Financial Plan
$135,000.00
$135,000.00
–55,299.50
107,861.17
0
–108,236.17
375.00
375.00
54,924.50
0
0
0
0
0
0
0
$135,000.00
$135,000.00
–135,000.00
–135,000.00
$0
$0
$75,000.00
75,000.00
0
$0
$75,000.00
183,236.17
0
$0
CHAPTER 26 CASE C-81
The interest calculations for each quarter and the net cash cost are:
Q1:
Q2:
Q3:
Q4:
Excess funds at start of quarter of
Excess funds at start of quarter of
Excess funds at start of quarter of
Shortage of funds at start of quarter of
$75,000.00
$75,000.00
$183,236.17
$53,265.82
Net cash cost
Q1
Q2
Q3
Q4
Cash generated by short-term financing
earns
earns
earns
costs
$375.00
$375.00
$916.18
$639.19
in income.
in income.
in income.
in interest.
$375.00
375.00
916.18
–639.19
$1,026.99
If the sales growth rate is 5 percent, the cash flows for each quarter will be:
Collections from previous quarter
Collections from current quarter
sales
Payments to suppliers for
previous quarter
Payments to suppliers for current
quarter
Expenses
Dividends and interest
Outlay
Net cash flow
Beginning cash balance
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus –deficit
Cash Flow
Q1
Q2
$607,500.00
$732,830.00
Q3
$758,765.00
Q4
$748,125.00
424,270.00
439,285.00
433,125.00
409,255.00
–340,701.67
–352,759.17
–347,812.50
–328,644.17
–246,265.83
–289,275.00
–185,000.00
–242,812.50
–299,512.50
–185,000.00
–249,740.75
–279,037.50
–185,000.00
–$29,472.50
$92,030.83
–229,430.83
–295,312.50
–185,000.00
–390,000.00
–$255,665.83
Cash Balance
Q1
Q2
$210,000.00
$180,527.50
–29,472.50
92,030.83
$180,527.50
$272,558.33
135,000.00
135,000.00
$45,527.50
$137,558.33
Q3
$272,558.33
–255,665.83
$16,892.50
135,000.00
–$118,107.50
Q4
$16,892.50
114,957.58
$131,850.08
135,000.00
–$3,149.92
$114,957.58
C-82 CASE SOLUTIONS
The short-term financial plan looks like this:
Target cash balance
Net cash inflow
New short-term investments
Income on short-term investments
Short-term investments sold
New short-term borrowing
Interest on short-term borrowing
Short-term borrowing repaid
Ending cash balance
Minimum cash balance
Cumulative surplus –deficit
Beginning short-term investments
Ending short-term investments
Beginning short-term debt
Ending short-term debt
Short-term Financial Plan
$135,000.00
$135,000.00
–29,472.50
92,030.83
0
–92,405.83
375.00
375.00
29,097.50
0
0
0
0
0
0
0
$135,000.00
$135,000.00
–135,000.00
–135,000.00
$0
$0
$75,000.00
75,000.00
0
$0
$75,000.00
167,405.83
0
$0
$135,000.00
–255,665.83
0
837.03
167,405.83
87,422.97
0
0
$135,000.00
–135,000.00
$0
$135,000.00
114,957.58
–26,485.54
0
0
0
–1,049.08
–87,422.97
$135,000.00
–135,000.00
$0
$167,405.83
0
0
$87,422.97
$0
26,485.54
87,422.97
$0
The interest calculations for each quarter and the net cash cost are:
Q1:
Q2:
Q3:
Q4:
Excess funds at start of quarter of
Excess funds at start of quarter of
Excess funds at start of quarter of
Shortage of funds at start of quarter of
Net cash cost
Q1
Q2
Q3
Q4
Cash generated by short-term financing
$75,000.00
$75,000.00
$167,405.83
$87,422.97
$375.00
375.00
837.03
–1,049.08
$537.95
earns
earns
earns
costs
$375.00
$375.00
$837.03
$1,049.08
in income.
in income.
in income.
in interest.
CHAPTER 26 CASE C-83
4.
Since the only period in which there is borrowing is the third period, we can set the ending shortterm debt in Quarter 3 equal to zero and use Solver. Doing so, we find the necessary sales growth
rate is 21 percent. The short-term financial plan would be:
Collections from previous quarter
Collections from current quarter
sales
Payments to suppliers for
previous quarter
Payments to suppliers for current
quarter
Expenses
Dividends and interest
Outlay
Net cash flow
Beginning cash balance
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus –deficit
Cash Flow
Q1
Q2
$607,500.00
$844,499.33
Q3
$874,386.33
Q4
$862,125.00
488,920.67
506,223.67
499,125.00
471,617.67
–392,618.11
–406,512.94
–400,812.50
–378,723.28
–283,792.06
–333,355.00
–185,000.00
–279,812.50
–345,152.50
–185,000.00
–331,651.19
–321,557.50
–185,000.00
–$98,344.50
$134,245.06
–264,391.72
–340,312.50
–185,000.00
–390,000.00
–$207,005.39
Cash Balance
Q1
Q2
$210,000.00
$111,655.50
–98,344.50
134,245.06
$111,655.50
$245,900.56
135,000.00
135,000.00
–$23,344.50
$110,900.56
Q3
$245,900.56
–207,005.39
$38,895.17
135,000.00
–$96,104.83
Q4
$38,895.17
116,810.70
$155,705.87
135,000.00
$20,705.87
$116,810.70
C-84 CASE SOLUTIONS
The short-term financial plan looks like this:
Target cash balance
Net cash inflow
New short-term investments
Income on short-term investments
Short-term investments sold
New short-term borrowing
Interest on short-term borrowing
Short-term borrowing repaid
Ending cash balance
Minimum cash balance
Cumulative surplus –deficit
Short-term Financial Plan
$135,000.00
$135,000.00
–98,344.50
134,245.06
0
–134,620.06
375.00
375.00
97,969.50
0
0
0
0
0
0
0
$135,000.00
$135,000.00
–135,000.00
–135,000.00
$0
$0
Beginning short-term investments
Ending short-term investments
Beginning short-term debt
Ending short-term debt
$75,000.00
75,000.00
0
$0
$75,000.00
209,620.06
0
$0
$135,000.00
–207,005.39
0
1,048.10
205,957.29
0
0
0
$135,000.00
–135,000.00
$0
$135,000.00
116,810.70
–116,829.02
18.31
0
0
0
0
$135,000.00
–135,000.00
$0
$209,620.06
3,662.77
0
$0
$3,662.77
120,491.78
0
$0
The interest calculations for each quarter and the net cash cost are:
Q1:
Q2:
Q3:
Q4:
Excess funds at start of quarter of
Excess funds at start of quarter of
Excess funds at start of quarter of
Excess funds at start of quarter of
Net cash cost
Q1
Q2
Q3
Q4
Cash generated by short-term financing
$75,000.00
$75,000.00
$209,620.06
$3,662.77
$375.00
375.00
1,048.10
18.31
$1,816.41
earns
earns
earns
earns
$375.00
$375.00
$1,048.10
$18.31
in income.
in income.
in income.
in income.
CHAPTER 27
CASH MANAGEMENT AT RICHMOND
CORP.
1.
The amount the company will have available is the future value of the transfers, which are an
annuity. The amount of each transfer is one minus the wire transfer cost, times the number of
transfers, which is four since there are four banks, times the amount of each transfer. So, the total
available in two weeks will be:
Amount available = (1 – .002){4[$185,000(FVIFA.068%,14)]}
Amount available = $10,385,104.15
2.
The bank will accept the ACH transfers from the four different banks, so the company incurs a
transfer fee from each collection center. The future value of the deposits will now be:
Value of ACH = [4($185,000 – 200)(FVIFA.075%,14)]/1.00075
Value of ACH = $10,391,608.36
The company should go ahead with the plan since the future value is higher.
3.
To find the cost at which the company is indifferent, we set the amount available we found in
Question 1 equal to the cost equation we used in Question 2. Setting up this equation where X stands
for the ACH transfer cost, we find:
[4($185,000 – $X)(FVIFA.075%,14)]/1.00075 = $10,385,104.15
X = $315.67
CHAPTER 28
CREDIT POLICY AT BRAAM
INDUSTRIES
To decide on the optimal credit policy, we need to calculate the NPV of each policy. We will begin with
the calculation of the NPV of the current policy.
Current Policy
First, we need to calculate the average daily sales, which are:
Average daily sales = $113,000,000/365
Average daily sales = $309,589.04
Now, we need to calculate the daily interest rate:
Daily interest rate = (1 + .06)1/365 – 1 = .01597%
Next, we need the average daily costs. We will begin with the average daily variable costs, which are 45
percent of sales. So, the average daily variable costs are:
Average daily variable costs = .45($113,000,000/365)
Average daily variable costs = $139,315.07
Under the current policy, the default rate is 2.1 percent, so the average daily defaults will be:
Average daily defaults = .021($113,000,000/365)
Average daily defaults = $6,501.37
The current policy has administrative costs equal to 1.6 percent of sales, so the average daily
administrative costs are:
Average daily administrative costs = .016($113,000,000/365)
Average daily administrative costs = $4,953.42
We also need the appropriate interest rate for the collection period. With a .01597 percent daily interest
rate, the periodic rate for the 38 day collection period is:
Interest rate = (1 + .0001597)38 – 1
Interest rate = .00609, or .609%
Since the credit policy will exist into perpetuity, the NPV is:
NPV = –$139,315.07 + ($309,589.04 – 139,315.07 – 6,501.37 – 4,953.42)/.00609
NPV = $25,961,698.61
CHAPTER 28 CASE C-87
Option 1
Under Option 1, the average daily sales are:
Average daily sales = $129,000,000/365
Average daily sales = $353,424.66
The average daily variable costs will be:
Average daily variable costs = .45($129,000,000/365)
Average daily variable costs = $159,041.10
Under Option 1, the default rate is 2.6 percent, so the average daily defaults will be:
Average daily defaults = .026($129,000,000/365)
Average daily defaults = $9,189.04
Option 1 has administrative costs equal to 2.4 percent of sales, so the average daily administrative costs
are:
Average daily administrative costs = .024($129,000,000/365)
Average daily administrative costs = $8,482.19
We also need the appropriate interest rate for the collection period. With a .01597 percent daily interest
rate, the periodic rate for the 41-day collection period is:
Interest rate = (1 + .0001597)41 – 1
Interest rate = .00657, or .657%
Since the credit policy will exist into perpetuity, the NPV is:
NPV = –$159,041.10 + ($353,424.66 – 159,041.10 – 9,189.04 – 8,482.19)/.00657
NPV = $26,751,158.21
Option 2
Under Option 2, the average daily sales are:
Average daily sales = $127,000,000/365
Average daily sales = $347,945.21
The average daily variable costs will be:
Average daily variable costs = .45($127,000,000/365)
Average daily variable costs = $156,575.34
Under Option 2, the default rate is 2.2 percent, so the average daily defaults will be:
Average daily defaults = .022($127,000,000/365)
Average daily defaults = $7,654.79
C-88 CASE SOLUTIONS
Option 2 has administrative costs equal to 1.9 percent of sales, so the average daily administrative costs
are:
Average daily administrative costs = .019($127,000,000/365)
Average daily administrative costs = $6,610.96
We also need the appropriate interest rate for the collection period. With a .01597 percent daily interest
rate, the periodic rate for the 51 day collection period is:
Interest rate = (1 + .0001597)51 – 1
Interest rate = .00818, or .818%
Since the credit policy will exist into perpetuity, the NPV is:
NPV = –$156,575.34 + ($347,945.21 – 156,575.34 – 7,654.79 – 6,610.96)/.00818
NPV = $21,507,756.71
Option 3
Under Option 3, the average daily sales are:
Average daily sales = $130,000,000/365
Average daily sales = $356,164.38
The average daily variable costs will be:
Average daily variable costs = .45($130,000,000/365)
Average daily variable costs = $160,273.97
Under Option 3, the default rate is 2.5 percent, so the average daily defaults will be:
Average daily defaults = .025($130,000,000/365)
Average daily defaults = $8,904.11
Option 3 has administrative costs equal to 2.1 percent of sales, so the average daily administrative costs
are:
Average daily administrative costs = .021($130,000,000/365)
Average daily administrative costs = $7,479.45
We also need the appropriate interest rate for the collection period. With a .01597 percent daily interest
rate, the periodic rate for the 49-day collection period is:
Interest rate = (1 + .0001597)49 – 1
Interest rate = .00785, or .785%
Since the credit policy will exist into perpetuity, the NPV is:
NPV = –$160,273.97 + ($356,164.38 – 160,273.97 – 8,904.11 – 7,479.45/.00785
NPV = $22,697,882.88
CHAPTER 28 CASE C-89
The company should choose Option 1 since it has the highest NPV.
The default rate and administrative costs of Option 2 are below those of Option 3. This is plausible.
Option 2 extends the credit period, while Option 3 extends the credit period and relaxes the credit policy.
The relaxation of the credit policy will increase the default rate since it will include companies with lower
credit ratings who are less likely to pay. This, in turn, will increase the administrative costs of managing
the delinquent accounts.
CHAPTER 29
THE BIRDIE GOLF-HYBRID GOLF
MERGER
1.
As with any other merger analysis, we need to examine the present value of the incremental cash
flows. The cash flow today from the acquisition is the acquisition cost plus the dividends paid today,
or:
Acquisition of Hybrid
Dividends from Hybrid
Total
–$282,000,000
76,000,000
–$206,000,000
Using the information provided, the cash flows to Birdie Golf from acquiring Hybrid Golf for the
next five years will be:
Dividends from Hybrid
Tax-loss carryforwards
Terminal value of
equity
Terminal value of debt
Total
Year 1
Year 2
Year 3
$24,877,500 $12,630,000 $21,950,000
12,800,000 12,800,000
$24,877,500 $25,430,000 $34,750,000
Year 4
$11,925,000
Year 5
$37,800,000
$11,925,000
460,800,000
–153,600,000
$652,200,000
To discount the cash flows from the merger, we must discount each cash flow at the appropriate
discount rate. The additional cash flows from the tax-loss carry forwards and the proposed level of
debt should be discounted at the cost of debt because they are determined with very little uncertainty.
The terminal value of the company is subject to normal business risk and must be discounted at a
normal rate. The current weight of debt and weight of equity in Hybrid’s capital structure is:
wD = .50/(1 + .50)
wD = .33
wE = 1 – .33
wE = .67
The beta for Hybrid’s debt is:
D = (.08 – .06)/(.13 – .06)
D = .29
CHAPTER 29 CASE C-91
Thus, the overall beta for Hybrid is:
H = (.33 × .29) + (.67 × 1.30)
H = .96
Now, we can calculate the required return for normal operations of Hybrid, which is:
E(RH) = .06 + .96(.13 – .06)
E(RH) = .1273, or 12.73%
To find the discount rate for dividends, we need to find the new beta of equity for the merged
Hybrid. The new debt-equity ratio is 1, which implies a weight of debt and a weight of equity equal
to 50 percent. The new beta for equity must be:
New = [Old – (wD–new × wD–old]/wE–new
New = [.96 – (.50 × .33)]/.50
New = 1.59
So, the discount rate for the dividends to be paid in future is:
E(RDiv) = .06 + 1.59(.13 – .06)
E(RDiv) = .1713, or 17.13%
Now we can find the present value of the future cash flows. The present value of each year’s cash
flows, along with the appropriate discount rate for each cash flow, is:
Dividends
Tax-loss
TV of equity
TV of debt
Total
Discoun
t
rate
17.13%
8%
12.73%
8%
Year 1
$21,238,617
Year 2
Year 3
$9,205,393 $13,658,186
10,973,937 10,161,053
$21,238,617 $20,179,330 $23,819,239
Year 4
$6,334,851
Year 5
$17,143,097
$6,334,851
253,075,864
(104,537,579)
$165,681,382
And the NPV of the acquisition is:
NPV = –$206,000,000 + 21,238,617 + 20,179,330 + 23,819,239 + 6,334,851 + 165,681,382
NPV = $31,253,418.08
C-92 CASE SOLUTIONS
2.
Since the acquisition is a positive NPV project, the most Birdie would offer is to increase the current
cash offer by the current NPV, or:
Highest offer = $282,000,000 + 31,253,418.08
Highest offer = $313,253,418.08
The highest share price is the total high offer price, divided by the shares outstanding, or:
Highest share price = $313,253,418.08/5,200,000 shares
Highest share price = $60.24
3.
To determine the current exchange ratio which would make a cash offer and a share offer equivalent,
we need to determine the new share price under the original cash offer. The new share price of Birdie
after the merger will be:
PNew = [$94 × 11,600,000 + $31,253,418.08]/11,600,000
PNew = $96.69
So, the exchange ratio which would make the cash offer and share offer equivalent is:
Exchange ratio = $63.25/$96.69
Exchange ratio = .6541
4.
The highest exchange ratio Birdie would accept is an exchange ratio that results in a zero NPV
acquisition. This implies the share price of Birdie remains unchanged after the merger, so the
exchange ratio is:
Exchange ratio = $63.25/$94
Exchange ratio = .6729
CHAPTER 31
EAST COAST YACHTS GOES
INTERNATIONAL
1.
The biggest advantage is the increased sales, while the biggest risk is exchange rate risk.
2.
If the dollar strengthens, the profit will decline. Conversely, if the dollar weakens, the profit
will increase.
3.
The company will pay the sales commission out of gross sales, so the after-commission sales
in euros is:
After-commission sales = €8,000,000(1 – .05)
After-commission sales = €7,600,000
At the current exchange rate of $1.34/€, the EBT in euros will be converted to dollars in the
amount of:
Dollar EBT = €7,600,000($1.34/€)
Dollar EBT = $10,184,000
East Coast Yachts has production costs equal to 80 percent of dollar sales at this exchange
rate. The total sales in dollars are:
Total sales = €8,000,000($1.34/€)
Total sales = $10,720,000
And the production costs are:
Production costs = $10,720,000(.80)
Production costs = $8,576,000
So, the profit at the current exchange rate is:
Profit = $10,184,000 – 8,576,000
Profit = $1,608,000
If the exchange rate changes to $1.25/€, the euros will convert to:
Dollar sales = €7,600,000($1.25/€)
Dollar sales = $9,500,000
Since the production costs are fixed, the profit at this exchange rate will be:
Profit = $9,500,000 – 8,576,000
Profit = $924,000
C-94 CASE SOLUTIONS
The break-even exchange rate is the exchange rate that will allow the after-commission costs
in euros to convert to a dollar amount that covers the production costs, so:
Break-even exchange rate = $8,576,000/€7,600,000
Break-even exchange rate = $1.1284/€
4.
The company could use options, futures, or forwards. The downside to all three hedging
vehicles is the cost. Over time, the company will gain on some contracts and lose on others.
5.
At the current exchange rate, the company will make a profit unless the exchange rate moves
dramatically. So, it is likely that hedging is not required at this point. Taking this into
account, the company should probably pursue international sales further.