2-1A.
Belmond, Inc.
Balance Sheet
As at December 31, 2003
ASSETS
Current assets
Cash
Accounts receivable
Inventory
Total current assets
Gross buildings & equipment
Accumulated depreciation
Net buildings & equipment
Total assets
$ 16,550
9,600
6,500
$ 32,650
$122,000
(34,000)
$ 88,000
$120,650
LIABILITIES AND EQUITY
Liabilities
Current Liabilities
Notes payable
Accounts payable
Total current liabilities
Long-term debt
Total liabilities
Equity
Common stock
Retained earnings
Total equity
Total liabilities and equity
$
600
4,800
$ 5,400
55,000
$ 60,400
$ 45,000
15,250
$ 60,250
$120,650
Belmond, Inc.
Income Statement
For the Year Ended December 31, 2003
Sales
Cost of goods sold
Gross profits
General & admin expense
Depreciation expense
Total operating expense
Operating income (EBIT)
Interest expense
Earnings before taxes
Taxes
Net income
$ 12,800
5,750
$ 7,050
$
850
500
$
$
$
$
1
1,350
5,700
900
4,800
1,440
3,360
2-6A.
T.P. Jarmon
Statement of Cash Flows
For the Year ended December 31, 2003
Operating Activities
Net Income
Adjustments to convert net income to a cash basis
Depreciation
Decrease in accounts receivable
Increase in inventory
Decrease in prepaid rent
Increase in accounts payable
Decrease in accrued expenses
Net cash provides by operating activities
$ 42,900
30,000
9,000
(33,000)
100
9,000
(1,000)
57,000
Investing Activities
Purchase of fixed assets
Net cash used in investing activities
(14,000)
(14,000)
Financing Activities
Decrease in notes payable
Decrease in long-term debt
Cash dividends paid
Net cash used in financing activities
(2,000)
(10,000)
(31,800)
(43,800)
Net decrease in cash and cash equivalents
Cash and cash equivalents at beginning of year
Cash and cash equivalents at end of year
2
$
(800)
21,000
20,200
3-3A.
Current ratio 
Debt ratio 
$3,500
$2,000
current assets
=
current liabilitie s
total debt
total assets
Average collection period
Inventory turnover
$4,000
$8,000
=
operating income
interest expense
Times interest earned =
=
=
net sales
=
fixed assets
Total asset turnover
=
net sales
total assets
=
Operating
income return 
on investment
Return on
equity

$8,000
$4,500
$8,000
$8,000
$4,700
$8,000
=
operating income
net sales
operating income
total assets
net income
common equity
.50 or 50%
$1,700
$367
$3,300
$1,000
=
gross profit
net sales
Operating profit margin 
=
=
=
Fixed asset turnover
Gross profit margin
1.75X
= 4.63X
accounts receivable
$2,000
=
=91 days
credit sales / 365
$8,000 / 365
cost of
goods sold
inventory
=
=
=
$800
$4,000
=
or, we can calculate return on equity as:
= Return on assets ÷ (1- debt ratio)
=
Net income
Total debt 

÷ 1 

Total assets
 Total assets 
=
800
 1 - .50  = .20 or 20%
8,000
3
=
=
3.3X
1.78X
=
1X
=
.59 or 59%
$1,700
=
$8,000
.21 or 21%
$1,700
$8,000
=
=
=
.21 or 21%
.20 or 20%
3-7A. a.
Salco’s total asset turnover, operating profit margin, and operating income
return on investment.
Total Asset Turnover
=
Sales
Total Assets
=
$4,500,000
$2,000,000
=
2.25 times
Operating Income
Sales
Operating Profit Margin =
Operating Income
Return on Investment
or
=
$500,000
$4,500,000
=
11.11%
=
Operating Income
Total Assets
=
$500,000
$2,000,000
=
25%
=
Operating Income
Sales
x
Sales
Total Assets
=
.1111 X 2.25
=
25%
b.The new operating income return on investment for Salco after the plant renovation:
Operating Income
Return on Investment
c.
=
Operating Income
Sales
=
.13 x
=
.13 x 1.5
=
19.5%
x
Sales
Total Assets
$4,500,000
$3,000,000
Return earned on the common stockholders’ investment:
Post-Renovation Analysis:
Net Income Available
Return on common
equity
to Common Stockholde rs
Common Equity
=
$217,500
=
$1,000,000  $500,000
=
4
14.5%
Net income available to common stockholders following the renovation was
calculated as follows:
Operating Income (.13 x $4.5m)
$ 585,000
Less: Interest ($100,000 + $50,000)
(150,000)
Earnings Before Taxes
435,000
Less: Taxes (50%)
(217,500)
Net Income Available to Common Stockholders
$ 217,500
The increase in Common equity was calculated as follows:
Total assets purchased
$ 1,000,000
Less: Increase in debt ($1,500,000 - $1,000,000)
Increase in equity to finance purchase
(500,000)
$ 500,000
The computation above is measuring the return on equity based on the
beginning-of-the-year common equity. The equity would increase $217,500 by
year end.
Pre-renovation Analysis:
The pre-renovation rate of return on common equity is calculated as follows:
Return on Common Equity
=
$200,000
$1,000,000
=
20%
Comparative Analysis:
A comparison of the two rates of return would argue that the renovation not be
undertaken. However, since investments in fixed assets generally produce cash
flows over many years, it is not appropriate to base decisions about their
acquisition on a single year’s ratios. There are additional problems with this
approach to fixed asset decision making which we will discover when we
discuss capital budgeting in a later chapter.
Instructor’s Note: To help convince those students who simply cannot accept
the fact that the renovation may be worthwhile even though the return on
common equity falls in the first year, we note that the existing plant is recorded
on the firm’s books at original cost less accounting depreciation. In a period of
rising replacement costs, this means that the return on common equity of 20%
without renovation may actually overstate the true return earned on a more
realistic “replacement cost” common equity base. In addition, the issue is
probably one of when to renovate (this year or next) rather than whether or not
to renovate. That is, the existing facility may require renovation in the next two
years to continue to operate. These considerations simply cannot be
incorporated in the ratio analysis performed here. We find this a very useful
point to make at this juncture of the course since industry practice still
5
frequently involves use of rules of thumb and ratio guides to the analysis of
capital expenditures.
3-8A.
T.P. Jarmon
a.
See the accompanying table.
b.
The most important ratios to consider in evaluating the firm’s credit request
relate to its liquidity and use of financial leverage. However, the credit analyst
can also evaluate the firm’s profitability ratios as a general indication as to how
effective the firm’s management has been in managing the resources available
to it. This latter analysis would be useful in evaluating the prospects for a long
and fruitful relationship with the new client.
c.
The DuPont Analysis for Jarmon is shown in the graph on the next page. The earning
power analysis provides an in-depth basis for analyzing Jarmon’s only deficiency, that relating
to its relatively large investment in inventories. However, even this potential weakness is
largely overcome by the firm’s strengths. The firm’s return on assets and its return on owner
capital (return on common equity) both compare well with the respective industry norms.
6
Calculation
Average
Current Ratio
Current Assets
Current Liabilities
$138,300
= 1.84
$75,000
1.8
Acid-Test Ratio
Current Assets - Inventory
Current Liabilitie s
$138,300  84,000
= .72
$75,000
.9
Debt Ratio
Total Debt
Total Assets
$225,000
$408,300
.5
Times Interest
Earned
Net Operating Income
Interest Expense
= .55
$80,000
= 8
$10,000
10
43
Average Collection
Period
Accounts Receivable
Credit Sales per Day
$33,000
$600,000 / 365
Inventory Turnover
Cost of Goods Sold
Inventory
$460,000
$84,000
Operating Income
Return on Investment
Operating Income
Total Assets
$80,000
= .196
$408,300
or 19.6%
Operating Profit
Margin
Operating Income
Sales
$80,000
= .133
$600,000
or 13.3%
=
= 5.48
20.1
days
20
days
7
16.8%
14%
Ratio
Formula
Calculation
Industry
Average
44
Gross Profit
Margin
Gross Profit
Sales
$140,000
= .233
$600,000
or 23.3%
Total Asset
Turnover
Sales
Total Assets
$600,000
= 1.47
$408,300
1.2
Fixed Asset
Turnover
Sales
Net Fixed Assets
$600,000
= 2.22
$270,000
1.8
Return on Assets
Net Income
Total Assets
$42,900
= .1051
$408,300
or 10.51%
Return on Equity
Earnings Available to
Common Stockholde rs
Common Equity
$42,900
= .234
$183,300
or 23.4%
25%
6%
12%
Return on Equity
23.4%
Return on Assets
10.51%
Net Profit Margin
Equity
Total Assets
0.45
divided by
Total Asset Turnover
multipled by
7.15%
Net Income
1.47
divided by
$42,900
Sales
$600,000
Sales
$600,000
divided by Total Assets
$408,300
Sales
$600,000
Fixed Assets
Current Assets
$138,300
$270,000
Other Assets
$0
less
Total costs and expenses
$557,100
Cost of goods sold
$460,000
Cash and
Marketable
Securites
$20,200
Accounts
Receivable
$33,000
Cash operating expenses
$30,000
Depreciation
$30,000
Inventory
Collection Period
Sales
$600,000
÷
Fixed
Assets
$270,000
Other Current
Assets
$1,100
20.08 days
Interest Expense
$10,000
Taxes
$27,100
$84,000
Fixed Assets
Turnover
2.22
Inventory Turnover
5.48
Daily Credit
Accounts
Sales
Receivables divided by
$33,000
$1,644
Cost of
Goods Sold divided by
$460,000
1
Inventory
$84,000
4-4A
(a)
Projected Financing Needs = Projected Total Assets
= Projected Current Assets + Projected Fixed Assets
$5m
{ $15m
=
(b)
x $20 m
} +{ $5m + $.1m} = $11.77m
DFN = Projected Current Assets + Projected Fixed Assets
- Present LTD - Present Owner's Equity
- [Projected Net Income - Dividends]
- Spontaneous Financing
$5m
{ $15m
=
x $20m
} + $5.1m - $2m
- $6.5m
{ $1.5m
$15m
}
- [.05 x $20m - $.5m] -
x $20m
DFN = $6.67m + $5.1m - $8.5m - $.5m - $2m = $.77m
(c)
We first solve for the maximum level of sales for which DFN = 0:
DFN = (
5
1.5
- .05 ) Sales – (5.1M-2M-6.5M +.5M)
15
15
DFN = .1833 SALES - $2.9M = 0
Thus, SALES = $15.82M
The largest increase in sales that can occur without a need to raise
"discretionary funds" is
$15.82M - $15M = $820,000.
2
4-6A. (a)
The Sharpe Corporation Cash Budget Worksheet
Nov
July
$220,000
67
Sales
Collections:
Month of sale (10%)
First month (60%)
Second month (30%)
Total Collections
Purchases
Payments (one month lag)
Cash Receipts
(collections)
Cash Disbursements
Purchases
Rent
Other Expenditures
Tax Deposits
Interest on Short-Term
Borrowing
Total Disbursements
Net Monthly Change
Beginning Cash Balance
Additional Financing
Needed (Repayment)
Ending Cash Balance
Cumulative Borrowing
(b)
Dec
Jan
$175,000
Feb
Mar
Apr
$ 90,000
$120,000
$135,000
$240,000
9,000
105,000
66,000
180,000
81,000
72,000
12,000
54,000
52,500
118,500
144,000
81,000
13,500
72,000
27,000
112,500
180,000
144,000
24,000
81,000
36,000
141,000
162,000
180,000
180,000
118,500
112,500
141,000
2
72,000
10,000
20,000
81,000
10,000
20,000
144,000
10,000
20,000
22,500
180,000
10,000
20,000
1
_______
$102,000
$78,000
22,000
_______
$111,000
$7,500
100,000
_______
$196,500
($84,000)
107,500
_______
$210,000
($69,000)
23,500
$1
$
________
$100,000
0
_______
$107,500
0
________
$ 23,500
0
60,500
$15,000
$ 60,500
(2
$
$
72,000
The firm will have sufficient funds to cover the $200,000 note payable due
in July. In fact, if the firm's estimates are realized they will have $222,009
in cash by the end of July.
3
$3
1
2
1
1
4-9A.
(a)
Estimating Future Financing Needs
Armadillo Dog Biscuit Co., Inc.
Projected Need for Discretionary Financing
Present
Level
Current Assets
$2.0m
Net Fixed Assets
$3.0m
Total
$.5m
Accrued Expenses
$.5m
1
Notes Payable
Current Liabilities
Long-Term Debt
Common Stock
2
Retained Earnings
Common Equity
Total
2
$2m
$5m = .40 or 40%
$3m
$5m = .60 or 60%
Projected Level
(Based on $7m Sales)
.40 x $7m = $ 2.8m
.60 x $7m = $ 4.2m
$5.0m
Accounts Payable
1
% of Sales
($5m)
$ 7.0m
$.5m
$5m = .10 or 10%
.10 x 7m = .7m
$.5m
.10 x 7m = .7m
$5m = .10 or 10%
---------Plug Figure = 1.11m
$1.0m
$ 2.51m
$2.0m
No Change
$2.00m
.5m
No Change
.50m
1.5m
$1.5m + .07 x $7m =
$ 1.99m
$2.0m
$2.49m
$5.0m
$ 7.00m
Notes payable is a balancing figure which equals discretionary financing needed, DFN, which equals: Total
Assets - Accounts Payable - Accrued Expenses - Long-Term Debt - Common Stock - Retained Earnings =
$7.0m - $0.7m - $0.7m - $2.0m - $0.5m - $1.99m = $1.11m.
The projected retained earnings is the sum of the beginning balance of $1.5m plus net income for the period
(.07 x $7m).
(b)
Current Ratio
Before
$2m
$1m = 2 times
After
$2.8m
$2.51m =
$3m
$5m = .60 or 60%
$4.51m
$7.0m
1.12
times
Debt Ratio
=
.644 or
64.4%
The growth in the firm's assets (due to the projected increase in sales) was
financed predominantly with notes payable (a current liability). This led
to a substantial deterioration in both the firm's liquidity (as reflected in the
current ratio) and an increase in its use of financial leverage.
4
6-4A.
Common Stock A:
(A)
Probability
P(ki)
(B)
Return
(ki)
(A) x (B)
Expected Return
k
Weighted
Deviation
(ki - k )2P(ki)
0.3
0.4
0.3
11%
15
19
3.3%
6.0
5.7
15.0%
4.8%
0.0
4.8
9.6%
3.10%
k =
2 =
 =
Common Stock B
(A)
Probability
P(ki)
(B)
Return
(ki)
(A) x (B)
Expected Return
k
0.2
0.3
0.3
0.2
-5%
6
14
22
-1.0%
1.8
4.2
4.4
9.4%
k =
Weighted
Deviation
(ki - k )2P(ki)
41.472%
3.468
6.348
31.752
2 = 83.04%
 = 9.11%
Common Stock A is better. It has a higher expected return with less risk.
6-6A.
(a)
Required rate
Risk-free
Market Risk
=
+
Beta
 of return 
 rate 
 Premium 
= 6 % + 1.2 (16% - 6%)
= 18%
(b)
The 18 percent "fair rate" compensates the investor for the time value of
money and for assuming risk. However, only nondiversifiable risk is
being considered, which is appropriate.
a.
The portfolio expected return, k p, equals a weighted average of the
individual stock's expected returns.
6-13A.
kp
=
(0.20)(16%) + (0.30)(14%) + (0.15)(20%) + (0.25)(12%) +
(0.10)(24%)
5
=
b.
15.8%
The portfolio beta, ßp, equals a weighted average of the individual stock betas
ßp
c.
=
(0.20)(1.00) + (0.30)(0.85) + (0.15)(1.20) + (0.25)(0.60) +
(0.10)(1.60)
=
0.95
Plot the security market line and the individual stocks
25.00
5
3
Expected Return
20.00
P 1
M
2
15.00
4
10.00
5.00
0.00
0.00
0.50
1.00
1.50
2.00
Beta
d.
A "winner" may be defined as a stock that falls above the security market
line, which means these stocks are expected to earn a return exceeding
what should be expected given their beta or systematic risk. In the above
graph, these stocks include 1, 3, and 5. "Losers" would be those stocks
falling below the security market line, which are represented by stocks 2
and 4 ever so slightly.
e.
Our results are less than certain because we have problems estimating the
security market line with certainty. For instance, we have difficulty in
specifying the market portfolio.
6
7-7A. a.
b.
Value
Par Value
Coupon
Required Rate of Return
Years to Maturity
Market Value
$1,000.00
$ 100.00
0.12
15
$ 863.78
Value at Alternative Rates of Return
Required Rate of Return
Market Value
0.15
$ 707.63
Required Rate of Return
Market Value
0.08
$1,171.19
c.
As required rates of return change, the price of the bond changes, which is
the result of "interest-rate risk." Thus, the greater the investor's required
rate of return, the greater will be his/her discount on the bond.
Conversely, the less his/her required rate of return below that of the
coupon rate, the greater the premium will be.
d.
Value at Alternative Maturity Dates
Years to Maturity
Required Rate of Return
Market Value
Required Rate of Return
Market Value
e.
5
0.15
$ 832.39
0.08
$1,079.85
The longer the maturity of the bond, the greater the interest rate risk the
investor is exposed to, resulting in greater premiums and discounts.
7-13A.
Value Bond I
Par Value
Coupon
Required Rate of Return
Years to Maturity
Market Value
$1,000.00
$ 130.00
7%
7
$ 1,323.36
Value Bond II
Par Value
Coupon
Required Rate of Return
Years to Maturity
Market Value
$1,000.00
$ 90.00
7%
6
$1,095.33
Value Bond III
Par Value
Coupon
Required Rate of Return
Years to Maturity
$1,000.00
$ 110.00
7%
12
7
Market Value
$1,317.71
Value Bond IV
Par Value
Coupon
Required Rate of Return
Years to Maturity
Market Value
$1,000.00
$ 125.00
7%
5
$1,225.51
Value Bond V
Par Value
Coupon
Required Rate of Return
Years to Maturity
Market Value
$1,000.00
$ 80.00
7%
10
$1,070.24
Bond
I
II
III
IV
V
Bond
Value
$1,323.36
$1,095.33
$1,317.71
$1,225.51
$1,070.24
Years
Ct
tPV(Ct)
Ct
tPV(Ct)
Ct
tPV(Ct)
Ct
tPV(Ct)
Ct
tPV(Ct)
1
$130
$121
$90
$84 $110
$103
$125
$117
$80
$75
2
$130
$227
$90
$157 $110
$192
$125
$218
$80
$140
3
$130
$318
$90
$220 $110
$269
$125
$306
$80
$196
4
$130
$397
$90
$275 $110
$336
$125
$381
$80
$244
5
$130
$463
$90
$321 $110
$392 $1,125 $4,011
$80
$285
6
$130
$520 1,090 $4,358 $110
$440
$80
$320
7
1,130 $4,926
$110
$480
$80
$349
8
$110
$512
$80
$372
9
$110
$538
$80
$392
10
$110
$559
$1,080 $5,490
11
1,110 $5,801
12
Sum of
t*PV(Ct)
$6,973
$5,415
$9,622
$5,033
$7,863
Duration
5.27
4.94
7.30
8
4.11
7.35
8-3A.
Value (Vps)
.14  $100
.12
=
=
$14
.12
=
$116.67
k ps
=
Dividend
Price
k ps
=
0.1091, or 10.91%
(b)
Value (Vps)
=
(c)
The investor's required rate of return (10 percent) is less than the expected
rate of return for the investment (10.91 percent). Also, the value of the
stock to the investor ($36) exceeds the existing market price ($33), so buy
the stock.
8-13A.
(a)
8-15A (a)
(b)
$3.60
$33.00
$3.60
Dividend
=
= $36
0.10
Required Rate of Return
Dividend yield: Dividend  stock price =
$1.12
= 0.0229, or 2.29%
$49
Using the nominal average returns of 12.2% for large-company stocks and
the 3.8% nominal average return for U.S. Treasury Bills as shown in Table
6-1, the computation would be as follows:
Expected
rate of return
(c)
=
Expected
rate of return
13.04%
 market risk  free 


rate 
 return
=
risk  free
+ beta 
rate
=
3.8% + 1.10  (12.2% - 3.8%) = 13.04%
=
Dividend in Year 1
+ Growth
Rate
Market Price
=
$1.12
+ g
$49
.1304 = .0229 + g
g = .1075, or 10.75%
8-19A. (a)
Growth rate =
=
(b)
return on equity x retention rate
(17%)  (30%) = 5.1%
(i) If retention rate is 40%:
Growth rate =
=
return on equity x retention rate
(17%)  (40%) = 6.8%
9
(ii) If retention rate is 25%:
Growth rate =
=
return on equity x retention rate
(17%)  (25%) = 4.25%
Solutions to Appendix 8A
8A-1. Using the NVDG model,
g
=
Vcs
=
EPS1
k cs
where kcs
=
the investor's required rate of return
EPS1
=
the firm's earning per share in year 1
+
PV1
k cs  g
the growth rate, which is the firm's earnings retention rate times its return
on equity.
PV1
=
 r x EPS1 x ROE 

 - (r x EPS1)
k cs


r
=
the firm's earnings retention rate
ROE
=
the firm's return on equity investment
=
 (0.65) x ($5) x (0.20) 

 - (0.65 x $5)
0.16


For our problem,
PV1
and
=
$4.0625 - $3.25
=
$0.8125
Vcs =
$5
$0.8125

.16
.16  (0.65)(0.20)
=
$31.25 + $27.08
=
$58.33
Using the more traditional dividend-growth model, we get:
Vcs
=
D1
k cs  g
Since D1
=
EPS1(1 - the retention rate), and
g =
the retention rate x return on equity
$1.75
($5)(1  .65)
=
= $58.33
.03
.16  (.65)(. 20)
8A-2. Given the EPS1 is expected to be $7 and the investor's required rate of return is
18 percent, the value of the stock, assuming no growth opportunities would be:
Vcs
=
10
Vcs
=
EPS1
$7

k cs
.18
where kcs
=
the investor's required rate of return
= $38.89
EPS1 =
the firm's earning per share in year 1
To compute the present value of the growth opportunities, NVDG, for each
scenario, we use the following equation:
NVDG
=
PV1
k cs  g
 r x EPS1 x ROE 

 - (r x EPS1)
k
cs


g
=
the growth rate, which is the firm's earnings retention rate
times its return on equity.
r
=
the firm's earnings retention rate
ROE
=
the firm's return on equity investment
where PV1 =
Given the different possible retention rates and ROEs, we may solve for the
respective PV1s. The results are as follows:
Possible
ROEs
16%
18%
24%
Different Retention Rates
0%
30%
0.00
-0.23
0.00
0.00
0.00
0.70
60%
-0.47
0.00
1.40
We next calculate the NVDG for each scenario by dividing the above PV1 values
by kcs - g, which gives the following results:
Possible
Different Retention Rates
ROEs
0%
30%
60%
16%
0.00
-1.77
-5.56
18%
0.00
0.00
0.00
24%
0.00
6.48
38.89
Adding the $38.89 price, assuming no growth, to the above NVDGs, we get:
Possible
ROEs
16%
18%
24%
Different Retention Rates
0%
30%
38.89
37.12
38.89
38.89
38.89
45.37
60%
33.33
38.89
77.78
Thus, our results show that value is created only when management reinvests at
above the investor's required rate of return. That is, growth may actually decrease
the firm's value if the profitability of the new investments are not adequate
enough to satisfy the investor's required returns.
X
11
9-2A. (a)
(b)
(c)
(d)
9-6A. (a)
I0
=
FCFt [PVIFAIRR%,t yrs]
$10,000
=
$1,993 [PVIFAIRR%,10 yrs]
5.018
=
PVIFAIRR%,10 yrs
Thus, IRR
=
15%
$10,000
=
$2,054 [PVIFAIRR%,20 yrs]
4.869
=
PVIFAIRR%,20 yrs
Thus, IRR
=
20%
$10,000
=
$1,193 [PVIFAIRR%,12 yrs]
8.382
=
PVIFAIRR%,12 yrs
Thus, IRR
=
6%
$10,000
=
$2,843 [PVIFAIRR%,5 yrs]
3.517
=
PVIFAIRR%,5 yrs
Thus, IRR
=
13%
NPVA
NPVB
(b)
6
$12,000
t 1
(1  .12) t

- $50,000
=
$12,000 (4.111) - $50,000
=
$49,332 - $50,000 = -$668
=
6
$13,000
t 1
(1  .12) t

- $70,000
=
$13,000 (4.111) - $70,000
=
$53,443 - $70,000 = -$16,557
=
$49,332
$50,000
=
0.9866
=
$53,443
$70,000
=
0.7635
$50,000
=
$12,000 [PVIFAIRR%,6 yrs]
4.1667
=
PVIFAIRR%,6 yrs
IRRA
=
11.53%
$70,000
=
$13,000 [PVIFAIRR%,6 yrs]
5.3846
=
PVIFAIRR%,6 yrs
PIA
PIB
(c)
=
12
IRRB
=
3.18%
Neither project should be accepted.
9-7A. (a)
Project A:
Payback Period = 2 years + $100/$200 = 2.5 years
Project A:
Discounted Payback Period Calculations:
Year
Undiscounted
Cash Flows PVIF10%,n
0
1
2
3
4
5
-$1,000
600
300
200
100
500
Cumulative
Discounted Discounted
Cash Flows Cash Flows
1.000
.909
.826
.751
.683
.621
-$1,000
545
248
150
68
311
-$1,000
-455
-207
-57
11
322
Discounted Payback Period = 3.0 + 57/68 = 3.84 years.
Project B:
Payback Period = 2 years + $2,000/$3,000 = 2.67 years
Project B:
Discounted Payback Period Calculations:
Year
Undiscounted
Cash Flows PVIF10%,n
Discounted
Cash Flows
Cumulative
Discounted
Cash Flows
0
1
2
3
-$10,000
5,000
3,000
3,000
1.000
.909
.826
.751
-$10,000
4,545
2,478
2,253
-$10,000
-5,455
-2,977
-724
4
5
3,000
3,000
.683
.621
2,049
1,863
1,325
3,188
Discounted Payback Period = 3.0 + 724/2,049 = 3.35 years.
Project C:
Payback Period = 3 years + $1,000/$2,000 = 3.5 years
Project C:
Discounted Payback Period Calculations:
13
Undiscounted
Cash Flows
Year
0
1
2
3
4
5
PVIF10%,n
Discounted
Cash Flows
Cumulative
Discounted
Cash Flows
1.000
.909
.826
.751
.683
.621
-$5,000
909
826
1,502
1,366
1,242
-$5,000
-4,091
-3,265
-1,763
-397
845
-$5,000
1,000
1,000
2,000
2,000
2,000
Discounted Payback Period = 4.0 + 397/1,242 = 4.32 years.
Project
Traditional Payback
Discounted Payback
A
Accept
Reject
B
Accept
Reject
C
Reject
Reject
9-9A. Project A:
$50,000
=
$10,000
(1  IRR A )
1
+
+
$15,000
(1  IRR A )
$25,000
(1  IRR A ) 4
+
2
+
$20,000
(1  IRR A )3
$30,000
(1  IRR A )5
Try 23%
$50,000
=
$10,000(.813) + $15,000(.661) + $20,000(.537)
+ $25,000(.437) + $30,000(.355)
=
$8,130 + $9,915 + $10,740 + $10,925 + $10,650
=
$50,360
=
$10,000(.806) + $15,000(.650) +$20,000(.524)
Try 24%
$50,000
+ $25,000(.423) + $30,000(.341)
Thus, IRR
=
$8,060 + $9,750 + $10,480 + $10,575 + $10,230
=
$49,095
=
just over 23%
=
$25,000 [PVIFAIRR%,5 yrs]
Project B:
$100,000
14
4.00
=
PVIFAIRR%,5 yrs
Thus, IRR
=
8%
$450,000
=
$200,000 [PVIFAIRR%,3 yrs]
2.25
=
PVIFAIRR%,3 yrs
Thus, IRR
=
16%
Project C:
n
9-11A. (a)
(b)
(c)
n
ACOFt
t 0
(1  k)

t

t 0
=
ACIFt (1  k) n  t
(1  MIRR) n
$10,000,000
=
$10,000,000
=
$10,000,000
=
MIRR
=
$10,000,000
=
$10,000,000
=
$10,000,000
=
MIRR
=
$10,000,000
=
$10,000,000
=
$10,000,000
=
MIRR
=
$3,000,000(FVIFA10%10years )
(1  MIRR) 10
$3,000,000(15.937)
(1  MIRR )10
$47,811,000
(1  MIRR )10
16.9375%
$3,000,000(FVIFA12%10years )
(1  MIRR) 10
$3,000,000(17.549)
(1  MIRR )10
$52,647,000
(1  MIRR )10
18.0694%
$3,000,000(FVIFA14%10 years )
(1  MIRR )10
$3,000,000(19.337)
(1  MIRR )10
$58,011,000
(1  MIRR )10
19.2207%
15
10-3A. Change in net working capital equals the increase in accounts receivable and
inventory less the increase in accounts payable = $18,000 + $15,000 - $24,000 =
$9,000.
The change in taxes will be EBIT X marginal tax rate = $475,000 X .34 =
$161,500.
A project’s free cash flows =
Change in earnings before interest and taxes
- change in taxes
+ change in depreciation
- change in net working capital
- change in capital spending
=
+
-
$475,000
$161,500
$100,000
$9,000
$0
= $404,500
10-7A. (a)
Initial Outlay
Outflows:
Purchase price
Increased Inventory
Net Initial Outlay
(b)
$1,000,000
50,000
$1,050,000
Differential annual cash flows (years 1-9)
First, given this, the firm’s net profit after tax can be calculated as:
Revenue
- Cash expenses
- Depreciation*
= EBIT
- Taxes (34%)
= Net income
$1,000,000
560,000
100,000
$340,000
115,600
$224,400
A project’s free cash flows =
Change in earnings before interest and taxes
- change in taxes + change in depreciation
- change in net working capital
- change in capital spending
= $340,000
- $115,600
+ $100,000*
- $0
- $0
= $324,400
*Annual Depreciation on the new machine is calculated by taking the purchase
16
price ($1,000,000) and adding in costs necessary to get the new machine in
operating order (in this case $0) and dividing by the expected life.
(c)
Terminal Cash flow (year 10)
Inflows:
Free Cash flow in year 10
Recapture of working capital (inventory)
Total terminal cash flow
(d)
NPV
$324,400
50,000
$374,400
= $324,400 (PVIFA10%,9 yr.) + $374,400 (PVIF10%, 10 yr.) - $1,050,000
= $324,400 (5.759) + $374,400 (.386) - $1,050,000
= $1,868,220 + $144,518 - $1,050,000
= $962,738
10-9A.
(a)
Initial Outlay
Outflows:
Purchase price
Installation Fee
Increased Working Capital Inventory
Net Initial Outlay
(b)
$100,000
5,000
5,000
$110,000
Differential annual free cash flows (years 1-9)
A project’s free cash flows =
Change in earnings before interest and taxes
- change in taxes
+ change in depreciation
- change in net working capital
- change in capital spending
= $35,000
- $11,900
+ $10,500*
- $0
- $0
= $33,600
* Annual Depreciation on the new machine is calculated by taking the purchase
price ($100,000) and adding in costs necessary to get the new machine in
operating order (the installation fee of $5,000) and dividing by the expected life.
(c)
Terminal Free Cash flow (year 10)
Inflows:
Free Cash flow in year 10
Recapture of working capital (inventory)
Total terminal cash flow
17
$33,600
5,000
$ 38,600
(d)
NPV
$110,000
= $33,600 (PVIFA15%,9 yr.) + $38,600 (PVIF15%, 10 yr.) = $33,600 (4.772) + $38,600 (.247) - $110,000
= $160,339.20 + $9,534.20 - $110,000
= $59,873.40
Yes, the NPV > 0.
18
10-12A
Section I. Calculate the change in EBIT, Taxes, and Depreciation (this becomes an input in the
calculation of Operating Cash Flow in Section II).
Year
0
1
2
Units Sold
70,000
120,000
Sale Price
$300
$300
Sales Revenue
Less: Variable Costs
Less: Fixed Costs
Equals: EBDIT
Less: Depreciation
Equals: EBIT
Taxes (@34%)
$21,000,000
9,800,000
$700,000
$10,500,000
$3,000,000
$7,500,000
$2,550,000
$36,000,000
16,800,000
$700,000
$18,500,000
$3,000,000
$15,500,000
$5,270,000
3
120,000
$300
$36,000,000
16,800,000
$700,000
$18,500,000
$3,000,000
$15,500,000
$5,270,000
264
Section II. Calculate Operating Cash Flow (this becomes an input in the calculation of Free Cash Flow in Section IV).
Operating Cash Flow:
EBIT
$7,500,000
$15,500,000
$15,500,000
Minus: Taxes
$2,550,000
$5,270,000
$5,270,000
Plus: Depreciation
$3,000,000
$3,000,000
$3,000,000
Equals: Operating Cash Flow
$7,950,000
$13,230,000
$13,230,000
Section III. Calculate the Net Working Capital (this becomes an input in the calculation of Free Cash Flows in Section
Change in Net Working Capital:
Revenue:
$21,000,000
$36,000,000
$36,000,000
Initial Working Capital Requirement
$200,000
Net Working Capital Needs:
$2,100,000
$3,600,000
$3,600,000
Liquidation of Working Capital
Change in Working Capital:
$200,000
$1,900,000
$1,500,000
$0
Section IV. Calculate Free Cash Flow (using information calculated in Sections II and III, in addition to the Change in
Free Cash Flow:
Operating Cash Flow
$7,950,000
$13,230,000
$13,230,000
Minus: Change in Net Working Capital
$200,000
$1,900,000
$1,500,000
$0
Minus: Change in Capital Spending
$15,000,000
$0
$0
$0
Free Cash Flow:
($15,200,000)
$6,050,000
$11,730,000
$13,230,000
NPV
$17,461,989
PI
2.15
IRR
45%
Should accept project
19
10-14A.(a)
NPVA =
NPVB
(b)
1  0.101
- $500
=
$636.30 - $500
=
$136.30
$6,000
=
1  0.101
=
$5,454 - $5,000
=
$454
=
$636.30
$500.00
=
1.2726
=
$5,454
$5,000
=
1.0908
$500
=
$700 [PVIFIRR%,1 yr]
0.714
=
PVIFIRR%,1 yr
Thus, IRRA
=
40%
$5,000
=
$6,000 [PVIFIRR%,1 yr]
0.833
=
[PVIFIRR%,1 yr]
PIA
PIB
(c)
$700
- $5,000
Thus, IRRB= 20%
(d)
10-15A.(a)
(b)
If there is no capital rationing, project B should be accepted because it has
a larger net present value. If there is a capital constraint, the problem then
focuses on what can be done with the additional $4,500 freed up if project
A is chosen. If Dorner Farms can earn more on project A, plus the project
financed with the additional $4,500, than it can on project B, then project
A and the marginal project should be accepted.
Payback A
=
3.2 years
Payback B
=
4.5 years
B assumes even cash flow throughout year 5.
NPVA
NPVB
=
5
$15,625
t 1
(1  0.10) t

- $50,000
=
$15,625 (3.791) - $50,000
=
$59,234 - $50,000
=
$9,234
=
$1,000,000
- $50,000
(1  0.10) 5
20
(c)
=
$100,000 (0.621) - $50,000
=
$62,100 - $50,000
=
$12,100
$50,000
=
$15,625 [PVIFAIRR %,5 yrs]
A
3.2
=
PVIFAIRR%,5 yrs
Thus, IRRA
=
17%
$50,000
=
$100,000 [PVIFIRR %,5 yrs]
B
.50
=
PVIFIRR %,5 yrs
B
Thus, IRRB
=
15%
(d)
The conflicting rankings are caused by the differing reinvestment
assumptions made by the NPV and IRR decision criteria. The NPV
criterion assumes that cash flows over the life of the project can be
reinvested at the required rate of return or cost of capital, while the IRR
criterion implicitly assumes that the cash flows over the life of the project
can be reinvested at the internal rate of return.
(e)
Project B should be taken because it has the largest NPV. The NPV
criterion is preferred because it makes the most acceptable assumption for
the wealth maximizing firm.
10-16A.
(a)
(b)
Payback A
=
1.589 years
Payback B
=
3.019 years
NPVA
=
3
$12,590
t 1
(1  0.15) t

=
$12,590 (2.283) - $20,000
=
$28,743 - $20,000
=
$8,743
9
NPVB
- $20,000
=

t 1
$6,625
- $20,000
(1  0.15) t
=
$6,625 (4.772) - $20,000
=
$31,615 - $20,000
(c)
=
$11,615
$20,000
=
Thus, IRRA
=
40%
$20,000
=
Thus, IRRB
=
$6,625 [PVIFAIRR %,9 yrs]
B
30%
21
$12,590 [PVIFAIRR %,3 yrs]
A
(d)
These projects are not comparable because future profitable investment
proposals are affected by the decision currently being made. If project A
is taken, at its termination the firm could replace the machine and receive
additional benefits while acceptance of project B would exclude this
possibility.
(e)
Using 3 replacement chains, project A's cash flows would become:
Year
0
1
2
3
4
5
6
7
8
9
NPVA
=
Cash flow
-$20,000
12,590
12,590
- 7,410
12,590
12,590
- 7,410
12,590
12,590
12,590
9
$12,590
t 1
(1  0.15)

t
- $20,000 -
$20,000
(1  0.15)
3

$20,000
(1  0.15)6
=
$12,590(4.772) - $20,000 - $20,000 (0.658) - $20,000 (0.432)
=
$60,079 - $20,000 - $13,160 - $8,640
=
$18,279
The replacement chain analysis indicated that project A should be selected as the
replacement chain associated with it has a larger NPV than project B.
Project A's EAA:
Step 1: Calculate the project's NPV (from part b):
NPVA =
$8,743
Step 2: Calculate the EAA:
EAAA =
NPV / PVIFA15%, 3 yr.
=
=
$8,743 / 2.283
$3,830
Project B's EAA:
Step 1: Calculate the project's NPV (from part b):
NPVB
=
$11,615
Step 2: Calculate the EAA:
EAAB
=
NPV / PVIFA15%, 9 yr.
=
$11,615 / 4.772
=
$2,434
Project A should be selected because it has a higher EAA.
22
10-17A.(a)
Project A's EAA:
Step1:
Calculate the project's NPV:
NPVA
=
$20,000 (PVIFA10%, 7 yr.) - $50,000
=
$20,000 (4.868) - $50,000
=
$97,360 - $50,000
=
$47,360
Step 2: Calculate the EAA:
EAAA =
NPV / PVIFA10%, 7 yr.
=
$47,360 / 4.868
=
$9,729
Project B's EAA:
Step 1: Calculate the project's NPV:
NPVB
=
$36,000 (PVIFA10%, 3 yr.) - $50,000
=
$36,000 (2.487) - $50,000
=
$89,532 - $50,000
=
$39,532
Step 2: Calculate the EAA:
EAAB
=
NPV / PVIFA10%, 3 yr.
=
$39,532 / 2.487
=
$15,895
Project B should be selected because it has a higher EAA.
(b)
NPV,A
NPV,B
=
$9,729 / .10
=
$97,290
=
$15,895 / .10
=
$158,950
10-18A.(a)
Project
A
B
C
D
E
F
G
Cost
$4,000,000
3,000,000
5,000,000
6,000,000
4,000,000
6,000,000
4,000,000
Profitability
Index
1.18
1.08
1.33
1.31
1.19
1.20
1.18
23
Present Value
of Future
Cash Flows
$4,720,000
3,240,000
6,650,000
7,860,000
4,760,000
7,200,000
4,720,000
NPV
$ 720,000
240,000
1,650,000
1,860,000
760,000
1,200,000
720,000
COMBINATIONS WITH TOTAL COSTS BELOW $12,000,000
Projects
A&B
A&C
A&D
A&E
A&F
A&G
B&C
B&D
B&E
B&F
B&G
C&D
C&E
C&F
C&G
D&E
D&F
D&G
E&F
E&G
F&G
A&B&C
A&B&G
A&B&E
A&E&G
B&C&E
B&C&G
Costs
$ 7,000,000
9,000,000
10,000,000
8,000,000
10,000,000
8,000,000
8,000,000
9,000,000
7,000,000
9,000,000
7,000,000
11,000,000
9,000,000
11,000,000
9,000,000
10,000,000
12,000,000
10,000,000
10,000,000
8,000,000
10,000,000
12,000,000
11,000,000
11,000,000
12,000,000
12,000,000
12,000,000
NPV
$ 960,000
2,370,000
2,580,000
1,480,000
1,920,000
1,440,000
1,890,000
2,100,000
1,000,000
1,440,000
960,000
3,510,000
2,410,000
2,850,000
2,370,000
2,620,000
3,060,000
2,580,000
1,960,000
1,480,000
1,920,000
2,610,000
1,680,000
1,720,000
2,200,000
2,650,000
2,610,000
Thus projects C&D should be selected under strict capital rationing as they
provide the combination of projects with the highest net present value.
(b)
Because capital rationing forces the rejection of profitable projects it is not an optimal strategy
24
11-2A. (a)
_
X
n
=

i 1
_
XA
Xi P(Xi)
= $35,000 (0.10) + $40,000 (0.40) + $45,000 (0.40)
+ $50,000 (0.10)
= $3,500 + $16,000 + $18,000 + $5,000
= $42,500
_
XB
= $10,000 (0.10) + $30,000 (0.20) + $45,000 (0.40)
+ $60,000 (0.20) + $80,000 (0.10)
= $1,000 + $6,000 + $18,000 + $12,000 + $8,000
= $45,000
n
(b)
NPV
=

t 1
NPVA
FCFt
- IO
(1  k*) t
= $42,500 (3.605) - $100,000
= $153,212.50 - $100,000
= $53,212.50
NPVB
= $45,000 (3.517) - $100,000
= $158,265 - $100,000
(c)
= $58,265
One might also consider the potential diversification effect associated
with these projects. If the project's cash flow patterns are cyclically
divergent from those of the company, the overall risk of the company
may be significantly reduced.
11-4A.
(A)
(B)
(A x B)
Present Value
Year
0
1
2
3
4
5
Expected
Cash Flow
-$90,000
25,000
30,000
30,000
25,000
20,000
t
1.00
0.95
0.90
0.83
0.75
0.65
(Expected
Cash Flow )  (t)
-$90,000
23,750
27,000
24,900
18,750
13,000
Factor at
Present
7%
Value
1.000
-$90,000
.935
22,206
.873
23,571
.816
20,318
.763
14,306
.713
9,269
NPV = $ -330
Thus, this project should not be accepted because it has a negative NPV.
25
11-5A.
n
NPVA
=

t 1
FCFt
- I0
(1  k*) t
= $30,000 (.893) + $40,000(.797) + $50,000(.712)
+ $90,000(.636) + $130,000(.567) - $250,000
= $26,790 + $31,880 + $35,600 + $57,240 + $73,710 - $250,000
= - $24,780
n
NPVB
=

t 1
FCF
- I0
(1  k*) t
= $135,000(3.127) - $400,000
= $422,145 - $400,000
= $22,145
26
Internal Rate
0 Year
Probability
0.09
0.09
1 Year
(A)(B)
of Return for
2 Years
Joint
3 Years
p = 0.5
$230,000
130.25%
$180,000
124.68%
$205,000
121.09%
$155,000
114.96%
$180,000
111.30%
$130,000
104.46%
$10,000
-42.44%
$0
-90.00%
11.72%
each Branch
p = 0.5
11.22%
$200,000
p = 0.3
0.15
18.16%
p = 0.5
p = 0.5
p = 0.5
300
0.15
p = 0.6
17.24%
$175,000
$100,000
p = 0.2
p = 0.5
$-100,000
0.06
6.68%
p = 0.5
0.06
6.27%]
p = 0.4
0.24
$150,000
p = 1.0
p = 0.6
-10.19%
$10,000
p = 1.0
0.16
$10,000
-14.40% p = 0.4
$0
d.
Expected internal rate of return
The range of possible IRR’s from –90.00% to 130.25%.
27
12-1A.
a.
Net price after flotation costs
10
$1068.75
=

t 1
kd
b.
c.
d.
e.
kncs
kcs
kps
=
=
$1,125 (1 - .05)
=
$1068.75
$1,000
$110
+
t
(1  k d )
(1  k d )10
9.89%
After tax
cost of debt
=
kd(1-T)
After tax
cost of debt
=
6.53%
=
D1
+ g
NPcs
=
$1.80(1  .07)
+ .07
$27.50(1  .05)
=
.1437 = 14.37%
=
D1
+ g
Pcs
=
$3.50
+ .07
$43
=
.1514 = 15.14%
=
.09 x$150
D
=
$175(1  .12)
NPps
=
$13.50
$154
=
.0877 = 8.77%
After tax
cost of debt = kd (1 - T)
= 12% (1 - .34)
= 7.92%
28
12-13A.
Net price after flotation costs
=
$975 - $15
=
$960.00
Cost of debt:
15
$960.00

=
t 1
For:
kd
$1,000
$60
+
t
(1  k d )
(1  k d )15
Rate
Value
6%
kd%
7%
$1,000.00
960.00
________
$ 40.00
$1,000.00
908.48
$ 91.52
 $40.00 
0.06 + 
  (0.01) = .064 = 6.4%
 $91.52 
=
After tax
cost of debt
Value
=
6.4%(1 - 0.30) = 4.48%
Cost of common stock, kncs
kncs
=
=
=
Source
 D1 

 + g
 NPcs 
$2.25
+ .05
$30(1  0.05)
.129 = 12.9%
Capital Structure
After-tax cost of capital Weighted cost
Debt
60%
4.48%
2.69%
Common Stock
40%
12.9%
5.16%
kwacc =
29
7.85%
12-14A.
Net price after flotation costs
=
$1,050 (1-.04)
=
$1,008.00
Cost of debt:
10
$1,008.00

=
t 1
For:
$1,000
$70
+
t
(1  k d )
(1  k d )10
Rate
Value
6%
kd%
7%
$1,096.84
1,008.00
________
$ 88.84
Value
$1,096.84
1,000.00
$ 96.84
kd
=
 $88.84 
0.06 + 
  (0.01) = .069 = 6.9%
 $96.84 
After tax
cost of debt
=
6.9 %(1 - 0.30) = 4.8%
Cost of preferred stock (kps)
Dividend
D
=
Net Price
NPps
kps =
=
$2.00
$2
=
$25  $3
$22
=
.091 = 9.1%
Cost of common stock, kncs
kncs
=
=
=
 D1 

 + g
NP
 cs 
$3(1  .10)
+ .10
$55  $5
.166 = 16.6%
Source
Market Value
Weight
After-tax cost of capital
Bonds
$4,000,000
.33
4.8%
1.6%
Preferred Stock
2,000,000
.17
9.1%
1.5%
Common Stock
6,000,000
.50
16.6%
8.3%
12,000,000
1.00
kwacc =
11.4%
30
Weighted Cost
13-2A.
Given:
Sales growth for years 1-3
10.0%
Operating profit margin
16.0%
Net working capital to sales ratio
13.0%
Property, plant, and equipment to sales ratio
18.0%
Beginning sales
$ 27,272.73
Cash tax rate
30.0%
Total liabilities
$
Cost of capital
4,000.00
12.0%
Number of shares
2,000.00
FREE CASH FLOWS:
Years
Sales
Operating income (Earnings Before Interest and Taxes)
Less cash tax payments
Net operating profits after taxes (NOPAT)
1
2
3
4
$30,000.00
$33,000.00
$36,300.00
$36,300.00
4,800.00
5,280.00
5,808.00
5,808.00
(1,440.00)
(1,584.00)
(1,742.40)
(1,742.40)
$ 3,360.00
$ 3,696.00
$ 4,065.60
$ 4,065.60
Less investments:
Investment in Net Working Capital
(354.55)
(390.00)
(429.00)
-
Capital expenditures (CAPEX)
(490.91)
(540.00)
(594.00)
-
$ (845.46)
$ (930.00)
$ (1,023.00)
$
$ 2,514.54
$ 2,766.00
$ 3,042.60
$ 4,065.60
2,245.13
2,205.04
2,165.66
$24,115.11
Total investments
Free cash flow
PV of FCF
Present value of free cash flows:
Planning horizon cash flows
Terminal value in year 4: 33,880.00
PV of terminal value
a) Firm value
Invested capital (year 0)
b) Market Value Added
Debt
Shareholder value ($30,730.94 – 4,000)
No. of shares
c) Value per share
$ 6,615.83
$ 24,115.11
$ 30,730.94
$ 9,818.18
$ 20,912.76
$ 4,000.00
$ 26,730.94
2,000.00
$
13.37
31
-
13-3A.
Sales growth for years 1-3
Operating profit margin
Net working capital to sales ratio
Current assets to sales ratio
Property, plant, and equipment to sales ratio
Beginning sales
Cash tax rate
Total liabilities
Cost of capital
Number of shares
10.0%
16.0%
13.0%
18.0%
18.0%
$27,272.73
30.0%
$ 4,000.00
12.0%
2,000.00
Years
0
Change in current assets
Current assets
Capital expenditures
Property, plant and equipment
Total Capital = Total Assets - Non-interest
liabilities
$ 4,909.09
4,909.09
$ 9,818.18
1
$ 354.55
$ 5,263.64
$ 490.91
$ 5,400.00
$10,663.64
2
$ 390.00
$ 5,653.64
$ 540.00
$ 5,940.00
$11,593.64
3
$ 429.00
$ 6,082.64
$ 594.00
$ 6,534.00
$12,616.64
4
$
$ 6,082.64
$
$ 6,534.00
$12,616.64
1
$30,000.00
4,800.00
(1,440.00)
$3,360.00
$(1,178.18)
2
$33,000.00
5,280.00
(1,584.00)
$ 3,696.00
$(1,279.64)
3
4 and beyond
$36,300.00 $ 36,300.00
5,808.00
$ 5,808.00
(1,742.40)
(1,742.40)
$ 4,065.60
$ 4,065.60
$ (1,391.24) $ (1,514.00)
$2,181.82
$2,416.36
$ 2,674.36
$ 2,551.60
$ 10,663.64
$11,593.64
$12,616.64
$12,616.64
a) Calculation of EVA:
Years
0
Sales
Operating income
Less cash tax payments
Net operating profits after taxes (NOPAT)
Less capital charge (Invested Capital x
Kwacc)
Economic Value Added
Invested Capital
b) Return on Invested Capital
(NOPATt  ICt-1)
c) Market Value Added = PV(EVAs)
Plus Invested Capital (year 0)
Firm Value
$ 9,818.18
34.22%
34.66%
35.07%
$20,640.89
9,818.18
$31,459.07
a. The EVAs are positive each year, indicating Bergman is creating value for its
shareholders.
b. The ROIC is greater than the cost of capital, so the firm is creating value for its
shareholders. When the ROIC is greater than the cost of capital, we should see
positive EVAs.
c. The present value of the EVAs exceeds the market value added in Problem 132A.
32
32.22%
15-1A.
Product Line
Piano
Violin
Cello
Flute
Sales
61,250
37,500
98,750
52,500
V.C.
41,650
22,500
61,225
25,725
C.M.
19,600
15,000
37,525
26,775
C.M. Ratio
32%
40%
38%
51%
Total
250,000
151,100
98,900
40%
Break-even Point
S* = F/(1-VC/S) = 50,000/(1-VC/S) = 50,000/.4 = 125,000
S* =
50,000
50,000
F
=
=
= 125,000
.4
 $151,100 
 VC 
1 

1 

S 

 $250,000 
15-4A.
(a)
Sales
Variable Costs
Revenue before
fixed costs
Fixed costs
EBIT
Jake's
Lawn Chairs
$600,640.00
$326,222.60
Sarasota
Sky Lights
$2,450,000
$1,120,000
Jefferson
Wholesale
$1,075,470
$957,000
$274,417.40
$120,350.00
$ 154,067.40
$1,330,000
$850,000
$ 480,000
$118,470
$89,500
$ 28,970
(b)
Jake's Lawn Chairs: QB =
F
$120,350
=
PV
$32  $17.38
=
$120,350
= 8,232
$14.62
=
$850,000
$850,000
=
= 1,789
$875  $400
$475
Jefferson Wholesale: QB =
$89,500
$89,500
=
= 8,310
$97.77  $87
$10.77
Sarasota Skylights: QB
(c)
Revenue Before
Fixed Costs
EBIT
=
Jake's
Lawn Chairs
Sarasota
Skylights
Jefferson
Wholesale
$274,417.40
$154,067.40
$1,330,000
$480,000
$118,470
$28,970
33
=
(d)
1.78 times
2.77 times
4.09 times
Jefferson Wholesale, since its degree of operating leverage exceeds that of
the other two companies.
15-5A.
(a)
(b)
Revenue Before Fixed Costs
EBIT
times
EBIT
=
EBIT  I
times
(c)
DCL45,750,000
(d)
S*
=
=
(e)
=
$22,950,000
$13,750,000
$13,750,000
$13,750,000  $1,350,000
=
=
$13,750,000
$12,400,000
1.67
= 1.11
= (1.67) (1.11) = 1.85 times
F
VC
1
S
$9,200,000
.502
=
$9,200,000
$22,800,000
1
$45,750,000
=
=
$9,200,000
1  .498
$18,326,693.23
(25%) × (1.85) = 46.25%
15-13A.
(a)
QB
=
(b)
S*
=
F
$540,000
$540,000
=
=
= 10,000 units
PV
$180  $126
$54
$540,000
$540,000
F
$540,000
=
=
=
VC
$126
1  0 .7
.3
1
1
S
$180
= $1,800,000
(c)
(d)
Sales
Variable costs
Revenue before fixed costs
Fixed costs
12,000
Units
$2,160,000
1,512,000
$ 648,000
540,000
15,000
Units
$2,700,000
1,890,000
$ 810,000
540,000
20,000
Units
$3,600,000
2,520,000
$1,080,000
540,000
EBIT
$ 108,000
$ 270,000
$ 540,000
12,000 units
$648,000
= 6 times
$108,000
15,000 units
$810,000
= 3 times
$270,000
34
20,000 units
$1,080,000
= 2 times
$540,000
Notice that the degree of operating leverage decreases as the firm's sales level rises above
the break-even point.
15-29A.a.
A
Sales
$40,000
Variable costs*
24,000
Contribution margin
$16,000
Contribution margin ratio
40%
B
$50,000
34,000
$16,000
32%
C
$20,000
16,000
$ 4,000
20%
D
$10,000
4,000
$ 6,000
60%
Total
$120,000
78,000
$ 42,000
35%
*Variable costs = (Sales) (1 - contribution margin ratio)
b.
35%
c..
Break-even point in sales dollars:
$29,400
$29,400
F
=
=
= $84,000
VC
1  0.65
0.35
1
S
15-30A.
A
B
C
D
Sales
$30,000
$44,000
$40,000
$6,000
Variable costs*
18,000
29,920
32,000
2,400
Contribution margin
$12,000
$14,080
$ 8,000 $ 3,600
Contribution margin ratio
40%
32%
20%
60%
S* =
Total
$120,000
82,320
$ 37,680
31.4%
*Variable costs = (sales) (1- contribution margin ratio).
b.
31.4%
c..
Break-even point in sales dollars:
S* =
$29,400
F
=
= $93,631
VC
0.314
1
S
Toledo's management would prefer the sales mix identified in problem 1529A. That sales mix provides a higher EBIT ($12,600 vs. $8,280) and a
lower break-even point ($84,000 vs. $93,631).
35
16-1A.
a.
FC
=
FC
=
FC
=
Interest + Sinking Fund
$15 million
($15 Million) (.18) +
30 years
$2,700,000 + $500,000 = $3,200,000
CBr
=
Cb0 + NCFr – FC
Where: CB0
=
$2,000,000
=
$3,200,000
b.
FC
and
NCFr =
$4,950,000 - $4,000,000 = $950,000
so,
CBr
=
$2,000,000 + $950,000 - $3,200,000
CBr
=
-$250,000
c.
We see that the company has a preference for a $2 million cash balance. The combination
proposed issue of bonds would put the firm’s recessionary cash balance (CBr) at -$250,000. The c
the statement that the firm likes a cash balance of $2 million suggest strongly that the proposed bo
16-4A.
(EBIT  I)(1  t)  P
Ss
=
(EBIT  I)(1  t)  P
Sb
(EBIT  $0)(1  0.5)  0
1,000,000
=
(EBIT  $600,000)(1  0.5)  0
700,000
0.5EBIT
10
=
0.5EBIT  $300,000
7
(a)
EBIT
(b)
$2,000,000
Plan A
$2,000,000
0
$2,000,000
1,000,000
$1,000,000
0
$1,000,000
$
1.00
EBIT
Interest
EBT
Taxes
NI
P
EAC
EPS
(c)
=
Plan B
$2,000,000
600,000
$1,400,000
700,000
$ 700,000
0
$ 700,000
$
1.00
See following analysis chart.
(d)Since $2,400,000 exceeds $2,000,000, the levered plan (Plan B) will provide for
higher EPS.
36
$2
1.5
Plan A
Plan B
1.0
$1.0 Indif. level
0.5
$600,000
0
$ 1 Mi l .
$ 2 Mi l .
16-5A.
(a)
($30) (900,000 shares) = $27,000,000
(b)
Kc =
Dt
E
$6
= t =
= 20%
Po
Po
$30
In the all equity firm Kc = Ko, Thus, Ko = 20%
(c)
Kc =
(1)
$6.21
= 20.7%
$30.0
EBIT
- Interest
EAC
÷
= Dt
$5,400,000
120,000
$5,280,000
850,000
$6.21
shares*
*$1,500,000 ÷ $30 = 50,000 shares retired.
(2)
$6.21  $6.00
= 0.035 or 3.5%
$6.00
(3)
20.7%  20.0%
= 0.035 or 3.5%
20.0%
37
$ 3 Mi l .
$ 4 Mi l .
(4)
16-15A.
(a)
(b)
(c)
25.5
1 .5
(20.7%) +
(8.0%) = 20.0%
27
27
Firm C appears to be excessively levered. Both its debt ratio and burden
coverage ratio are unfavorable relative to the industry norm. The firm's
price/earnings ratio is significantly lower (6 versus 10) than the industry
norm.
Firm B.
The investing market place seems to place more weight on coverage ratios
than balance sheet leverage measures. Thus, Firm B's price/earnings ratio
exceeds that of Firm A.
17-1A. Dividend Policies
a.
Constant payout ratio of 40%
Year
1
2
3
4
5
b.
$ Dividend
0.40
0.80
0.64
0.36
1.20
Profits × payout/shares
1,000,000 × 0.4 / 1,000,000
2,000,000 × 0.4 / 1,000,000
1,600,000 × 0.4 / 1,000,000
900,000 × 0.4 / 1,000,000
3,000,000 × 0.4 / 1,000,000
Stable target payout of 40%
8,500,000
 0.4
1,000,000
Target dividend =
= 0.68
5
c.
Small regular dividend of $0.50 plus year-end extra
Base profits: 1,500,000
% of extra profits: 50%
Year
$ Dividend
Payout Calculation
38
1
2
3
4
5
17-3A.
0.50
0.75
0.55
0.50
1.25
0.50
0.5 + [(2,000,000 – 1,500 000 * 0.5 / 1,000,000]
0.5 + [(1,600,000 -,1,500,000) * 0.5 / 1,000,000]
0.50
0.5 + [(3,000,000 – 1,500,000) * 0.5 / 1,000,000]
Flotation Costs and Issue Size
Flotation costs
Stock price
Net to firm
17-4A.
Dollar issue size
= $ 7,073,171
Number of shares
= $ 7,073,171 ÷ $85/share
83,214 shares
=
$5,800,000/(1-.18)
Terra Cotta - Residual Dividend Theory
Total financing needed
Retained earnings
Debt ratio
Equity ratio
Equity financing needed
Dividends
17-5A.
0.18
$85.00
$5,800,000
$640,000
$400,000
0.4
0.6
$384,000 =
$
16,000 =
$640,000(.6)
$400,000 - $384,000
RCB - Stock Dividend
Before dividend
Shares outstanding
Net income
Price/Earnings
Stock dividend
Investor's share
2,000,000
$ 550,000
10
20%
100
Current price
$
Value before dividend
$
After dividend
Shares outstanding
New price
$550,000
2,400,000
Investor's shares
Value after dividend
275.00
=
2,400,000
Change
550,000
2,000,000
$2.75 x 100 shares
2.75= P/E x EPS = 10 ×
= 2,000,000 x (1 + 0.2)
$2.29
= P/E x EPS=10 x
120
$ 275.00
=
=
100 x 1.2
120 x $2.29
$
=
$275 (before)
- $275 (after)
0.00
The value of the investors' holdings does not change because the price of
the stock reacted fully to the increase in the shares outstanding.
17-7A.
Stetson Manufacturing, Inc. - Long Term Dividend Policy
39
Debt ratio
Equity ratio
Shares outstanding
Year
1
2
3
4
5
a.
0.35
0.65
100,000
(A)
(B)
Investment
$ 350,000
475,000
200,000
980,000
600,000
Funds Available
Internally
$ 250,000
450,000
600,000
650,000
390,000
$2,340,000
(C)
Equity
Contribution
(A x .65)
$ 227,500
308,750
130,000
637,000
390,000
$1,693,250
Residual Dividend
Year
1
2
3
4
5
Dividend =
Funds Available  Equity Contributi on
100,000 Shares
$0.225
$1.41
$4.70
$0.13
$0.00
40
($2,340,000  $1,693,250)/5
100,000 Shares
b.
Target Dividend = $1.29 =
c.
The target dividend allows for consistency of income to the stockholder and income in all
would not pay a dividend in year five.
17-8A.
Trexco Corporation - Stock Split
a.
b.
17-10A.
Market price
Split multiple
Shares outstanding
$
You own
Investor's shares
Position before split
0.05
1,250
$122,500
x
Price after split
Your shares after split
Position after split
Net gain
$
= $98 ÷ 2
= 1,250 x 2
= 2,500 shares x $49 per share
Price fall
Price after split
Position after split
share
Net gain
0.4
$ 58.80
$147,000
= $98.00 (1 - .4)
= 2,500 Shares x $58.80 per
$ 24,500
= $147,000 - $122,500
=
98.00
2
25,000
49.00
2,500
$122,500
$
0
25,000
= 1,250 Shares x $98 per share
Dunn Corporation - Repurchase of Stock
Proposed dividend
Shares outstanding
Earnings per share
Ex-dividend price
Proposed dividend/share
$ 500,000
250,000
$
5.00
$
50.00
$2.00
a.
Repurchase price
$
b.
$2)
Number of shares repurchased
c.
The capital gains to be received by the stockholder would not be equal to
the intended dividend, thus resulting in a dollar benefit or loss to the
stockholders.
d.
Unless you have a need for current income, you would probably prefer the
stock repurchase plan.
41
52.00
= $50 + $2
9,615
= $500,000 ÷ ($50 +
18-1A.
The financial statements for both firms are found below:
Firm A
Cash
Accounts Receivable
Inventories
Net Fixed Assets
Total
100,000
100,000
300,000
1,500,000
2,000,000
Accounts Payable
Notes Payable
Bonds
Common Equity
Total
200,000
200,000
600,000
1,000,000
2,000,000
150,000
50,000
300,000
1,500,000
2,000,000
Accounts Payable
Notes Payable
Current Liabilities
Bonds
Common Equity
Total
400,000
200,000
600,000
400,000
1,000,000
2,000,000
Firm B
Cash
Accounts Receivable
Inventories
Net Fixed Assets
Total
Financial measures of firm liquidity
Working Capital
Net Working Capital
Current Ratio
Acid Test Ratio
Cash
Firm A
500,000
100,000
1.25
0.5
100,000
Firm B
500,000
(100,000)
0.83
0.33
150,000
Firm B is obviously the more aggressive of the two firms. Note the fact that it has
negative net working capital (current liabilities exceed current assets) and both its current
ratio and acid test ratio are lower. Notice that the higher level of cash for Firm B is more
than offset by it more aggressive use of current liabilities.
42
18-2A. The information contained in the problem provides the basis for the following:
Purchases =
Discount Period =
Cash Discount =
Deferred Period =
Maximum Credit Period =
Purchases per day =
$480,000
15 days
1%
30 days
45 days
480,000 ÷ 360 = 1,333.33
a. Purchases/day x 15 day discount period
b. Purchases/day x 45 day maximum credit period
c. The Annual Percentage Rate for forgoing the discount
=
=
=
20,000.00
60,000.00
12.12%
18-3A.First we calculate the interest expense for the three month loan as follows:
Interest = .12 x $100,000 x 3/12 = $3,000.
Assuming that Paymaster has to leave 10% of the loan idle in a compensating
balance the effective cost of credit can be calculated as follows:
APR = [$3,000/($100,000 - 10,000 - 3,000)] x (12/3) = 13.79%
If the company already has sufficient funds in the bank to satisfy the
compensating balance requirement then the cost of credit drops to 12.37%.
18-4A.
Interest expense for the commercial paper issue is calculated as follows:
Interest = .11 x $20 million x (270/360) = $1,650,000
The effective rate of interest to Burlington Western (including the issue fee of
$200,000) is calculated as follows:
APR = [($1,650,000 + 200,000)/($20 million - 1,650,000 - 200,000)] x (360/270)
= 13.59%
Note that both the interest expense and the issue fee are prepaid.
18-7A. (a)
Interest
= .14 x $100,000
= $14,000
Therefore, the effective rate of interest on the loan is calculated as follows:
APR
=
1
$14,000
x
360 / 360
$100,000  14,000
= .1628 or 16.28%
Dealer Financing Alternative
43
APR
=
1
$16,300
x
360 / 360
$100,000
= .163 or 16.3%
Analysis. The costs of the two sources of financing are identical for practical
purposes. The final choice can now be made based upon other nonquantitative
factors. For example, the firm may find that using dealer financing is less time
consuming and allows the firm to leave its credit line within the bank unchanged.
Since bank credit can be used for a much wider array of financing needs than
dealer financing, R. Morin would find that using dealer financing leaves the firm
with greater flexibility in raising funds for its future needs.
(b)
If the compensating balance becomes binding, then the effective rate on
the bank loan alternative will be
Interest
= .14 x $100,000
= $14,000
Compensating Balance
= .15 x $100,000
= $15,000
APR =
1
$14,000
x 360/360
$100,000  14,000  15,000
= .197 or 19.7%
Thus, where the 15 percent compensating balance requirement is binding on R.
Morin, the cost of the bank loan rises to 19.7 percent. In this case, dealer
financing is clearly less costly.
Note that equipment dealers will frequently price their merchandise so as to
compensate them for offering "below market" rates of interest for financing. This
may well be the case here such that R. Morin should use the dealer financing
unless it can negotiate a price concession equal to the value of "bargain
financing."
44
20-6A.
Step 1:
Estimate the Change in Profit.
=
=
=
($1,000,000 x .20) - ($1,000,000 x .08)
$200,000 - $80,000
$120,000
Step 2: Estimate the cost of additional investment in accounts receivable and
inventory.
Estimate the additional investment in accounts receivable:
=
($6,000,000 / 360) x 90 - ($5,000,000 / 360) x 60
=
$1,500,000 - $833,333
=
$666,667
Additional accounts receivable and inventory times the
required rate of return:
=
=
Step 3:
Estimate the change in the cost of the cash discount
=
Step 4:
=
($666,667 + $50,000) .15
$107,500
$0 (no change)
Compare incremental revenues with incremental costs.
Step 1 - (Step 2 + Step 3)
=
$120,000 - $107,500
=
$12,500
The policy should be adopted.
45
46