September 2015 Professional Examination
Paper 2.2: Questions & Solutions
Corporate Finance
Equity Valuation and Analysis
Fixed Income Valuation and Analysis
Level 2
Page 1 of 12
SECTION B:
Question 2 – Corporate Finance
The appraisal of a new project needed for the expansion of production capacity has just been
completed and the NPV is negative, with the implication that the project should be rejected.
Then the operations manager argued that the discount rate used to calculate NPV was too
high. He claimed “The entire investment for the project should be funded with bond issues,
and when calculating NPV we should use the cost of debt as the discount rate.”
Do you agree with the operations manager? Provide two reasons supporting your point of
view.
(3 marks)
Solution to question 2
(i)
Generally for an investment project to be adopted it must generate greater returns than
the rate of return (cost of capital) demanded by the providers of funds (shareholders
and creditors) from investment opportunities with equivalent risk. This project would
increase production capacity, so its risk profile should be similar to the average risk
profile of the company as a whole. It is therefore more reasonable to apply the
company-wide WACC as the discount rate because it reflects the capital structure for the
company as a whole.
(1½ marks)
(ii)
The method by which investment funds are raised for a project has no direct bearing on
the project's discount rate. The project itself does not bring the company any increase in
debt capacity. In addition, it does not have any impact on the target debt ratio.
(1½ marks)
(3 marks)
Question 3 – Equity Valuation and Analysis
Under what circumstances might a company be tempted to pay dividends which are in excess
of earnings, and what are the dangers associated with such an approach? Ignore taxation.
(3 marks)
Solution to Question 3
Payment of dividends from reserves
If a company pays dividends in excess of earnings, then this payment must be made out of
reserves. The effect of this will be reduce the asset value of the business.
Reasons for payment from reserves
i) The company believes that it must continue to pay a high level of dividends in order to
support the share price. If profits for the year are too low to support the previous level
of dividends, the directors may decide that it should make a payment out of reserves rather
than reduce the level of dividends
ii) If a company has a high level of reserves for which it cannot find an attractive
investment opportunity, it may decide that appropriate to repay part of those reserves to
investors by means of dividend payment.
(1 mar k)
Problems with payment from reserves
i) The fall in asset value of the business may make it more vulnerable to takeover bid.
ii) The market may see the payment out of reserves as a desperate measure on the part of
the directors, and this may trigger a significant drop in the price.
iii) Payment of dividends that are in excess of earning could lead to a shortage of cash
for the business.
(2 marks)
(3 marks)
Page 2 of 12
Question 4 – Fixed Income Valuation and Analysis
4a)
When using duration to approximate the price change of a bond due to interest rates
change, certain assumptions are made.
List four of these assumptions.
(2 marks)
4b) You want to immunise a liability occurring in 8 years with two bonds: A and B. Bond A
has a maturity of 2.5 years and a duration of 2 years; Bond B has a maturity of 12.5
years and a duration of 10 years. Calculate the weight of the portfolio invested in bond
A and bond B.
(2 marks)
Solution to Question 4
4a)
The key assumptions are:
i)
ii)
iii)
iv)
The yield curve is flat.
A parallel change in yield
A small change in yield.
An instantaneous change in yield.
(1/2 marks per valid point)
(2 marks)
4b)
Let
w= weight of bond A and.
1 – w = weight of bond B
To be immunised, duration of asset must equal duration of liability:
2w+10(1-w) = 8
2w+10-10w
=8
-8w=-2
w=-2⁄-8
= 0.25
Bond A 25%
Bond B 75%
(2 marks)
4 marks
Page 3 of 12
SECTION C:
Question 5 – Corporate Finance
You are a financial consultant to Iwelabi Plc, a company listed on the stock exchange.
Iwelabi is involved in publishing books mainly for primary, secondary and university
students.
The company is currently considering a project to manufacture ink which is a key raw
material needed in its publishing business.
A major concern at this stage is the determination of the appropriate cost of capital for the
company.
The company has compiled the following data:
Debt capital
The company’s debt capital exclusively consists of two bonds:
Bond
Maturity
Annual coupon
Repayment
A
B
1year
5years
5%
0%
100%
100%
Current market
price
102%
84%
Outstanding
amount
N20m
N40m
Equity capital and market
Current value per share
Number of shares
Forecast dividend for next year
Growth rate in dividend
Equity beta
Risk-free rate
Equity market risk premium
Tax rate
5(a)
₦16
5,000,000
₦1
5%
0.8
3%
10%
25%
Compute the average cost of debt capital, taking into account tax effect.
(5 marks)
5(b) Calculate the cost of equity capital using:
5b1)
Dividend valuation model
5b2)
Cost of equity using CAPM
(3 marks)
5(c) In general, do the dividend valuation model and the CAPM lead to the same result?
Explain your answer.
(1 mark)
5(d)
5(e)
Determine the WACC, assuming cost of equity of 10%.
(3 marks)
The CEO informs you that funding of the new project will not be a problem since
shareholders have agreed to an appropriate right issue of shares. He suggests that
the financial appraisal of the project should proceed, using the WACC determined in
(d) above. Do you agree with the CEO on the use of the WACC calculated in (d)
above?
Justify your answer.
(4 marks)
Page 4 of 12
Solution to Question 5 – Corporate Finance
5(a)
First, we need to compute the YTM of each bond
Bond A:
YTM
=
=
= 2.94%
(1 mark)
Bond B (zero coupon bond):
YTM
=
=
= 3.55%
(1 mark)
Next, we determine the weighted average cost of the two bonds
Bond
Market
value
Cost
(Nm)
Hash
Total
(Nm)
A
20.40
0.0294
B
33.60
0.035
0.60
1.176
54.00
1.776
(2 marks)
Average cost, before tax
=
= 3.29%
(½ mark)
After tax cost of debt = 3.29% (1 – 0.25)
= 2.47%
(½ mark)
(5 marks)
5(b) Calculate the cost of equity capital using:
5b1)
KE =
5b2)
Dividend valuation model
D1
VE
Cost of equity using dividend model:
+𝑔=
1
16
+ 0.05 = 11.25%
(1½)
(1½ marks)
Cost of equity using CAPM
KE
= RF + β(Rm – RF)
= 3 + 0.8(10)
= 11%
(1½ marks)
(3 marks)
Page 5 of 12
(5c)
The results may differ due to the fact that models are based on different
assumptions.
The assumptions may not apply to all models or they may not be fulfilled for both
models
(1mark)
5(d)
Total market value of equity:
5m × N16
= N80m
(½ mark)
The WACC is computed as follows:
Capital
Debt
Equity
Market value
(Nm)
54
80
134
Cost (%)
2.47
10
WACC = 9.3338 / 134 = 6.97%
Hash Total
(Nm)
1.3338
8.0000
9.3338
(2½ marks)
(3 marks)
5(e)
The WACC computed above cannot be used to appraise the new project because
its use will violate the following assumptions WACC:

Constant business risk
The use of WACC assumes that the business risk of the new project is the same
as the average business risk of the company. This will probably be the case if
the new project represents an expansion of existing activities in the existing
industry.
In the scenario here however, the new project is a diversification into a new
industry (ink production vs publishing). The project is likely to belong to a
radically different business risk class and if so the use of the existing WACC will
be invalid.
(2 marks)

Constant financial risk
It is assumed that the financing of the new project will not significantly alter the
company’s financial leverage and hence financial risk. It is being proposed
however, to finance the project wholly with equity (rights issue). This will alter
the company’s financial leverage and its financial risk. The use of the existing
WACC will not be appropriate in such situations.
(1½ marks)
What is required is that the company should determine the appropriate project
specific discount risk that considers the project’s business risk (its asset beta)
and the company’s method of financing.
(½ mark)
(4 marks)
Page 6 of 12
Question 6 –Equity Valuation and Analysis
Glasy Plc is the world’s premier manufacturer of glass. The global industry is estimated to be
growing at an annual rate of 8%. Currently the company has a market share of 6% in the
global glass industry.
In the last 5 years, the company has average ROA (return on asset) of 16% and a payout
ratio of 30%. The average interest rate on its debt capital has been 6%. The company has
maintained a constant debt/equity ratio of 40% in the period.
In the year just ended the company reported EPS of N20. The current stock price is N162.
6(a) Calculate the sustainable growth rate of dividends for the stock assuming that the firm
will maintain the ROA of 16% and the payout ratio of 30%
(2 marks)
6(b) Using the constant growth model, calculate the cost of equity of the company based on a
current EPS of ₦20. Assume the long term sustainable growth rate equals the industry growth
of 8%.
(3 marks)
6(c) You feel that input prices (raw materials and labour) will drop significantly (as a result of
world-wide crash in oil prices) in the medium term i.e. the next four years.
Consequently, you expect there will be a margin expansion resulting in the EPS growing
at 25% for four years and then settling down to an 8% growth rate. Calculate the value
of the stock with these assumptions using the dividend discount model. Assume cost of
capital 13.5% and current EPS as N20. Is the stock currently overvalued or
undervalued?
(3 marks)
6(d) What is the current P/E ratio of the company? Indicate how the P/E ratio will be
affected by each of the following independent events? Indicate whether the ratio will
increase, stay the same or reduce by each of the events. Justify your response.
(4 marks)
6d1)
An increase in investors’ risk aversion.
6d2) An investment in an advanced production technology that cuts unit variable
production cost but increases fixed operating costs.
6d3)
A reduction in the payout ratio.
6d4)
A right issue of shares with the proceeds used to pay off part of long-term debt.
Solution to Question 6 –Equity Valuation and Analysis
6(a)
Growth rate (g) is given by:
g = (ROE)(b),
where b = retention rate.
ROE = ROA + (ROA – i) × D/E
Where i = average interest rate on debt.
ROE = 16 + (16 – 6)% × (0.40) = 20%
g = (20) (1 – 0.30) = 14%
(2 marks)
Page 7 of 12
6(b)
Po
= 162
g
= 8%
EPS1
= 20(1.08)
DPS1
= 21.60(0.30)
Po =
= 21.60
(1/2 mark)
= 6.48
(1/2 mark)
𝐷1
𝑟−𝑔
162 =
6.48
𝑟−0.08
(1 mark)
162(r – 0.08) = 6.48
r – 0.08 = 0.04
r = 12%
(1 mark)
(3 marks)
6(c)
Eo
= 20
Do
= 20 × 0.30 = 6
D1
= 6 × 1.25
= 7.5
2
D2
= 6 × (1.25)
= 9.375
D3
= 6 × (1.25)3
= 11.719
D4
= 6 × (1.25)
4
= 14.648
D5
= 6 × (1.25)4 × (1.08) = 15.82
= 14.648(1.08) = 15.82
The current stock price is the present value of future dividends
₦
Year 1
7.5 ×
2
9.375 ×
3
11.719 ×
4
14.648 ×
1
= 6.61
1.135
1
2
= 7.28
1.135
1
3
= 8.01
1.135
1
1.135
4
= 8.85
30.75
Year 5 – infinity:
15.82
×
0.135−0.08
1
1.135
4
= 173.32
204.07
(3 marks)
Page 8 of 12
Alternative method
The PV of dividends for the first 4 years can also be calculated using growing annuity:
1+𝑔 𝑛
𝐷
1
PV = 𝑟−𝑔
1−
1+𝑟
7.5
= .135− 0.25 1 −
1.25
4
= 30.73
7.5
1.25
= .135− 0.25 1 − 1.135
1.135
4
Add PV of dividends from year 5 – infinity as above
= 30.73
= 173.32
204.05
At ₦162, the stock seems to be clearly undervalued according to our expectations.
6(d)
Current P/E = Po / Eo
= 162/20
= 8%
To assess the impact of the various events, we know that
𝑃
P/E ratio = 𝐸0 =
𝑜
Or
𝑃0
𝐸1
=
1−𝑏
1−𝑔
1−𝑏
1−𝑔
(1 + 𝑔)
.
(Trailing P/E ratio)
(Leading P/E ratio)
6d1)
An increase in investors’ risk aversion will make the investors to demand a higher
risk premium. This increases ‘r’ in the formula and reduces P/E ratio.
(1 mark)
6d2)
This transaction increases the operating leverage, the asset beta and ‘r’ in the
formula. P/E ratio will drop.
(1 mark)
6d3)
A reduction in payout ratio increases retention rate and that leads to higher ‘g’ in
the formula. P/E ratio should increase.
(1 mark)
6d4)
A right issue of shares with the proceeds used to pay off part of long-term debt.
This transaction reduces financial leverage and hence financial risk. The value of
‘r’ should drop and P/E ratio should increase.
(1 mark)
(4 marks)
Question 7 – Fixed Income Valuation and Analysis
7(a) Table 1 shows the characteristics of two annual pay bonds from the same issuer with
the same priority in the event of default, and Table 2 displays spot interest rates.
Neither bond’s price is consistent with the rates.
Table 1: Bond Characteristics
Coupons
Maturity
Coupon rate
Yield to maturity
Price
Bond A
Annual
3 years
10%
10.65%
98.40
Bond B
Annual
3 years
6%
10.75%
88.34
Page 9 of 12
Table 2: Spot Interest Rates
Term
1 year
2 year
3 year
Spot Rates
(zero coupon )
5%
8%
11%
Using the information in Table 1 and Table 2 recommend either Bond A or Bond B for
purchase. Justify your choice.
(6 marks)
7(b)
A bond for the Kudi Plc has the following characteristics
Coupon payment
Maturity
Yield to maturity
Macaulay duration
Convexity
Noncallable
Semi-annual
12 years
9.50%
5.8 years
58
7b1)
Calculate the approximate price change for this bond (using only its duration)
assuming its yield to maturity increased by 150 basis points. Discuss the impact
of the calculations, including the convexity effect.
7b2)
Calculate the approximate price change for this bond (using only its duration) if
its yield to maturity declined by 300 basis points. Discuss (without calculation)
what would happen to your estimate of the price change if this was a callable
bond.
(3½ marks)
7(c)
Explain how each of the following two ratios should be used to evaluate a firm’s
financial risk
c1)
7c2)
Total debt to total capital
Pretax interest coverage
(2½ marks)
(6 marks)
Solution to Question 7 – Fixed Income Valuation and Analysis
7(a)
The essence of the answer is to price each bond's cash flows using the spot curve (Table 2).
The non-arbitrage price of bond A is
10
1.05
+
10
1.08 2
+
110
1.11 3
= 98.53
(21/2 marks)
The market price 0 f Bond A is 98.40, which is 13 kobo (13.2 basis points of market
price) less than the non-arbitrage price.
The non-arbitrage price of Bond B is
6
1.05
+
6
1.08 2
+
106
1.11 3
= 88.36
(21/2 marks)
The market price of Bond B is 88.34, only 2 kobo (2.3 basis points of market price) less
than the non-arbitrage price.
Page 10 of 12
Conclusion: Despite having the lower yield to maturity (10.65 percent versus 10.75
percent), Bond A is the better value because the excess of its non-arbitrage
price over market price is greater than for Bond B.
(1 mark)
6 marks
7(b)
7b1)
Assuming semiannual interest payments
Modified duration =
= 5.442 years
Percentage change in price = – Dmod × ∆i
= – (5.54) × (+ 150/100)
= –8.31 percent
(11/2 marks)
A misestimate of the price change will arise because the modified-duration line is
a linear estimate of a curvilinear function. That is, convexity measures the rate of
change in modified duration as yields change. The effect of convexity on price
should be added to the effect of duration on price in order to obtain an
improved approximation of the change in price given a change in yield.
(1/2 mark)
7b2)
Percentage change in price = –5.54 × –3% = + 16.62%
(½ mark)
The 3% decline in rates may not elevate the bond price by 16.33% if the bond's
call price is violated and protection against a call has elapsed.
(½ mark)
3 marks
7c1)
The total debt to total capital ratio measures the degree of leverage of the firm.
Leverage is the relationship of debt owed to the company's total resources as
valued on the balance sheet. An analyst would evaluate the absolute leverage
and the change in the use of leverage for a firm and compare the level of
leverage to that of other companies in the same industry. A firm with a high total
debt-total capital ratio will be perceived as having a higher level of credit risk. By
comparing this ratio to its competitors' ratio, an analyst can judge the prudence
of such leverage for a company in the particular industry. A firm increases its
financial leverage when it takes on more debt in proportion to its total
capitalization (resources). The change in financial leverage may indicate a change
in the company's attitude towards risk taking. The firm will lose some financial
flexibility financing alternatives and ability to access funds -and will generally pay
a higher price to acquire funds than a lower-leveraged company. Higher financial
leverage may also reduce the firm's choices for financing future growth and
paying dividends. Covenants may restrict the company's ability to use its
financial resources as it sees fit when this ratio becomes too high.
(11/2 marks)
7c2)
The pretax interest coverage ratio measures the annual interest burden (the
amount the firm must pay its creditors) placed on a firm relative to its earning
capacity. This coverage ratio is important because it looks at the firm's ability to
pay its annual interest expense from pretax earnings (EBIT). A high coverage ratio
is considered positive; a low coverage ratio may indicate more risk, which is a
financial constraint. The ratio also suggests the protection afforded creditors to
continue to receive interest income, despite a business downturn or an increase in
leverage by the firm. Although this ratio indicates the ability of the company to pay
cash to its creditors, the numerator includes noncash earnings and is reduced by
noncash expenses. Finally, the comfort level of coverage should be based on the
expected consistency of earnings (an industry issue) and with consideration given
to the firm's access to cash.
(11/2 marks)
3 marks
Page 11 of 12
FORMULAE
Levered/unlevered beta:
Annuities:
Yield to maturity of a bond:
Valuation of perpetual bonds:
Price change approximated with duration:
Portfolio duration:
Macaulay duration:
Page 12 of 12