# Solutions for Financial Calculations (Midterm) ```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
.
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.
Sales
Total operating costs
EBIT
Interest
Earnings before tax (EBT)
Taxes (40%)
Net income available to
common shareholders
Dividends to common (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
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.