Solutions for Financial Calculations
Analysis of Financial statements
.
Financial statement analysis
BEP = EBIT/TA
0.15 = EBIT/$100,000,000
EBIT = $15,000,000.
ROA = NI/TA
0.09 = NI/$100,000,000
NI = $9,000,000.
EBT = NI/(1 - T)
EBT = $9,000,000/0.6
EBT = $15,000,000.
Therefore interest expense = $0.
2.
Market price per share
EPS = $15,000/10,000 = $1.50.
P/E = 5.0 = P/$1.50.
P = $7.50.
3.
Market price per share
Total market value = $1,250(1.5) = $1,875.
Market value per share = $1,875/25 = $75.
Alternative solution:
Book value per share = $1,250/25 = $50.
Market value per share = $50(1.5) = $75.
4.
ROA
Net income = 0.15($20,000,000) = $3,000,000.
ROA = $3,000,000/$22,500,000 = 13.3%.
5.
TIE ratio
TIE
7
7I
6I
I
=
=
=
=
=
EBIT/I
($300 + I)/I
$300 + I
$300
$50.
6.
ROE
Equity = 0.25($6,000) = $1,500.
Current ROE =
New ROE =
NI
$240
=
= 16%.
$1,500
E
$300
= 0.20 = 20%.
$1,500
ROE = 20% - 16% = 4%.
7.
Profit margin
Current inventory turnover =
New inventory turnover =
S
$10,000
=
= 2.
$5,000
Inv
S
$10,000
S
= 5; Inv =
=
= $2,000.
5
5
Inv
Freed cash = $5,000 - $2,000 = $3,000.
Increase in NI = 0.07($3,000) = $210.
New Profit margin =
8.
NI
$240 + $210
=
= 0.0450 = 4.5%.
$10,000
Sales
Du Pont equation
First, calculate the
ROA = NI/TA = 0.04.
Sales/Total assets =
PM = (NI/TA)(TA/S) =
profit margin, which equals NI/Sales:
[TA is Total assets.]
S/TA = 2.
0.04(0.5) = 0.02. [TA/S = 1/2 = 0.5.]
Next, find the debt ratio by finding the equity ratio:
E/TA = (E/NI)(NI/TA). [ROE = NI/E and ROA = NI/TA.]
E/TA = (1/ROE)(ROA) = (1/0.06)(0.04) = 0.667, or 66.7% equity.
Therefore, D/TA must be 0.333 = 33.3%.
9.
P/E ratio and stock price
EPS = $750,000/100,000 = $7.50.
P/E = Price/EPS = 8.
Thus Price = 8  $7.50 = $60.00.
Financial Planning
.
Additional funds needed
Balance sheet solution:
Pro Forma Balance Sheet
Cash
$ 1,600
Accounts payable
Accounts receivable
900
Accrued wages
Inventory
1,900
Notes payable
Net fixed assets
34,000
Mortgage
Common stock
Retained earnings
Total liabilities
Total assets
$38,400
& equity
$
700
300
2,000
26,500
3,200
5,000
$37,700
AFN = $38,400 - $37,700 = $700.
Formula solution:
S0 = S; MS1 = $1,000.
L*
A*
AFN =
(S) (S) - MS1(1 - d) = $2,200 - $500 - $1,000(1) = $700.
S0
S0
2.
Forecasting additions to retained earnings
Sales
Total operating costs
EBIT
Interest
Earnings before tax (EBT)
Taxes (40%)
Net income available to
common shareholders
Dividends to common (50%)
Additions to retained earnings (50%)
3.
2004
Forecast Basis
$7,000 1.1
3,000 0.4286
$4,000
200
$3,800
1,520
2005
$7,700
3,300
$4,400
200
$4,200
1,680
$2,280
$2,520
$1,260
$1,260
Additional funds needed
AFN =
Required asset
Spontaneous
Increase in
- liability increase - retained earnings
increase
= $70/$100($20) - $2 - (0.05)($120)(1 - 0.40)
= $14 - $2 - $3.6
= $8.4 million.
4.
AFN with excess capacity
S0 = $400.
S1 = S0  1.05 = $420.
SCapacity = $400/0.80 = $500.
sales increase.
Cash
Accounts receivable
Inventory
Fixed assets
Total assets
No new fixed assets are needed to support the
Pro Forma Balance Sheet
$ 21
Accounts payable
21
Notes payable
21
Long-term debt
180
Common stock
Retained earnings
Total liabilities
$243
and equity
$ 21.0
40.0
80.0
80.0
28.4
$249.4
Addition to retained earnings = $420  0.05  0.4 = $8.40.
AFN = $243.0 - $249.4 = -$6.4. Surplus of 6.4.
Formula solution:
$60
$20
($20) ($20) - $420(0.05)(0.40)
$400
$400
= $3.0 - $1.0 - $8.4 = -$6.4.
AFN =
Fixed assets are not included in the formula equation since full capacity
sales ($500) has not been reached.
5.
AFN with excess capacity
S0 = $100.
S1 = $150.
SCapacity =
$100
= $117.65.
0.85
Target fixed assets
$75
Fixed assets
=
=
= 0.6375.
Sales ratio
Full capacity sales
$117.65
S1  Target ratio = New fixed assets level.
Cash
Accounts receivable
Inventory
Net fixed assets
Total assets
$150  0.6375 = $95.62.
Pro Forma Balance Sheet
$ 15.00
Accounts payable
37.50
Notes payable
60.00
Accrued wages and taxes
95.62
Long-term debt
Common equity
Total liabilities
$208.12
and equity
$ 22.50
20.00
22.50
30.00
73.00
$168.00
Addition to retained earnings = $150  0.05  0.40 = $3.00.
AFN = $208.12 - $168.00 = $40.12  $40.
6.
AFN with excess capacity
S0 = $200; S1 = $210; S2 = $220; S3 = $230; S4 = $240.
$200
SCapacity =
= $250. Fixed assets will not need to be increased since S4
0.80
< SCapacity; $240 < $250.
Cash
Accounts receivable
Inventory
Fixed assets
Total assets
Pro Forma Balance Sheet
$ 12
Accounts payable
12
Notes payable
12
Long-term debt
90
Common stock
Retained earnings
Total liabilities
$126
and equity
$ 12
20
40
40
28
$140
Addition to retained earnings: (S1 + S2 + S3 + S4)  0.05  0.40 = $18.00.
AFN = $126 - $140 = -$14 Surplus.
Formula solution:
AFN =
$30
$10
($40) ($40) - (0.05)($900)(0.4) = -$14 (Surplus).
$200
$200
The $900 is the sum of sales over the 4-year period. Fixed assets are not
included in the formula equation since full capacity sales ($250) is never
reached.
7.
AFN with excess capacity
S0 = $2,000.
S1 = $2,750.
SCapacity = $2,000/0.80 = $2,500.
Target fixed assets to sales ratio =
Fixed assets
SalesCapacity
=
$100
= 0.04.
$2,500
New fixed assets level = 0.04  $2,750 = $110.
Cash
Accounts receivable
Inventory
Net fixed assets
Total assets
Pro Forma Balance Sheet
$ 13.75
Accounts payable
55.00
Accruals
68.75
Notes payable
110.00
Long-term debt
Common stock
Retained earnings
Total liabilities
$247.50
and equity
$ 20.625
6.875
20.000
20.000
20.000
153.000
$240.500
Addition to retained earnings = $2,750  0.03  0.40 = $33.00.
AFN = $247.50 - $240.50 = $7.00.
8.
Expected growth rate
Formula solution:
Let S1 = S0(1 + g).
Let S/S0 = g or growth rate.
$2 = (A*/S0) S - (L*/S0) S - MS1(1 - d)
$2 = A*(g) - L*(g) - MS0(1 + g)(1 - d)
$2 = $7g - $1.5g - 0.04($10)(1 + g)(0.70)
$2 = $5.5g -$0.28g - $0.28
$5.22g = $2.28
g = 0.437  44%.
Risk and Return
Solutions
1

r = (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)
= 11.40%.
σ2 = (-50% - 11.40%)2(0.1) + (-5% - 11.40%)2(0.2) + (16% - 11.40%)2(0.4)
+ (25% - 11.40%)2(0.2) + (60% - 11.40%)2(0.1)
σ2 = 712.44; σ= 26.69%.
CV =
2
Total
26.69%
= 2.34.
11.40%
Investment
Beta
$35,000
0.8
40,000
1.4
$75,000
($35,000/$75,000)(0.8) + ($40,000/$75,000)(1.4) = 1.12.
3
rRF = 5%; RPM = 6%; rM = ?
rM = 5% + (6%)1 = 11%.
rs when b = 1.2 = ?
rs = 5% + 6%(1.2) = 12.2%.
4 a.

r m= (0.3)(15%) + (0.4)(9%) + (0.3)(18%) = 13.5%.

r j= (0.3)(20%) + (0.4)(5%) + (0.3)(12%) = 11.6%.
b. σM
= [(0.3)(15% - 13.5%)2 + (0.4)(9% - 13.5%)2 + (0.3)(18% -13.5%)2]1/2
= 14.85% = 3.85%.
σJ = [(0.3)(20% - 11.6%)2 + (0.4)(5% - 11.6%)2 + (0.3)(12% - 11.6%)2]1/2
=
c. CVM =
CVJ =
5
a.
38.64% = 6.22%.
3.85%
= 0.29.
13.5%
6.22%
= 0.54.
11.6%
rA = rRF + (rM - rRF)bA
12% = 5% + (10% - 5%)bA
12% = 5% + 5%(bA)
7% = 5%(bA)
1.4 = bA.
b. rA = 5% + 5%(bA)
rA = 5% + 5%(2)
rA = 15%.
6.Portfolio beta
1.2 = 1/20(0.7) + (19/20)b
b is average beta for other 19 stocks.
1.165 = (19/20)b.
b for 19 stocks =1.165(20/19) = 1.226
New Beta = 19/20(1.226) + 1/20(1.4) = 1.235.
= 1.165+ 0.07 = 1.235
7.Portfolio return
r̂p = 0.9(12%) + 0.1(20%) = 12.8%.
bP = 0.9(1.2) + 0.1(2.0) = 1.28.
8.Market risk premium
12.25% = 5% + (RPM)1.15
7.25% = (RPM)1.15
RPM = 6.30%.