AB1201
Proposed answers for AB1201 Exam Sem 2 AY2021-22
Section A
Question 1 (9 marks each) (TOTAL 45 marks)
1a)
CAPM is a model based on the proposition that any stock’s required rate of return is equal to
the risk-free rate of return plus a risk premium that reflects only the risk remaining after
diversification (i.e., risk premium that is based on the systematic risk of the stock).
Market risk is the risk that remains in a portfolio after diversification has eliminated all
company-specific risk (diversifiable risk). Market risk, or systematic risk, affects the
performance of the entire market simultaneously. It cannot be eliminated through
diversification. Market risk is measured by beta.
A firm can influence its market risk (its beta) through changes in the composition of its assets
and through changes in the amount of debt it uses. For example, when a firm uses more debt,
its beta increases with higher financial leverage, as can be quantified by the Hamada equation.
𝑏𝐿 = 𝑏𝑈 [1+(1-T)(D/E)],
When a firm’s debt increases, D/E increases. So does the firm’s beta.
A firm’s beta can also change as a result of external factors such as increased competition in
its industry, recessions, changes to interest rates and inflation rates. Increased competition can
create lower market share and fewer profits for a firm hence a firm’s business risk may increase.
1b)
Both analysts are unlikely to arrive at the same intrinsic value for the shares of the company
even if they use the same Gordon Model. Each of the variables (D1, rs and g) in the Gordon
Model may be estimated differently by the two analysts because the analysts may possess
different information, or may interpret the same information differently, or may use different
approaches when estimating the value of each variable, or may use different proxies for the
same variable. This will result in different estimated intrinsic values for the shares.
1c)
WACC=𝑤𝑑 𝑟𝑑 (1 − 𝑇) + 𝑤𝑠 𝑟𝑠 + 𝑤𝑝 𝑟𝑝
Where 𝑟𝑑 , 𝑟𝑠 and 𝑟𝑝 are the costs of new debt, common equity, and preferred stock, respectively.
𝑤𝑑 , 𝑤𝑠 and 𝑤𝑝 are the target weight of each capital component. 𝑇 is the tax rate.
Part i)
We should use the target capital structure since it refers to how company plans to raise capital
to fund its future projects. This is more relevant to determining future projects.
We should use market values since generally investors are more concerned about the current
market value of the company’s debt and equity.
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AB1201
Part ii)
WACC of a company is computed based on the company’s existing risk profile. However,
investors would require higher returns on riskier investment and therefore the computed
WACC needs to be adjusted when applying on such a project. Companies that are raising
capital to take on risky projects will have higher cost of capital than companies that are
investing in safer projects.
For a riskier project, the WACC needs to be adjusted higher for project appraisal.
1d)
WACC = wdrd(1- TC) + wcrs
Initially when debt/capital ratio is zero and company is an all-equity firm, WACC = rs.
rs is always higher than rd as equity is riskier than debt because share prices are more volatile
than bond prices, and shareholders get lower priority claim to the liquidation proceeds than
bond holders when the company goes bankrupt.
As level of debt/capital increases, the firm is substituting cheaper after-tax cost of debt for
relatively more expensive cost of equity, hence WACC declines initially.
Beyond a certain debt/capital level, WACC increases even though the firm continues to have
more relatively cheaper debt. This is because both after-tax cost of debt and cost of equity
would increase as the risk of the firm increases with financial leverage.
Hamada equation:
bL = bU [1 + (1-T)(D/E)]
SML/CAPM equation:
rs = rRF + (rM- rRF)bL
bL is the leverage beta of the firm. Assuming the total capital is kept constant, when the firm
increases debt, it correspondingly reduces equity. Hence D/E will always increase with debt
and therefore bL will also increase with debt.
The impact of higher bL will then lead to higher cost of equity (rs) when debt increases
(assuming the standard assumption that the market risk premium is positive).
1e)
Students can indicate any three of the following:
Stable versus irregular dividend payment
- Stable dividend policy – stable dollar dividends, which do not fluctuate with volatile
annual earnings.
- Constant payout dividend policy – pay a fixed percentage of annual earnings as
dividends (hence, may result in irregular dividend payment).
High dividend payout versus low dividend payout
- Decide whether to fix a high dividend payout ratio or to fix a low dividend payout ratio
Residual dividend policy
- Grant priority to building up retained earnings for required future investments; any
leftover is paid out as dividends.
Frequency of dividend payment
- Decide whether dividends are to be paid quarterly, semi-annually, or annually.
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Cash dividend versus Stock dividend
- Decide whether to pay dividends by means of cash, or by means of issuing new dividend
shares.
Cash dividend versus Share Buyback.
- Decide whether to distribute cash by means of a Cash Dividend or distribute it by means
of a Share Buyback.
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Section B
Question 2 (TOTAL 10 marks)
Original PMT:
Iper per month = 0.06/12 = 0.005
𝑃𝑀𝑇
120
1
100000 = 0.005 [1 − (1.005)
]  PMT=$1,110.2050
Remaining balance at end of year 3:
1110.2050
PV=
0.005
84
1
[1 − (1.005) ] = $75,996.91
New PMT:
Iper Per month = 0.08/12
75996.91=
𝑃𝑀𝑇
00.08/12
[1 − (
84
1
) ] PMT = $1,184.50
1+0.08/12
(Rounding error is expected if students use 0.67% instead of 8%/12)
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Question 3 (TOTAL 10 marks)
a)
(7 marks)
Bowin’s:
𝑟𝑆 = 4% + 5(1.2) = 10%
𝑉𝐵 =
𝐷0 (1+𝑔)
𝑟𝑆 −𝑔
Doodle’s:
=
0.6(1.05)
0.1−0.05
= $𝟏𝟐. 𝟔𝟎
𝑟𝑆 = 4% + 5(1.6) = 12%
𝑉𝐷 =
𝐷0 (1+𝑔)
𝑟𝑆 −𝑔
=
0.48(1.0625)
0.12−0.0625
0.51
= 0.0575 = $8.87
VB – VD = 12.6 – 8.87 = $3.73
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AB1201
Bowin’s stock intrinsic value is higher than Doodle’s by $3.73.
b)
(3 marks)
Assume w is the amount to invest in Bowin’s stock.
𝑤
1.35 = 120,000 (1.2) +
120,000−𝑤
 w = $75,000
120,000 – w = $45,000
120,000
(1.6)
Hence, the amount to invest in Bowin’s stock is $75,000, and the amount to invest in
Doodle’s stock is $45,000.
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Question 4 (TOTAL 10 marks)
P0 =
30
30
1200 + 30
+
+
1
2
(1.15)
(1.15)
(1.15)3
P0 = 857.5162 = $857.52
Calculator
N = 3, I/Y = 15, PMT = 30, FV = 1,200, CPT PV = -857.5162
857.52 =
30
+
(1+𝑋)1
30
30
30
+ ⋯ + (1+𝑋)9 +
(1+𝑋)2
857.52 = ∑10
𝑡=1 (1+𝑋)𝑡 +
X = 4.83%
1000+ 30
(1+𝑋)10
or
1000
(1+𝑋)10
Calculator
N = 10, PV = -857.5162, PMT = 30, FV = 1,000, CPT I/Y = 4.83
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Question 5 (TOTAL 15 marks)
a)
(9 marks)
Market capitalization 6 years ago = 20m × $30 = $600m
Current market capitalization = $600m × (1 + 80%) = $1,080m
Current number of shares = $1,080m / $32 = 33.75m shares
No. of shares before the 3-for-2 share split = 33.75m x 2/3 = 22.5m shares
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Percentage of stock dividend, x = (22.5m – 20m) / 20m = 12.5%
b)
(6 marks)
r = r* + IP + MRP + DRP + LP
= 2.5% + IP + 0.1(t – 1) + (DRP + LP)
For the 6-year bond
IP6 = [3(3%) + 3(4%)] / 6 = 3.5%
10.5% = 2.5% + 3.5% + 0.1(6 – 1)% + (DRP + LP)
 (DRP + LP) = 4%
For the 10-year bond
IP10 = [3(3%) + 7(4%)] / 10 = 3.7%
r10 = 2.5% + 3.7% + 0.1(10 – 1)% + 4% = 11.1%
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Question 6 (TOTAL 10 marks)
Items
Year 0 ($)
Cost of machine
Maintenance
Maint. tax
savings
(Maint. × T)
(50,000 × 20%)
Deprec. tax
savings
(Deprec. × T)
AT residual
value
Cash Flow
PV cost at
8%(1 – 20%) or
6.4%
-1,000,000
-50,000
10,000
Lease payment
Tax saving on
pmt
AT lease pmt
Year 1 ($)
Borrow and
Buy Analysis
Year 2 ($)
-50,000
10,000
-50,000
10,000
66,000
90,000
Year 3 ($)
30,000
94,000
-1,040,000
-868,455
26,000
50,000
-400,000
80,000
Lease Analysis
-400,000
80,000
-400,000
80,000
-320,000
-320,000
-320,000
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124,000
AB1201
PV cost at
I(1 − T) or 6.4%
Calculations:
MACRS factor
Depreciation
-903,413
0.33
330,000
0.45
450,000
Residual value
before taxes
Book value
(Cost − Total
deprec.)
Taxable residual
value (gain
from sale)
Tax on residual
value
AT residual
value (residual
value before
tax - tax)
0.15
150,000
100,000
70,000
30,000
-6,000
94,000
The net advantage to leasing is -$868,455 – (-$903,413) = $34,958 (i.e., it is cheaper to
borrow and buy the equipment, instead of leasing it.)
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