TUTORIAL QUESTIONS
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Corporate Finance
Tutorial 1 Questions
Q1 NPV CALCULATION
Hardy Ltd is considering whether to set up a division to make a new product, the Tess. A
feasibility study recently undertaken (but not yet paid for) at a cost of £85,000 suggests that
the Tess should be sold for £35, generating sales of about 10,000 units for each of the next 8
years. However, after the preparation of the following statement showing that the new
division would make an annual loss, the directors have decided not to go ahead with
producing the Tess.
£ £
Annual income (10,000 × £35) 350,000
Expenses:
Feasibility study (cost spread over life of 10,625
project)
Wages (note 1) 135,000
Salaries (note 2) 12,000
Materials (note 3) 70,000
Variable overheads (note 4) 43,000
Rent (note 5) 12,000
Depreciation (note 6) 50,000
Head office charge (note 7) 30,000
(362,625)
Loss (12,625)
Notes:
1. The wages figure represents three hours per unit at £4.50 per hour.
2. The salaries figure is made up of a manager’s salary of £7,000 p.a. and a supervisor’s
salary of £5,000 p.a. Both are currently employed by Hardy. If the Tess is not
produced the manager will remain in employment, but the supervisor will be
‘persuaded’ to take early retirement at a pension of £2,000 p.a. Otherwise, the
supervisor will retire as soon as the project ends.
3. Each Tess needs 2kg of material costing £3.50 per kg.
4. Variable overheads would be £4.30 per unit.
5. The new division would occupy a factory for 8 years at an annual rent of £12,000.
6. Manufacture of the Tess would require a machine costing £400,000, with no scrap
value at the end of eight years. Hardy Ltd charges depreciation on a straight-line
basis.
7. Hardy Ltd apportions its fixed head office costs at the rate of £1 per square metre of
floor space. Total head office costs would increase by £5,000 p.a. if the new division
were set up.
8. The cost of capital of Hardy Ltd is estimated at 6% p.a. and, other than the cost of the
machine, cash flows arise at the end of the year to which they relate.
REQUIRED:
(a) Prepare calculations to show whether the directors have made the right decision.
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(b) Explain the assumptions underlying the calculations you have performed in part (a)
and the reasons for your treatment of the various costs.
(c) Produce a statement showing how sensitive your decision is to the estimates of:
(i) direct labour costs;
(ii) annual sales volume;
(iii)product life (work in whole years)
(Hint: Sensitivity analysis involves calculating by what amount each of the factors
above has to change to produce an NPV of zero. A change in sales volume affects
variable costs too.)
Q2 NPV AND IRR CALCULATION
Diggers plc is considering the viability of a contract to supply tractors to a new customer for
a 5 year period. The company accountant provides you with the following information.
Immediate capital outlays:
£
New machinery 1,800,000
Set-up costs 60,000
Scrap value of machinery in 5 years 200,000
During each year of the contract it is expected that 25 tractors will be supplied. Each will
need £15,000 of parts and £3,000 of other variable costs including labour.
Assume that unit variable costs will be the same each year. Fixed costs of the company will
not change but the project will be apportioned these costs at a rate of £1,000 per tractor.
The company is currently operating close to capacity and if the contract is accepted, cash
income from other operations will be reduced by £12,000 per annum in years 1 to 4 and by
£60,000 in year 5. Other than immediate cash flows, all cash flows arise at the end of the year
to which they relate.
REQUIRED:
(a) If the company’s cost of capital is 10% and the price per tractor is £40,000:
(i) calculate the NPV of the project.
(ii) calculate the ‘break-even price’ per tractor (that at which the !"# $ %).
(b) Would you recommend acceptance of the contract? Why?
(c) Explain your treatment of the fixed costs and of the reduction in income from other
operations.
(d) Assuming that the price per tractor is £40,000, estimate the IRR of the project for
Diggers plc using linear interpolation.
(e) What factors other than the NPV or IRR of the contract might be considered in
making the decision?
37
Corporate Finance
Tutorial 2 Questions
Q3 NPV with inflation
Oz plc is considering a new project, manufacturing and selling Wizards. The directors
commissioned a firm of accountants to evaluate the project and their report suggests that it is
viable. The directors are not sure that the effects of inflation have been correctly dealt with,
so they have asked you to check the calculations. The following information is available.
Cost of accountants’ report £5,000
Cost of plant and machinery which
must be purchased at the beginning of £60,000 (Note 1)
the project
Projected sales at current prices £21,000 per annum (Note 2)
Expected labour costs at current prices £5,000 per annum (Note 3)
Other costs at current prices £3,000 per annum (Note 4)
Notes:
1. The project will last for five years, at the end of which the machinery is expected to
fetch £3,000 (at current prices). The scrap proceeds are expected to rise in line with
the retail price index (RPI) and the RPI is predicted to increase at 5% per annum.
2. Sales prices will be subject to controls by the government. They will be allowed to
increase at only 3% per annum.
3. Skilled labour is required to operate the machinery and a skill shortage is expected
over the next five years. This will result in an annual increase of 9% in labour costs.
4. Other costs are expected to rise in line with the RPI. They consist of £2,000 direct
production costs and £1,000 apportioned overheads. The overheads represent the costs
of the building in which the company operates at present; no new premises will be
required to accommodate the project.
The company has been promised a loan from the bank with which to finance the project. The
real rate of return on this is 4% and it is linked to the RPI. Note that the relationship between
real and nominal rates of interest is:
!! " nominal rate, # !! " real rate, $ !! " inflation rate,
All cash flows arise at the end of the year to which they relate. The company does not pay
corporation tax.
REQUIRED:
(a) Calculate the net present value of the project. We saw in Lecture 1 how discount rates
can be adjusted to allow for inflation. Use discount factors to 3 decimal places. (Hint:
find the nominal required rate of return and adjust this for the inflation of each cash
flow as appropriate)
(b) Advise the directors on how to proceed, making clear any reservations you may have
about your advice.
(c) Explain (without calculations) how you would incorporate corporation tax into the
project appraisal.
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(d) Describe the payback and accounting rate of return methods of investment appraisal
and discuss why the discounted cash flow (DCF) method is preferable.
Q4 THE OPTION TO EXPAND – CASE STUDY
Example 12.6, Chapter 12, HGT
PLEASE LOOK AT THE ANSWER PROVIDED BELOW TO THIS QUESTION WHICH WE WILL GO
THROUGH DURING THE TUTORIAL, AND THEN ATTEMPT QUESTION 5 BELOW.
Clacher Industries is considering building another cider brewery. The brewery will generate
cash flows two years from now, as follows:
WITHOUT EXPANSION OPTION
!!" Economy at ! ! # Economy at ! ! $ !!$
Good +£200m
–£140m Good
Bad +£150m
Good +£150m
–£140m Bad
Bad +£100m
The cash flows from the brewery will be £200 million following two good years, £150
million following one good and one bad year and £100 million following two bad years. The
initial cost of the plant is £140 million.
After one year, however, if the state of the economy looks good, the firm has the option to
double the plant’s capacity by investing another £140 million. This has the following effect
on the cash flows:
WITH EXPANSION OPTION
!!" Economy at ! ! # ! ! # Economy at ! ! $ !!$
–£140m Good +£400m
–£140m Good
–£140m Bad +£300m
0m Good +£150m
–£140m Bad
0m Bad +£100m
Doubling the brewery’s capacity will have the effect of doubling the cash flows to either
£400 million or £300 million in its final year.
Assume a risk-free rate of 5 per cent per year and that £1.00 invested in the market portfolio
today yields future values, depending on the state of the economy, as follows:
Economy at ! ! # ! ! # Economy at ! ! $ !!$
Good £1.60
Good £1.30
Bad £1.10
Good £1.10
Bad £0.80
Bad £0.70
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Compute the value of building a plant under two scenarios: in Scenario 1, the option to
double the brewery’s capacity is ignored; in Scenario 2, it is not ignored.
Q4 THE OPTION TO EXPAND – ANSWER
Risk neutral probabilities (from Lecture 2)
The 3 equations to solve are
!"#$!!"$%" & '!"($# ) '!"!$*! + #, (1)
$"-$!!"$%" & '!"!$# ) '$".$*! + #, (2)
!"$$!!"$%" & '!"#$# ) '$"-*! + #, (3)
Economy at $ & ! $ & ! Economy at $ & / $ & /
Good #*!, 0.53
Good #*#, 0.5
Bad *! + #,*!, 0.47
Good #*/, 0.35
Bad *! + #,*#, 0.5
Bad *! + #,*/, 0.65
Expected future cash flows with risk neutral probabilities
NO EXPANSION:
$&/
Good / Good £53m *'/$$% 2 $"% 2 $"%#,
*01 $"% 2 $"%#,
Good / Bad £35.25m
*01 $"% 2 $"3.,
Bad / Good £26.25m
*01 $"% 2 $"#%,
Bad / Bad £32.5m
*01 $"% 2 $"(%,
Total £147m
405 & +!3$ ) !3.6!"$%! & +'("(.%
EXPANSION:
$&! $&/
Good / Good +'#."!m *'!3$% 2 $"% 2 £106m *'3$$% 2 $"% 2 $"%#,
*01 $"% 2 $"%#, $"%#,
Good / Bad +'#/"7m £70.5m
*01 $"% 2 $"3.,
Bad / Good £26.25m
*01 $"% 2 $"#%,
Bad / Bad £32.5m
*01 $"% 2 $"(%,
Total +'.$"$m £235.25m
Note that the $ & ! cash flow is simply '!3$% 2 $"% (the probability of a good outcome)
40
NPV $ %140 % 70/1.05 - 235.25/1.05! $ £6.7122
Q5 THE OPTION TO CONTRACT – CASE STUDY
Exercise 12.2, Chapter 12, HGT
The XYZ firm can invest in a new DRAM chip factory for $425 million. The factory, which
must be invested in today, has cash flows two years from now that depend on the state of the
economy. The cash flows when the factory is running at full capacity are as follows:
Economy at 3 $ 1 Economy at 3 $ 2 3$2
Very Good +$1billion
Good
Medium +$200m
Medium +$200m
Bad
Very Bad –$500m
In year 1, the firm has the option of running the plant at less than full capacity. In this case,
workers are laid off, production of memory chips is scaled down and the subsequent cash
flows are half of what they would be when the plant is running at full capacity.
An alternative use for the firm’s funds is investment in the market portfolio. In the states that
correspond to the table above, $1 invested in the market portfolio grows as follows:
Economy at 3 $ 1 3 $ 1 Economy at 3 $ 2 3$2
Very Good $1.20
Good $1.10
Medium $1.05
Medium $1.05
Bad $0.95
Very Bad $0.90
Assume that the risk-free rate is 5 per cent per year, compounded annually.
Compute the project’s present value (a) with the option to scale down and (b) without the
option to scale down. Compute the difference between these two values, which is the value of
the option.
41
Corporate Finance
Tutorial 3 Questions
Q6 WACC
Greystoke plc is a geared company. Its directors have asked you to estimate the weighted
average cost of capital (WACC) of the company and have provided you with the following
information.
A dividend of 11 pence per share is just about to be paid on the ordinary share capital, of
which there are 200,000 shares in issue with a market price of £1.31 per share. Past growth
rates in dividends have varied, but average growth has been about 10%.
The company has £50,000 (nominal value) 8% irredeemable debentures in issue. They are
not traded, so no market price is available. However, the risk-free rate of return in the
economy is about 7% pa and the directors estimate that debt holders require a 3% annual
premium to reflect the riskiness of the debentures. Interest is paid annually and the company
earns sufficient profits to utilise all tax relief on the interest. The corporation tax rate is
currently 31%.
Over the past few years, the company’s returns have had a correlation coefficient of about 0.8
with returns on the FT All Share index. The index returns have had a standard deviation of
0.2 per annum, while the annualised standard deviation of Greystoke’s returns has been 0.3.
The historic market risk premium (that is the excess return on the index, over and above the
risk-free rate) is 9%.
Note from Lecture 3: ! ! "#$%&! " &" '#(#$!
From basic statistics we know that: "#$%&! " &" ' ! )!" (! ("
where )!" ! the correlation between returns on asset * and returns on asset M.
REQUIRED:
(a) Assuming that tax relief is received on interest payments as they arise, estimate the
costs of equity and debt capital of Greystoke plc, giving reasons for the figures which
you use in the calculations.
(b) Estimate the WACC of Greystoke plc.
(c) Discuss the theoretical assumptions underlying your calculations in (a).
(Ignore income tax)
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Q7 WACC & APV
General Motors Case Study (adapted from HGT)
In 1985, General Motors (GM) was evaluating the acquisition of Hughes Aircraft
Corporation. Recognizing that the appropriate WACC for discounting the projected cash
flows for Hughes was different from General Motors’ WACC, GM assumed that Hughes was
of approximately the same risk as Lockheed or Northrop, which had low-risk defence
contracts and products that were similar to those of Hughes. GM plan to acquire Hughes for
$3 billion ($3,000 million) and to maintain their current Debt/Equity ratio.
The following data are available:
Beta of Equity Debt/Equity
GM 1.20 1
Lockheed 0.90 0.90
Northrop 0.85 0.70
Hughes expected cash flow before interest = $300m per annum in perpetuity
Corporation tax rate = 34%
Required return on debt = risk free rate = 8%
Expected return on tangency portfolio = 14%
REQUIRED:
(a) Assume that the Hamada model applies (fixed perpetual debt).
(i) Compute the betas of the comparison firms, Lockheed and Northrop, as if they
were all equity financed.
(ii) Compute the asset beta of the Hughes acquisition, by taking the average of the
asset betas of Lockheed and Northrop.
(iii)Compute the equity beta for the Hughes acquisition at the target debt level.
(iv) Compute the WACC for the Hughes acquisition.
(v) Compute the NPV of the acquisition of Hughes employing the WACC.
(vi) Apply the APV method. First, compute the value of the Hughes acquisition as if
all equity financed using the opportunity cost of capital (the return on assets).
Next, compute the present value of the tax shield. Finally, add the two numbers.
(b) Re-evaluate the Hughes acquisition via the APV method assuming that it will be
made with a constantly rebalanced amount of debt (Miles and Ezzell model).
(c) Explain the differences between your answers to (a) and (b) above.
(d) What are the advantages of using the APV method relative to the WACC?
43
Corporate Finance
Tutorial 4 Questions
Q8 DIVIDEND POLICY 1
Notes: Under the Lintner model companies have long-run target dividend payout ratios.
Managers smooth dividends to avoid big changes so that transitory earnings changes don’t
affect dividend payouts. Managers adjust only slowly towards the target payout rate. In this
example two companies have adjustment rates (toward target dividends). The dividend for
the current year can be calculated via the Lintner model as follows:
!"#! $ !"#!"# % Adjusted Change in Dividend
Adjusted change in dividend $ Adjustment factor & Target change in dividend
Target change in dividend $ Earnings & Target payout ratio 4 Last year's dividend
Example
Nietzsche plc bases its dividend policy on the Lintner model. It has a target payout rates of
60% and an adjustment rate of 0.3.
The recent pattern of EPS is:
EPS (pence)
20x1 26.2
20x2 30.1
20x3 20.5
It paid a dividend of 11.8 pence per share in 20x0. Calculate the dividend per share each year
and the actual payout ratio.
Answer to example
20x1:
Target change in dividend = Earnings (26.2) & Target payout ratio (0.6) – Last year’s
dividend (11.80) = 3.92
Adjusted change in dividend = Adjusted factor (0.3) & Target change in dividend (3.92) =
1.18
!"#! $ !"#!"# 611.80; + Adjusted Change in dividend (1.18) = 12.98
Payout ratio = Dividend (12.98) / Earnings (26.2) = 49.5%
Niet. 1 2 3 4 5 6 7
!"#!"# <=>! Target !"#! Target Adjusted !"#! Actual payout
(col 2 × target Δ!"# Δ!"# (col 1 ratio %
payout ratio) (col 3 – (col 4 × +
col 1) adj.rate) col 5)
20x1 11.80 26.20 15.72 3.92 1.18 12.98 49.5
20x2 12.98 30.10 18.06 5.08 1.52 14.50 48.2
20x3 14.50 20.50 12.30 –2.20 –0.66 13.84 67.5
REQUIRED:
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Two companies, Nietzsche plc and Wittgenstein plc, base their dividend policy on the Lintner
model. Both have target payout rates of 60%. Neitzsche plc’s adjustment rate is 0.3, and
Wittgenstein’s is 0.8.
The recent pattern of their EPS is identical:
EPS (pence)
20x1 26.2
20x2 30.1
20x3 20.5
20x4 27.7
20x5 29.0
They both paid a dividend of 11.8 pence per share in 20x0. For each company, calculate the
dividend per share each year and the actual payout ratio. Draw a graph showing the earnings
and dividends per share on the vertical axis and time on the horizontal axis. Discuss the
intuition behind the Lintner model equation, illustrating your explanation with the results of
your calculations. (You may want to use Excel for this exercise.)
Q9 DIVIDEND POLICY 2
Noble plc, a listed company, has for a number of years paid an annual dividend of 90p per
share on its 200,000 ordinary shares, which have a total market value of £930,000 cum div.
The next annual dividend of £180,000 is due to be paid within a few days. It is generally
expected that the company’s dividends will always be at the current level. Noble has no debt
capital.
The directors of Noble plc are considering an investment project that would involve the
immediate investment of £100,000 and would produce net annual receipts of £26,400
indefinitely. The first receipt would arise after one year. Details of the project have not yet
been made public. All receipts from the project would be distributed as dividends when
received. The directors believe that the project has the same business risk as the current
operations of the company.
If the project were undertaken, it would be financed in one of two ways:
(i) A reduction of £100,000 in the current dividend.
(ii) A public issue of ordinary shares; the new shares would rank for dividend one year
after issue.
Assume that, if the project were accepted, the directors’ expectations of future results would
be communicated to, and believed by, the stock market, and that the market would perceive
the risk of the company to be unaltered.
REQUIRED:
(a) Estimate the new market price per ordinary share, ex div, if the project is accepted and
financed by a reduction in the current dividend.
(b) At (a) above all of the gains from the project went to the old shareholders. Calculate
the price at which new shares would be issued, the number of new shares to be issued
and the new future dividend per share under financing option (ii) above, assuming that
the benefit from the project is to go to the existing shareholders.
45
(c) Under the MM dividend irrelevancy proposition the method of financing the new
investment shouldn’t matter to the shareholders. Show that this is the case employing
the example of a holder of 100 existing shares in Noble.
(d) Discuss the relative merits of each of the two sources of equity finance in practice.
(Ignore issue costs of new shares and taxes in parts (a) to (c), but not in part (d))
46
Corporate Finance
Tutorial 5 Questions
Q10 CAPITAL STRUCTURE 1
Granby Biotech has no debt financing and an asset beta of 0.7. Assume a risk free rate of 5%
and that the CAPM holds and the expected return on the market portfolio is 13%.
REQUIRED:
(a) There are no corporate taxes or costs of financial distress or bankruptcy !"! !
#" # $$%& % "" '. Assume that the company repurchases its equity by issuing debt at
the risk free rate of 5%. As more debt is issued the return on debt does not change.
Calculate the WACC, return on equity and return on debt at 0%, 20%, 40%, 60%,
80% and 99% debt and plot these figures on a graph.
(b) Explain your results with reference to the Modigliani Miller capital structure
irrelevancy theorem.
(c) Now assume that debt attracts corporation tax relief at 35%. Recalculate the return on
equity [again, assume "! ! #" # $$%& % "" ], the return on debt and the WACC at
0% debt, 20%, 40%, 60%, 80%, 100%. Plot your results on a graph.
(d) What conclusions do you draw from your graph at (c) above.
(e) How do personal taxes and costs of financial distress affect the conclusions drawn at
(d) above.
Q11 CAPITAL STRUCTURE 2
Helix started an internet company, Survey-Partner.com, which, unlike others in the industry,
generated taxable earnings almost immediately. Helix owns 10 per cent of the shares, and the
rest of the shares are held by tax-exempt institutions. The firm needs to raise £100 million in
new capital. Helix would like to see the firm issue equity and would be willing to purchase
£10 million of the new equity to keep his ownership stake constant. However, the institutions
would like to see the firm raise the capital through debt. Explain how part of this
disagreement might be related to taxes.
Q12 CAPITAL STRUCTURE 3
Locatelli plc is a racing car manufacturer, which is considering making a donation of
£1,000,000 to a political party. The donation is expected to result in increased inflows of
£180,000 p.a. in perpetuity before corporation tax. The donation in no way affects the
operating risk of the company. The company intends to finance the donation by issuing
£500,000 of 10% debentures at par and £500,000’s worth of ordinary shares.
The current capital structure of the company is as follows:
MV (£’000) Required Return (%)
Debt (riskless) 2,000 10
Equity 8,000 18
47
The corporation tax rate is 30%. There is no time lag between taxable flows and the tax
payments or receipts arising from those flows. The required return on the market portfolio is
18% and the risk free rate is 10%. Ignore income tax.
The assumptions of the Hamada model apply throughout.
&# '
!"## ! $!" " %# $ )
'%(
',# $ &# .
*$ ! +# % / " *!"
(
REQUIRED:
(a) Calculate the WACC, the return on unlevered assets and the beta of the unlevered
assets of Locatelli before the donation.
(b) Explain how you expect each of the above to change if the new project goes ahead.
(c) Use the APV method to calculate the net present value of the project, clearly showing
the NPV due to financing versus that due to the project.
(d) Calculate the new market value of equity by adding the PV of after tax cash flows
from the project to the existing market value of the company and deducting the
market value of debt.
(e) Calculate the new equity beta, required return on equity and WACC if the project
goes ahead. Compare these to the equity beta and WACC before the project and
explain the difference.
(f) Calculate the new dividend if the project goes ahead under the assumption that
dividends can be treated as perpetuities (Hint: Calculate the value of the old dividend
needed to return 18% and add the value of the new dividend). Discount this dividend
at the required return on equity to obtain a further estimate of the market value of
equity if the project goes ahead. Calculate the NPV of the project for equity holders
by comparing the total contribution to company financing after the project with the
discounted value of new dividends.
(g) Similarly calculate the NPV for debt holders by showing total contribution to
company financing of debt after the project and returns to this financing discounted at
the appropriate rate of return.
(h) Discuss the practical difficulties encountered in estimating a cost of capital suitable
for appraising a new project.
48
