Decision with respect to the financial viability of the project
TOOLS FOR INVESTMENT APPRAISAL
1. ACCOUNTING RATE OF RETURN (ARR) METHOD
 Comparison is made with the Return on Capital Employed (ROCE) or required rate of return.
 APR of investment = Net average profit p.A. / Average investment value
 Average investment Value = Opening value + closing value / 2
 Closing value of investment = opening value – depreciation on straight line basis
 Gives an average return and is misleading if calculated on yearly basis
 It gives an average return of “profits” which is very subjective
 Ignores the time value of money
2. SIMPLE PAYBACK PERIOD
 Tool for initial screening of the project
 Represents the time taken for the recovery of the initial capital outlay of the investment
 Payback period (last year fraction) = (Required inflow from the year / Total inflow for the
period) x 12 or 365 for month or days respectively
 Ignores the future profitability of the project
 Ignores the time value of money
3. DISCOUNTED CASH FLOW METHOD
 Most preferred method
 Two main aspects / tools
i.
Implicit rate of return (IRR)
ii.
Net Present Value (NPV)
 For both of the above we need
i.
Cash flows and
ii.
Required rate of return / discount rate / cost of capital
Page 1 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – CASH FLOWS DETERMINATION
DO’S AND DON’T’S OF CASH FLOW DETERMINATION
DO’S / INCLUSIONS
DON’T’S / EXCLUSIONS
Non cash items
Irrelevant costs
Financing cash flows
Relevant costs
Taxation (excluding tax savings on interest)
Inflation
Working capital changes
IMPORTANT ASPECTS IN CASH FLOW DETERMINATION
 Cash flow period
 Cash-flows are made on an annual basis unless specifically mentioned in the questioned
 If cash flows for different period then effective interest rate is calculated as follows:
Where,
a = annual rate
e = effective periodic rate
en = number of periods in a year (e.g. quarterly = 4)
 Depreciation on WDV basis
 Depreciation = Depreciation for the first year x (1-d%)
 WDV = cost x (1-d%)^n
Where ‘n’ is the number of periods for which depreciation is charged and ‘d’ is the depreciation
rate
 Annuity formulae
Gives present value one
period before the start
of cash flow
Gives value at the end
of the period of the
cash flow
 Taxation
 In case of taxable loss, it is assumed that other benefits would be available from which the
same can be set off.
 If nothing is said about the payment of tax, better assumption is that it is paid in the same
year
 In case any tax related information is given (e.g. tax rate, tax depreciation percentage etc.)
it is necessary to prepare the post tax cash-flows and discount them using post tax
discount rate.
 Working capital changes
Method
Incremental working capital changes
(Indirect cash flow method)
Important points
 Normal profit and loss account is adjusted for the
incremental working capital changes
Page - 2 - of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – CASH FLOWS DETERMINATION
Cumulative working capital (Direct
Cashflow Method)
 Inflation
 The working capital investment is realized in the
last year
 Revenue and cost of production taken on cash
basis
 (1+n) = (1+i) (1+r)
Where, n = nominal rate, i = inflation rate & r = real rate
 Real cash-flows are discounted using real discount rate and nominal cash-flows are
discounted at the nominal discount rate. In other words, the discount rate should confirm
to the cash flows.
 Important
Where the cash-flows and the discount rates are both inflated by the same rate of inflation, the
result of discounting nominal cash-flows at the nominal rate of return and real cash-flows at the
real rate of return are same. However, care must be taken for;

Depreciation and

Gain / loss on disposal of assets
Since these are the actual / real world figures and needs to be deflated to year ‘0’ using the
inflation rate
 Care needs to taken to note the price levels of the cost and revenue given in the question
and inflate the cash-flows accordingly. In addition, carefully examine the state of the cash
flows i.e. whether given in real terms or in nominal terms.
 Multiple discount rates
Note: should not be mixed with multiple growth rates in case of cash flows.
Multiple real rates of return
Multiple inflation rates
Discount each year cash-flows at the Calculate the nominal rate of return for each year using
relevant rates (one year at a time)
the relevant inflation rates
Use the above for discounting the relevant year cashflow (one year at a time)
OTHER CONCEPTS LINKED WITH CASH FLOWS
 Sensitivity analysis
 Identifies the cushion available in NPV w.r.t. each CF component and volume (CM)

 Discounted payback period

Same as the simple payback period

Use the net discounted cash-flows to determine the discounted payback period

 The component with the minimum percentage value is the most sensitive cash flow item
Page - 3 - of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – CASH FLOWS DETERMINATION
 Cyclical cash-flows
 Cash flows repeating itself on a cyclical basis
 PV of one cycle is computed in the normal manner
 By using above PV, the annual rental (cash flow) is calculated using the PV annuity formula.
This is the “Equivalent Annual cash flows” or “Annualized Cash flows” (represented by ‘R’
in the formula)
 Asset Replacement Decisions
 Identical assets replacement (Question of ‘How Frequently’)

Inherent assumption that the replacement is to continue till infinity

Methods for the decision
−
LCM method
 Take LCM of the options which will give the number of years for which the cash flows
are to be made under each option and discount the cash flows over that period
 NOTE: the method will fail if the replacement cycle is of more than 3 years
−
Finite Horizon Method
 Plot cash flows over a fairly long period (say 20 years) for each option
−
Annualized Cash Flow Method
 Plot cash flows for one cycle under each option
 Determine the NPV of this cycle
 Calculate ‘R’ using the PV Annuity Formula
 Using perpetuity determine the NPV
 Option with least annualized cost is the most feasible option
 When calculating ‘R’ in the PV annuity formula, n = the period of the cycle / option
under consideration (e.g. if replacement after 4 years n=4, important to remember in
case tax payment is deferred to the next year but no effect is given to that as
annualization comes over the problem)
 The method fails in case there is inflation rate given, therefore use the above two
methods in such case. However, where condition for real rate = nominal rate is
satisfied, this method will remain applicable.
 Non identical replacement (Question of ‘When’)

Determine the NPV of the new asset as done in the above case

Prepare the cash flows for the remaining life of the existing asset (under each option
considered for replacement time) incorporating the NPV of above at the end.

Compute the NPV of these cash flows under each option

The option with the least NPV is the feasible option
Page - 4 - of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – CASH FLOWS DETERMINATION
 Capital Rationing
(Non-Identical replacement of assets)
“A Company has different projects with each having positive NPV but the Company has limited
capital. So the capital is rationed (Divided) & get maximum profit.”
1
Hard Capital Rationing
Due to external factors, e.g IBP would require a bane so invest at maximum a certain
percentage in the identified projects.
Soft Capital Rationing
Due to internal factor e.g company would establish a policy to invest a certain percentage
(at maximum) in the identified projects.
2
Assumptions of capital Rationing
(Points to be kept in mind)
Projects must be feasible i.e NPV must be
1. Dividing
2. Risks of projects must be same if risks are diff. for different projects; the decision is not
based on return.
i.e Same required rate of return is used.
3. It is only for single period.
4. Projects are divisible i.e project is flexible.
5. Projects are not mutually exclusive i.e the can be undertaken at the same time.
Mutually exclusive means “not undertaken both at one point of time.
1
Profitability Index
Example:
A Company is having a capital Rationing situation to day with available capital of Rs.180 m.
The company has identified following three projects for investments.
Projects
Capital Outlay
now
NPV of Cash
flows
Profitability
Index (P.I)
Ranking
1
100
50
0.50
3rd
2
60
60
1.00
1st
3
50
35
0.70
2nd
210
Profitability Index =
NPV/Capital Outlay
Projects
Capital
Allocation
NPV Earned
1 Balance
70
35
2
60
60
3
50
35
180
130
Page - 5 - of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – CASH FLOWS DETERMINATION
Postponability Index
It measures the projects as if the projects are postponed for one year or more that what loss would
be incurred.
e.g
0
Investment
1
2
120 m
58 m
(100 m)
Cash flows
PV @ 10%
150 m
+50m
If this NPV be discounted for one year later, i.e should be equal to 46 m (50/1.1).
Explanation:
Investment
0
1
(91)
(100)
Cash flows
PV @ 10%
137
2
3
120
50
99
38
46
Postponability Loss
If the project is postponed for one year then loss of NPV will be 4m (50m – 46m).
Example;
Project
Capital
Outlay
NPV of
Project A
NPV if
Project is
postponed
for one year
(A/1.1)
1
100
50
45.5
4.5
0.045*
3rd
2
60
60
54.5
5.5
0.092
1st
3
50
35
31.8
3.2
0.064
2nd
Loss in
NPV
Loss PV of
Capital
Ranking
* It tells that, we are suffering a loss of Re 0.045 for every Re 1 of Capital
Page - 6 - of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – CASH FLOWS DETERMINATION
PROJECTS ARE INDIVISIBLE / NOT DIVISIBLE
When the projects are indivisible them we compare it on the basis of absolute NPV, not on the basis of
Profitability Index.
Example;
Projects
Capital
NPV
1&2
160
110*
1&3
150
85
2&3
110
95
* The highest absolute NPV of project 1 & 2 (i) Rs 110, so we must invest in project 1 & 2.
Example;
Projects
Investment
Amount
NPV X @ 15%
A
80,000
33,000
B
60,000
60,000
C
50,000
35,000
* Same rates is applied since the risks are same limit of finance = Rs.150,000 project are Indivisible,
required rate = 15%.
Combination of
Project
Total
Capital
NPV
Ranking
NPV of
Surplus Cash
(Given)
Calculated on
next page)
A&B
140,000
93,000
2nd
(870)
92,130 (1st)
A&C
130,000
68,000
3rd
(1,739)
66,261
B&C
110,000
95,000
1st
(3,478)
91,522 (2nd)
Net NPV
It is assumed that surplus Cash will be earning the return @ 5%.
A&B
Page - 7 - of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – CASH FLOWS DETERMINATION
0
Investment
1
(10,000)
Return @ 5 %
500
Capital
10,000
NPV @ 15%
9,130
NPV
(870)
A&C
0
Investment
1
(20,000)
Return @ 5 %
1,000
Capital
20,000
NPV @ 15%
18,261
NPV
(1,739)
B&C
0
Investment
1
(40,000)
Return @ 5 %
2,000
Capital
40,000
NPV @ 15%
36,522
NPV
(3,478)
Note:
It not told in the about the rate of return for surplus Cash then we would assure that surplus cash
would earn the required rate of return, therefore, no loss will be computed / arise.
MULTIPERIOD CAPITAL RATIONING
From BFD Module ‘F’ study tax PBP.
Summary of Capital Rationing
 Decision making scenario with ‘finance’ as the limiting factor
Page - 8 - of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – CASH FLOWS DETERMINATION
 Reasons for capital rationing

Hard capital rationing – rationing due to ‘external factors’

Soft capital rationing – rationing due to ‘internal factors’
 Inherent assumptions

All projects are financially viable

Limitation of the capital is for one period only
 Formula
 To check in each case (Important)
Check the available finance for the period with the outflows during the period to determine if
finance is actually a limiting factor during that period. Determine the PI for the period only if
finance is a limiting factor. This is specifically significant when financing and cash flows for more
than one year are given. The year when the finance is not a limiting factor, no working or decision
making will be done.
In case the finance is a limiting factor for more than one year, PV of the investment in all years is
calculated.
Moreover, check whether the projects are mutually exclusive or mutually dependant since this will
affect the combinations and the decision with respect to investment.
 Doing capital rationing question

Check the available finances

Check the projects with positive NPVs

Check the starting period of the cash flows since this will affect the annuity factor

Remember to bring such cash flows to year 0

Check whether the projects are mutually exclusive or dependant

Check the divisibility of the projects
 Cases


Projects are divisible and not mutually exclusive
−
Calculate profitability index for each option by using the formula above
−
Prioritize the investment options as per PI
−
Allocate finance to the projects as per the prioritizing
Projects are divisible and few are mutually exclusive
−
All steps in first case except allocating finance to the investments according to PI
−
Prepare combinations with each of the investments that are mutually exclusive limiting the
components of the portfolio to the available finance i.e. total investment required for the
portfolio should not exceed the available finance (Ranking while preparing the
combinations will remain the same as done as per PI)
Page - 9 - of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – CASH FLOWS DETERMINATION


−
Sum the NPV of the combinations that form part of the portfolio within the limited finance
(make sure to take proportionate NPV of the project not fully financed)
−
Compare the portfolios – the one with the greatest NPV is the option to choose
Projects indivisible and not mutually exclusive
−
Ranking of investment portfolios is done on gross NPV basis and no PI is calculated in this
case
−
Incorporate the [return / deduction] on [surplus / unutilized cash flow] as follows:
S. No.
I
Case
Actual return > required return
II
III
Actual return = required return
Actual return < required return
Incorporate in the cash flows
Income at the differential rate discounted at
the required rate of return
No effect
Deduction at the differential rate discounted at
the required rate of return
−
Note: for Case I and III, the return for remaining period i.e. one year shall be incorporated.
In case the question is silent, assume Case II.
−
Portfolio with the maximum NPV will be selected
Projects indivisible and some are mutually exclusive
−
Ranking on gross NPV basis under each option (i.e. with each of the mutually exclusive
investment)
−
Rest of the procedure is same
 Net Terminal Value (NTV)
 NTV is the surplus at the end of the project life, computed by inflating the positive cash
flows at the actual rate of return and negative cash flows at the required rate of return.
 Incorporates the fact that positive cash flows for each year may be reinvested till the end of
the project at a different rate than required rate. Traditional method inherently assumes
that positive cash flows also earn at required rate. (i.e. earning on NPV is also at required
rate)
 Cases:

Actual rate of return < Required rate of return
−

Actual rate of return = Required rate of return
−

In this case the NPV computed by the traditional method > PV of NTV @ RR using S = P(1+i)n
In this case the NPV computed by the traditional method = PV of NTV @ RR using S = P(1+i)n
Actual rate of return > Required rate of return
−
In this case the NPV computed by the traditional method < PV of NTV @ RR using S = P(1+i)n
 NTV therefore, incorporates the ‘reinvestment risk’ associated with the net positive cash
flows of the project over its life, which is ignored by the traditional NPV method.
 Effective / equivalent periodic rate of return for non-annual cash flows
 Rate = p.a., therefore, if the cash flows are made on a periodic basis other than annual, an
effective rate is needed which is calculated by the following formula:
Page - 10 - of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – CASH FLOWS DETERMINATION
(1+a) = (1+e)en
Where,
a – annual rate
e – effective periodic rate
en – number of periods in one year (e.g.
quarterly =4)
 Specific case of leasing (w.r.t to the bank or the leasing company)
 Don’t plot annual cash flows while evaluating leasing as part of option(s)
 PV of the lease rentals is computed through the PV annuity formula
 Purchase of asset by ‘lessor’ needs to incorporated in the cash flows
 Cash flows are however plotted only for determining the PV of tax impact and therefore,
the lease rentals are taken at face (e.g. 4 installments of 100 – for tax take the rental as 400
for the year and apply the tax rate)
 Tax impacts are to incorporated for:

Lease rentals

Depreciation

Tax gain / loss on disposal of asset
Page - 11 - of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
INTERNAL / IMPLICIT RATE OF RETRURN (IRR)
 Rate at which the PV of cash flows = 0
 Discounting at a rate > IRR = NPV will be negative
 Discounting at a rate < IRR = NPV will be positive
 Formula
Where, A is the lower rate, P is the positive NPV and N is the negative NPV
OR
 Difference between 2 rates used for discounting should preferably be < 5-6%
 Starting off with IRR – Rule of thumb
ARR x 2/3
Where,
 Limitation
Where cash flows change their signs with material amounts, more than one time, IRR fails as NPV =
0 at more than one rate.
WHY FINANCING CASH FLOWS NOT INCLUDED IN CASH FLOWS
Cost of capital is the IRR of all financing cash flows which in turn becomes the required rate of return.
DETERMINATION OF REQUIRED RATE OF RETURN
 Expected return is what the debt holders and shareholders expect from the company. This is the
cost of capital and in turn the required rate – i.e. Weighted Average Cost of Capital (WACC)
Where,
Ke = Cost of equity
D = Market value of Debt
E = Market Value of equity
Kd = Cost of Debt (always post tax)
 In case of a new project, the required rate of return for a company is the Marginal Cost of Capital
(MCC)
Where,
Kea = cost of equity after the financing
Keb = cost of equity before the financing
 Therefore, concluded that WACC is not always equal to the required rate of return.
Page 12 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
 Ke is always greater than Kd since the debt is more secured and gets a fixed return irrespective of
the financial position of the company. Therefore, concluded that Equity holder is the ‘Risk bearer’
and Debt holder is the ‘Risk Creator’
WACC COMPUTATION
 Determination of ‘Ke’ and ‘E’
 Price Earning Ratio
MV = EPS x P/E
 Dividend Valuation Model

As per the model, the present value of all future CASH dividend expected discounted @
shareholder required rate of return would give the market value of equity.

It is to be noted that it is the only model for the determination of market value of equity i.e. E.

It should also be noted that if the company does not pay dividend in any period, the
shareholders would recover the same return through capital gain, since the company would
invest the same retained amount in some profitable venture which would automatically affect
the share market price of the company. As a result the shareholder would benefit with the
extra capital gain earned.

In a question where the examiner requires the market value of Equity, preference should be
given to this model. However, as mentioned above, not only dividends but capital gains also
contribute to the share value and therefore, needs to be considered. In addition, cash profits
may also be used for the purpose.

Constant dividend model
−
Assumptions of the model;
 Operating in a stable industry
 Same profitability per annum
 100% dividend payout ratio i.e. the same capital base
−
Formula
E = Do / Ke,
Where ‘Do’ is the last / latest dividend paid out, ‘Ke’ is the shareholder’s required rate of
return and ‘E’ is the market value of the equity.

Dividend growth model
−
Assumptions of the model;
 Constant dividend payout ratio
 Retained profit earning at a rate b%
−
Growth rate
 Since the retained profits are retained @ a constant ‘r%’ and earning @ ‘b%’, the
dividend will grow at ‘g%’ calculated as under;
g=rxb
 Points to note in the above formula;
‫ג‬
g is calculated at per share level
Page 13 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
‫ג‬
‘r’ in case of limited information is taken as ROCE
 Alternate method of calculating growth rate;
S = P (1+i)n
Where, ‘S’ is the latest dividend paid and ‘P’ is the earliest dividend in the given data, ‘I’
is the growth rate and ‘n’ is the number of periods under consideration
−
Calculating ‘E’ under the model
 E = market value of the equity and is Ex-dividend
 Do and E should be at the same level, i.e. if one is taken at per share level, the other is
also at the per share level.


−
The model will give the value one period before the start of the cash flow i.e. the time of
the Do.
−
In case the investor’s tax rate is given, we will replace the Do with Do(1-t), since the
shareholder will receive dividend net of tax and the value of the company will alter
accordingly.
−
Model can also be used where there is a constant growth rate in the Cash flows.
−
In addition, by keeping appropriate cash flow as the Do, and replacing Ke with WACC, the
Market Value of the Company can be determined.
Limitations of the model
−
Method is not applicable for companies paying no or very low cash dividend.
−
If g > Ke, the method fails
−
Retained profits may not earn enough profit to maintain the dividend stream
Important MISTAKE to note
−
If formula applies at later than Yr ‘0’, discount the value of ‘E’ here and dividends in interim
years at the required rate of return of shareholder, i.e. Ke to obtain ‘E’
 Determination of ‘Kd’ and ‘D’
 Important terms

Face value = nominal value of the debt

Coupon rate = rate at which the interest is paid on the debt

Redemption;
Redemption at
Face value
> face value
< face value

Means
At par
At premium
At discount
D fluctuates with respect to Kd as D is present value of debt cash flows discounted at Kd (always
pre-tax) since the tax rate w.r.t. the company and the investor will not be same. Therefore, in
order to compute a market value (same for both the parties) a pre-tax Kd is used. The only
exception to using pre tax Kd is determining D for an irredeemable debt.
 Calculation of ‘Kd’ and ‘D’
Irredeemable debt
Redeemable debt
Page 14 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
Calculation of ‘D’
Calculation of ‘D’
The only cash flow in irredeemable debt is the
interst payments (Coupon rate x Face value of
the debt). D can be calculated by discounting
pre-tax interest cash flows at a pre tax Kd or
discounting post tax interest cash flows with a
post tax Kd (Kd x (1-t) would suffice the need).
The value of D can be calculated by plotting the
cash flows (Interest – Coupon rate x Face value
of the deb) of the debt, including the
redemption of the debt. The cashflows should
however, be from the investors perspective to
keep calculation simple. These cashflows
should be pre-tax, or if investor’s tax rate is
Calculation of ‘Kd’
given then post tax by the rate of tax of the
investor. Discount these cash flows at the pre
Since interest (Coupon rate x Face value of the tax market rate (kd). The present value of
debt) is the only cash flow and D is given, the these cash flows will be the market value of
IRR of the cash flows is Kd. In other words, if the debt.
the interest cash flow is divided by the market
value of the debt, the Kd is obtained, pre tax or Calculation of ‘Kd’ (for the company)
post tax would depend on the status of the
cash flow.
Kd for the company is always post tax (using
the tax rate of the company). However, it
cannot be made post tax by Kd x (1-t). For
determining the Kd, plot the debt cash flows
from the investor’s perspective, including the
redemption of the debt. Put the market value
of the Debt as determined above. The IRR of
these cash flows will be the post tax Kd of the
debt for the company.
 Present value of all cash flows (other than
initial Year ‘0’ one) @ ‘Kd’
 Kd is determined by calculating the IRR of
the cash flows with initial cash flow in year
‘0’ equal to the Market value of Debt ‘D’ –
Also see the concept of ‘Simple Annualized
Return’ below for the starting point of
calculating the IRR.
 Important tips:

Calculate / plot cash flows for Face value of Rs. 100 for easy calculations

Cash flows are made with respect to the company from the investor’s perspective to keep
calculation simple i.e. outflow first and then inflow at the end.
 Simple Annualized Return;
Interest @ coupon rate p.a.
xxx
Tax @ x%
(xx)
xxx
Capital Gain per year of debt life
xxx
(assumed as tax free)
xxx – A
B = Market value of debt ‘D’
Starting point = A / B = x%
Page 15 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
 WACC calculation for Company with specific assumptions
 The WACC of a company with the following assumptions;

Earning (PBIT) is constant p.a.

100% dividend payout

Irredeemable debt (additional condition from the dividend model)
 Can be calculated by the formula;

Without tax

With tax
 Optimum capital structure
 Maximizing shareholder wealth
 Minimizing the cost of capital (WACC)

 As per MMT without tax – Any structure of finance will not alter the WACC, therefore, the existing
structure would remain constant.
 As per MMT with tax – The greater the Debt portion, the greater would be benefit of Dxt, therefore,
increasing debt will result in reduction of WACC
 As per traditional theory – The structure at which WACC is minimum
 As per CAPM theory with Beta Debt = 0 – No impact on the WACC since the existing WACC will
remain constant.
 As per CAPM theory with Beta Debt > / < 0 – D will increase the value of the company.
 Convertible debt (Optimum time to convert)
 Calculate all cash flows from all options at the time of the decision making and opt for the option
with maximum value.
 In case where conversion option is with the debt holder, with respect to WACC, redemption would
be taken the higher cost to the company, i.e. the redemption of debt or the conversion into shares,
whichever results in higher cost to the company.
 Possible options
Option
Immediate selling of debt
Immediate conversion of debt
Holding the debt till redemption
Calculations to perform
Discount future cash flows @ market rate of debt
Number of shares x current market price
All future cash flows discounted @ required rate of return of
investor
 All comparisons should be made at the same point in time i.e. all options should be at any one point
in time level
 Question may ask for a

possible growth rate in share price or
Page 16 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL

share price at the end of debt period i.e. at redemption year which if prevailing give the
required rate of return.
In such situations calculate / inflate / discount the cash flows at that time at the required rate of
return (i.e. calculate NTV) and the
Balancing amount ÷ Number of shares = Share price
 WACC used as a discount rate
 If WACC = Marginal cost of the capital i.e. Existing WACC = Revised WACC, the WACC can be used as
the discount rate
 The above situation is only created if the Debt / Equity ratio or the financial risk and the business
risk remain constant.
 To keep the financial risk constant care should be taken when deciding the financing ratio of the
new project.
 The following procedure should be followed; (Required D/E ratio)

Equity includes the effect of the NPV of the new project. The NPV would be calculated using the
existing WACC since we are about to keep the financial risk constant and can use the WACC as
the discounting rate for the new project.

Add the NPV of the project calculated above in the financing requirement of the new project

Distribute the new figure calculated in step 2, in the D/E ratio.

Deduct the amount of NPV from the share of Equity

The resultant amount is the Debt and Equity portion of the financing required for the new
project, and will keep the D/E ratio before and after the project constant.
 Problem with marginal cost of capital
The marginal cost of capital need not be used for discounting the project, since when computing the
marginal cost of capital a problem is encountered for the value of ‘E’, since ‘E’ would include the NPV of
the project which is unknown and therefore, the rate of marginal cost of capital to be used for
discounting is not available.
Page 17 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
1. TRADITIONAL THEORY
 As per the traditional theory, till a certain point, if we keep on introducing debt,
Kd = fairly constant
Ke = increase marginally
WACC = keep on decreasing
 Subsequently;
Ke = increase sharply
Kd = increases
WACC = starts increasing
 Conclusion: with change in D/E ratio, WACC changes, therefore, WACC is not equal to the
marginal cost of capital and consequently can’t be the required rate of return for any new
project.
However, NPV can be calculated by incorporating DEBT cash flows in the normal cash flows and
the discounting the net cash flows i.e. the residual cash flows available to the equity holder of the
company, using Ke.
2. MM THEORY
 Arbitrage gain:
 “Without altering the magnitude of investment risk profile, if the investor earns more, it is
called Arbitrage gain.”
 It is due to Market in efficiency.
 If two companies holding similar business risk have same WACC and their earnings are equal
then their Market value will be equal.
 If this holds not true (i.e even the same business risk, WACC and earnings but market values are
not equal), it is a temporary situation and would create a chance of Arbitrage gain.
 Arbitrage gain is made when an investor moves from an overvalued company to an
undervalued company.
 The valuation of the company and their status with respect to over / under valuation is
determined on the basis of the PBIT i.e. by comparing their WACCs. The company with the
lower WACC is overvalued.
ASSUPMTIONS;
1) All earnings are paid all as dividend;
2) Debt is irredeemable;
3) Kd is constant for all types of business.
Example;
Pharma Cos.
Page 18 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
Same Business
U
G
Risk
(Un Geared Co.)
(Geared Co.)
1,000,000
1,000,000
--
160,000
1,000,000
840,000
10m
7m 69%
Annual Earnings *
Interest
Market Value of Equality (E)
Market Value of Equality (i)
3.2m 31%
10m
]
Risk Profit
10.2m
Thus, their MVs should be same which is not the case.
If MV of U is actual, then G is overvalued.
If MV of ‘G’ is actual, then ‘U’ is undervalued.
‘U’
‘G’
Ke
10%
12%
Kd
-
5%
WACC
10%
9.8%
Must be Equal
Example;
Bank ‘A’
Bank ‘A’
Corporate Branch
Other Branch
Take advance of loan @ 10%
Invest @ 11 %
1% is Arbitrage gain
Mr. A has 20% equity in G ltd
Total Value of Investment
Page 19 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
(20% of 7m)
1.4m
Total Earnings per annum
(20% of Rs .840m
0.168m□
Same risk profit
Now, Mr. A divested in G ltd.
1.4m
69%
(1.4/7 x 3.2)
0.64m
31%
Investment in ‘U’ ltd
2.04m
Taken personal borrowings
Return of total investment in ‘U’ ltd.
2.04/10 x 1,000,000
204,000
Interest @ 5% (0.64m x 0.05
(32,000)
Total earnings in ‘U’ ltd
172,000
Earnings that taken in ‘G’ ltd.
(168,000)
Arbitrage gain
4,000
Fair value of security (Share)
Overvalued ------------- SELL
Undervalued------------- BUY
Example;
Annual Earnings
‘U’
‘G’
1,000,000
1,000,000
Page 20 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
Interest @ 5%
--
(160,000)
1,000,000
840,000
E
10m
6.8m
D
--
3.2m
10m
10m
10%
10%
WACC
Mr. A hold 20% Equity in ‘G’ ltd
Total value of Investment
(6.8m x 20%)
Total earnings per annum
(0.84m x 20%)
1.36m
0.188m*
Now divestment in ‘G’ ltd
Taken personal borrowings
Investment in ‘U’ ltd
1.36m
0.64m
2.64m
Earning in ‘U’ ltd 2m/10 x 1,000,000
Interest @ 5% an borrowings (5% x 640,000)
Earning in ‘U’ ltd.
Earning in ‘G’ ltd
200,000
(32,000)
168,000
*168,000
-
-
Arbitrage gain
MM THEORY (WITH TAXES)
ASSUMPTIONS:
Assumption of “Taxes are ignored” has been withdrawn.
Market value of Geared Co. would be higher than market value of ungeared Co. it is because tax savings
from interest payments of debts are available to geared company.
Page 21 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
Since Market values is inversely proportional to WACC therefore
WACCg <
MVg
WACCu
>
MVu
Explanation
Company ‘A’
(Geared)
Company ‘B’
(Ungeared)
PBIT
1,000,000
1,000,000
Interest
(200,000)
--
800,000
1,000,000
240,000
300,000
560,000
700,000
MV of Equity ‘E’
6M
10m
MV of debt ‘D’
4m
--
Kd=5% (Pre-Tax)
10M
10m
Tax @ 30%
It should be greater than 10m
Actual Market Value
= 10m + PV of Tax savings
= 10m + 4 (30%)
= 10m + 1.2m
= 11.2m
Actual MV of equity
= 11.2m – 4m
= 7.2m
Increased by 1.2m which is PV of Tax Savings, It is because tax savings are beneficiated to shareholders and
not debtholders.
WACC of Ungeared Co. B Ltd.
700,000/10,000,000
=
7%
WACC of geared Co. A ltd.
PBIT (1-t)
MV of Co.
Page 22 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
1,000,000 (1-30%)
11,200,000
Keg =
=6.25%
Profit attributable to equity holders/PV of equity
560,000 / 7,200,000 = 7.78%
WACC =
(Ke x E)+(Kd x D)
E+D
(7.78 % x 7,200,000) + (*3.5% X 4,000,000)
7,200,000 + 4,000,000
=
*
3.5% =
5% (1-30%)
=
560,160+14,000/11,200,000 = 700,160/11,200,000
=
6.25%
Thus,
WACCg <
WACCu
MVg
>
MVu
DXT
It is present value of all tax savings available as a result of debt;
1
2
3
4
5
------
∂
60,000
Dxkdxt
(1+kd)1
60,000
Dxkdxt
(1+kd)2
60,000
60,000
60,000
------
∂
------
------
------
------
∂
0
Tax savings
4,000,000x5%x30%
Pre Tax Rate
Perpetually Formula
PV
Therefore
PV
=
R/i
=
D x K x t / Kd
PV
=
Dxt
=
4,000,000 X 30%
=
1,200,000
Page 23 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
 Interest is allowable expense, so it has tax benefit.
 Dividend is not allowable expense, so it has no tax benefit.
So,
MVg
>
MVu
MVf
=
MVu + (Dt)
Since coupon rate Applicable at face value
Therefore / and Market rate
MVg
=
PV of all Tax Saving
Market Value
MVu + Dxt (Tax shield or tax related benefits.)
According to MM theory, when company borrows, its, market value of equity increases; Therefore, to
further increase the Market value of equity (& ultimately of the Company itself), the company should
Continue to borrow.
Example:
Company ‘A’
Company ‘B’
E
100m
70m
D
-
30m
PBIT
10m
10m
Kd
--
5%
Tax Rate
40%
40%
WACC
WACC
=
=
PBIT (1-t)/Total MV
10 (1-40%)/100m
10(1-40%)/112m
=
6/100
6/112
=
6%
5.3%
100+Dt
Market Value
=
100m
100+(30x40%)
100+12
112m
Example;
Earnings (PBIT)
Interest
‘U’ Ltd
[Ungeared]
‘G’ Ltd.
[Geared]
1,000,000
1,000,000
-
(160,000)
1,000,000
840,000
Page 24 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
Tax @ 30%
Market value of equity (E)
(300,000)
(252,000)
700,000
588,000
10m
8m
Market value of debt (D)
3.2m
10m
11.2m
WACC of ‘U’ ltd.
Kd of ‘U’ ltd
=Profit attributable & equity holders/Total market value
=700,000/10,000,000=7%
WACC
=PBIT(1-t)/Total MV
=1,000,000 (1-30%)/10,000,000=7%
WACC of ‘G’ ltd =
Kd
=I(1-t)/D = 160,000(1-30%/3,200,000=3.5%
Kd
=5%(1-t)
=5%(1-30%)
=3.5% after tax rate of interest
Ke
=Profit Attributable & equity holder/Market value of equity
=588,000/8,000,000=7.35%
WACC
=(Ke x E)+(Kd x D)/E+D
=(7.35% x 8,000,000) + (3.5% x 3,200,000)/8,000,000+3,200,000
=588,000+112,000/11,200,000
=700,000/11,200,000=6.25%
ALTERNATIVE METHOD (WACC)
WACC
=PBIT(1-t)/E+D
=1m(1-30%)/8+3.2=0.7/11.2
=6.25%
MVu
=10m if it is true then accordingly of MM Theory
MVg
=MVu + Dt
=10m + 3.2m x 30%
Page 25 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
=10m + 0.96m
=10.96m so ‘G’ overvalued this should be value of ‘G’ ltd accordingly of MM Theory
MVg
=11.2m if it is true then; accordingly of MM Theory
MVu
=MVg – Dt
=11.2 – 0.96
=10.24 so ‘U’ is under valued
Arbitrage gane
Mr. A owns 20% of ‘G’ ltd. Current MV for Mr.A (20% of 8m)
Current earnings) 20% of 588,000)
D/E ratio of ‘G’ ltd
As per above, it would be:
D
3.2/11.7
28.6% :
1.6M
117,600
:
E
:
8/11.2
71.4%
However, if we Consider the Tax saving (which will reduce the cost of debt) then:
D
:
E
3.2
:
8
Tax savings (D x t)
(0.96)
:
-2.24
:
8
=10.24
2.24/10.24
:
8/10.24
22%
:
78%
This value can also be calculated as
0
Gross with payable @ 5%
Tax savings
Net of benefit
PV
112,000/.05
=
2,240,000
1
160,000
(48,000)
112,000
or
2
160,000
(48,000)
112,000
3
160,000
(48,000)
112,000
-----------------
∂
∂
∂
∂
2.24m
Assumed that, there is no individual / personal taxes.
Investment proceeds in ‘G’ ltd.
1,600,000
Amount borrowed (1.6/8 x 2.24)
448,000
Page 26 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
Total amount invested in ‘U’ Ltd.
2,048,000
Now after investment
Earnings {2,048,000/10,000,000x700,000}
143,360
Interest Exp. (448,000x5%)
(22,400)
Earnings in ‘U’ ltd.
120,960
Earnings is ‘G’ ltd.
117,600
Arbitrage gain
3,360
Note: According to MM Theory if market values are not equal, this creats a chance of Arbitrage gain.
TAX SHIELD EXHAUSTION POINT
Debt provides tax shield i.e tax savings on interest payments. The more the debt obtained, more tax shield
will be available in Co. however at a point if further debt is obtained but tax shield is not available or further
debt is cannot be obtained and thus no further Tax Shield is available. This point is called Tax shield
exhaustion point.
It would be due to the reason that:
Legal restriction e.g specified D/E rates
No taxable profits are available to absorb interest expense.
If MV of ‘U’ according
MM Theory
Market value of equity ‘E’
Market value of debt ‘D’
‘U’
10.24m
--10.24m
‘G’
8m
3.2m
11.2m
Mr. B Owns 20% of ‘G’ ltd.
Current investment
(20% of 8m)
Current earning (20% of 588,000)
1.6m
117,600
Market value of equity divested by Mr. B and invested in ‘U’ ltd.
Divested proceed
1,600,000
Borrow (1.6/8 x 2.24) (3.2-0.96)
448,000
Investment in ‘U’ Ltd.
2,048,000
Earnings 2.048/1.024 x 0.7
140,000
Interest 448,000 x 5%
(22,400)
Earnings in ‘U’ ltd
117,600
Earnings in ‘G’ ltd
117,600
Arbitrage gain
-
-
Page 27 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
FINANCIAL RISK PREMIUM
1).
2).
MM THEORY (WITHOUT TAXES)
Keg
=
Keu + {(Keu – Kd) D/E}
MM THEORY (WITH TAXES)
Keg
Pre-Tax
=
Keu + {(Keu – Kd) D(1-t)/E}
=
D(1-t)/E
FINANCIAL RISK (WITH TAXES)
Financial Risk (With Taxes)
Pre-Tax
Keg
=
Keu + {(Keu – Kd x D(1-t)/E}
After-Tax
WACCg
=
Keg x E + Kd x D) / E+D
According to MM Theory:
WACCg
=
Keu {1-
Dt
E+D
}
Explanation:
Tax Rate
=
30%
WACCg =
Keu {1 – 20% x 30% / 100%}
=
Keu {1 – 0.06}
=
Keu {94%}
WACCg =
Keu {1 – 40% x 30% / 100%}
=
Keu {1 – 0.12}
=
Keu {0.88}
=
Keu {88%}
If ‘D’ is 20% of g Capital
If ‘D’ is 40% of g Capital
Thus from above as ‘Debt’ of the company increases WACC decreases
D
=
WACC
Example:
A PLC is all equity Co. and current cost of capital is 12% B PLC is similar to A PLC in all
respects except that it is geared Co. with current market value of debt is Rs.500m and that of equity is
Rs.1.5billion. cost of debt is 6% pre-tax. Debt of B PLC is irredeemable; corporation tax rate is 30%
REQ:
Calculate cost of equity and WACC of B PLC.
Solution:
Page 28 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
Keg
WACCg =
=
Keu + {(Keu – Kd) D(1-t)/E}
=
12 % + {(12% - 6%) 500(1-30%)/1500}
=
12% + 1.4%
=
13.4%
Keu {1 – Dt/E+D}
=
12% {1 – 500 x 30% / 1500 + 500}
=
12% {1 – 0.075} = 12% (0.925)
=
11.10%
ALTERNATIVELY,
WACCg =
(Keg x E) + (Kd x D) / E + D
=
(13.4% x 1,500) + (4.2% x 500) / 1,500+500
=
222/200
= 11.10%
If debt is redeemableE
MM Theory assumes that debt is irredeemable.
However, if a debt is redeemable, it can also be considered as irredeemable, it is further rolled over after
redemption.
Thus, in Question, it can be assumed that debt is irredeemable (for MM Theory). For irredeemable debt Kd
can be calculated by Kd (1 – t).
KEEPING FINANCIAL RISK SIMPLE WHEN CONVERTING INVESTMENT From Ungeared Co. to Geared Co.
Geared Co.
Ungeared Co.
E
60
100
D
40
--
100
100
Investment:
10M
If Cos. gone into liquidation:
Geared Co.
Ungeared Co.
Liquidation Proceeds
70
70
Debt holders Share
40
--
Remaining
30
70
Receivable
=
10/60 x 30 = 5m
1/100 x 70 = 7m
Page 29 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
Return decreased, because financial Risk not remained same.
NEW Investment (To keep return same)
Geared Co.
Ungeared Co.
E
60
100
D
40
--
Investment
100
100
E
6
D
4
If Cos. Gone into liquidation.
Luquidation proceeds
Debt holder’s store
Remaining for equity holders
70
40
30
Receivable:
From Equity 6/60 x 30
From Debt 4/40 x 40
=
3m
=
=
4m
7m
Thus from above, if the financial risk is kept same, returns also remain same.
IMPORTANT CONCLLISION:
In world without taxes, WACC can be used as discount rate. (Since WACC remains Constant with changes in
DEBT)
In world with taxes, existing WACC cannot be used as discount rate. (Since Dt impacts market value of the
firm and thus upon the WACC.)
Page 30 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
Case I - All equity
Case II - Geared Co.
Data
PBIT
200
PBIT
Keu
Kd
20%
10%
Keg
Kd
E
1,000
E
D
200
?
10%
800
200
Computation of WACC
WACC
PBIT / E+D WACC
20%
PBIT / E+D
20%
Effect of gearing on Keu
Keg = Keu + (Keu - Kd) x D/E
Keg
22.50% a
Reconciliation through PBIT
PBIT
Interest
PBT
Ke
200
200
PBIT
Interest
PBT
PBT/E
Ke
20.00%
200
(20)
180 Distributable to Equityholders
PBT/E
22.50% b
therefore, a = b
Keu - Kd in terms of amount
Keu on D
Kd on D
Difference
40
(20)
Since the amounts are calculated as
percentage of D, we will multiply by D and
bring the difference as a percentage of E.
20 A
This is the additional amount available for
'E' due to lower percentage of Kd. i.e. if 200
was E, the required return would have been
20% rather than 10%.
A as %age of E
2.5% B
This is the percentage by which the Keu
increases due to gearing.
A as %age of D
10% C
D/E ratio
Which is equal to B
This represents
Keu
Kd
Difference
20%
10%
10%
25% D
2.5% CxD
Which is why we multiply (Keu - Kd) with the D/E ratio
Page 31 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
Case I - All equity
Case II - Geared Co.
Data
PBIT
Keu
Kd
E
t
200
20%
10%
1,000
PBIT
Keg
Kd
E
200
?
10%
860
30%
D
t
Mvu
Increase by Dxt
MVg
Debt
Equity
1,000
60
1,060
(200)
860
200
30%
Computation of WACC
WACC
PBIT(1-t) / E+D WACC
14%
PBIT(1-t) / E+D
13.2%
WACCu
Decrease by (Dxt) / E+D
(of the geared co.)
WACCg
14% A
6% B
13.2% A x (1 - B%)
Effect of gearing on Keu
Using pretax Kd and Post tax Keu
Keg = Keu + (Keu - Kd) x D(1-t)/E
Keg
14.65% a
Reconciliation through PBIT
PBIT
Interest
PBT
Tax
PAT
Ke
200
200
(60)
140
PBIT
Interest
PBT
Tax
PAT
PBT/E
Ke
14.00%
200
(20)
180
(54)
126
Distributable to Equityholders
PBT/E
14.65% b
therefore, a = b
Keu - Kd in terms of amount
Keu on D
Kd on D
Difference
28
(20)
8 A
Since the amounts are calculated as percentage of
D, we will multiply by D and bring the difference as a
percentage of E.
This is the additional amount available for 'E' due to
lower percentage of Kd. i.e. if 200 was E, the required
return would have been 20% rather than 10%.
Tax on A
Distributed to E
(2.4)
5.6 B
B as %age of E
0.65% C
This is the percentage by which the Keu increases
due to gearing.
As %age of D
4.00% D
This represents
Keu
14%
Kd
10%
Difference 4%
D(1-t)/E ratio
Which is equal to B
16% E
0.65% DxE
which is why we multiply (Keu - Kd) with the D/E ratio
Page 32 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
MM The ory w ithout taxation
Arbitrage Gain Exam ple - Ge are d Com pany ove rvalue d
Arbitrage Gain - A gain that an investor can make, w ithout changing investment or / and w ithout changing risk prof ile
U Limited
PBIT
Interest
1,000,000
1,000,000
G Limited
1,000,000
(160,000)
840,000
As s um ptions
- Constant earnings
- 100% Payout ratio
E
D
10,000,000
10,000,000
WACC
7,000,000
3,200,000
10,200,000
10.00%
Undervalued
Kd
5%
Interest divided by D
9.80%
Overvalued
The decision is made on the f act that in a w orld w ithout taxation, tw o
companies at the same prof itability levels w ill have the same market values
and consequently same WACC
Arbitrage gain w ill arise by moving f rom an over valued company to an undervalued company
As per MMT, situations as above are inequilibirium situation, and are very temporary and such situations are bound to generate arbitrage
gain
Extending our example, say
Mr. A ow ns 20% shares of G Limited
Current earnings i.e. 20% of PBT
Value of investment i.e. 20% of E
168,000
1,400,000
To generate arbitrage gain;
A should sell share so he gets
1,400,000
To keep risk prof ile same as G Limited;
A borrow s 1.4M / 7M x 3.2M
Total investment in U Limited
A
640,000
2,040,000
Revised Earnings i.e. 2.04M / 10M x 1M
Interest on Debt i.e. 640K x 5% (kd)
204,000
(32,000)
Net earning
172,000
Arbitrage gain
4,000
B
A-B
As a result of above, there w ill be selling pressure on G Limited and buying pressure on U Limited since shareholder w ould w ant to avail
the arbitrage gain. Thereby, the MV of U Limited w ould increase and that of G Limited w ould decrease, till a point w he
In consequence of above the position of the companies w ould change as below ;
U Limited
PBIT
E
D
G Limited
1,000,000
840,000
10,100,000
6,900,000
3,200,000
10,100,000
10,100,000
Extending our example
Mr. B ow ns 10% shares of G Limited
Current earnings i.e. 10% of PBT
Value of investment i.e. 10% of E
84,000
690,000
To generate arbitrage gain;
B should sell share so he gets
690,000
To keep risk prof ile same as G Limited;
A borrow s 0.69M / 6.9M x 3.2M
320,000
Total investment in U Limited
Revised Earnings i.e. 1.01M / 10.1M x 1M
Interest on Debt i.e. 640K x 5% (kd)
Net earning
Arbitrage gain
A
1,010,000
100,000
(16,000)
84,000
-
B
A-B
Theref ore, no arbitrage gain w hen there is equilibirium condition
Page 33 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
M M The ory w ith taxation
Arbitrage Gain Exam ple - Ge are d com pany ove rvalue d
Arbitrage Gain - A gain that an investor can make, w ithout changing investment or / and w ithout changing risk prof ile
A (Ungeard)
PBIT
Interest
Tax @ 30%
E
D
1,000,000
1,000,000
(300,000)
700,000
B (Geared)
1,000,000
(160,000)
840,000
(252,000)
588,000
10,000,000
10,000,000
8,000,000
3,200,000
11,200,000
Undervalued
Overvalued
Kd
5%
Decision about the under / over valuation is made as f ollow s:
As s um ing Rs .10M to be corre ct, M Vb w ould be
MVg = MVu + D x t
As s um ing Rs .11.2M to be corre ct, M Va w ould be
10,960,000
MVg = MVu + D x t
10,240,000
Alternatively, the decision could be reached on the basis of WACC
Caculating WACC of A
As per MMT WACCg = WACCu x 1 - (Dxt / E+D)
Actual WACC of B
7.00%
(PAT / E+D)
6.40%
6.25% Overvalued since the WACC is low er than as computed through MMT
Theref ore, MMT is not being complied, and opportunities of arbitrage gain exist f or investors moving f rom B to A.
Extending our example, say
Mr. A ow ns 20% shares of B Limited
Current earnings i.e. 20% of PAT
Value of investment i.e. 20% of E
117,600
1,600,000
To generate arbitrage gain;
A should sell share so he gets
1,600,000
To keep risk prof ile same as G Limited;
A borrow s 1.6M / 8M x 2.24M
Total investment in U Limited
A
448,000
D:E ratio in MMT w ith taxes
2,240,000
8,000,000
D = D(1-t)
E
2,048,000
Revised Earnings i.e. 2.048M / 10M x 0.7M
Interest on Debt i.e. 448K x 5% (kd)
143,360
(22,400)
Net earning
120,960
Arbitrage gain
3,360
As s um ption
No personal taxation
B
A-B
As a result of above, there w ill be selling pressure on B Limited and buying pressure on A Limited since shareholder w ould w ant to
avail the arbitrage gain. Thereby, the MV of A Limited w ould increase and that of B Limited w ould decrease, till a point w he
In consequence of above the position of the companies w ould change as below ;
A Limited
PAT
E
D
B Limited
700,000
588,000
10,240,000
8,000,000
3,200,000
10,240,000
11,200,000
Extending our example
Mr. B ow ns 20% shares of G Limited
Current earnings i.e. 20% of PAT
Value of investment i.e. 20% of E
117,600
1,600,000
To generate arbitrage gain;
B should sell share so he gets
1,600,000
To keep risk prof ile same as G Limited;
A borrow s 1.6M / 8M x 2.4M
Total investment in U Limited
448,000
2,048,000
Revised Earnings i.e. 2.048M / 10.24M x 0.7M
Interest on Debt i.e. 448K x 5% (kd)
140,000
(22,400)
Net earning
117,600
Arbitrage gain
A
-
B
A-B
Theref ore, no arbitrage gain w hen there is equilibirium condition
Page 34 of 108
INVESTMENT APPRAISAL
DISCOUNTED CASH FLOW METHOD – REQUIRED RATE OF RETURN / COST OF CAPITAL
ANALYSING THE IMPACT OF CHANGE IN THE FINANCIAL RISK (BUSINESS RISK CONSTANT)
2,500,000
2,140,000
11,600,000
11,600,000
8,600,000
2,000,000
10,600,000
- Constant earnings
- 100% Payout ratio
E
D
WACC
21.55%
Over valued
Kd
18%
Interest divided by D
23.58%
Under valued
The decision is made on the f act that in a w orld w ithout taxation, tw o
companies at the same prof itability levels w ill have the same market values
and consequently same WACC
Mr A ow ns Rs.100,000 investment in Arizona i.e. 1%
Current earnings i.e. 1% of PBIT
Value of investment i.e. 1% of E
25,000
116,000
To generate arbitrage gain;
A should sell share so he gets
116,000
To keep risk prof ile same as Arizona Limited;
A lends 116K / 10.6M x 2M
A invests in equity 116K / 10.6M x 8.6M
Total investment
21,887
94,113
116,000
Revised Earnings i.e. 2.14M x 94,113 / 8.6M
Interest on Debt i.e. 360K x 21,887 / 2M
23,419
3,940
Net earning
27,358
Arbitrage gain
2,358
A
B
A-B
As a result of above, there w ill be selling pressure on Arizona Limited and buying pressure on Low a Limited since shareholder w ould
w ant to avail the arbitrage gain. Thereby, the MV of Low a Limited w ould increase and that of Arizona Limited w ould decrease
In consequence of above the position of the companies w ould change as below ;
Arizona
PAT
E
D
Low a
2,500,000
2,140,000
11,600,000
9,600,000
2,000,000
11,600,000
11,600,000
Existing earnings A above
Existing value as above
25,000
116,000
A
Divest f rom Arizona and invest in Low a as f ollow s:
Investment in E 116K / 11.6M x 9.6M
Investment in D 116K / 11.6M x 2M
Total investment
Revised earnings
f rom equity 2.14M * 96K / 9.6M
f rom debt 360K * 20K / 2M
Total earnings
Arbitrage
96,000
20,000
116,000
21,400
3,600
25,000
B
-
A-B
Page 35 of 108
INVESTMENT APPRAISAL
PORTFOLIO THEORY
It relates to quantification of risk and returns of the assets and portfolios.
 SINGLE ASSET


Where R = Return on specific probability P
(standard deviation from expected return)
Note: Where σ = 0, the security is a zero risk security. Also note that Variance =
and standard
deviation cannot be added whereas variance can be added.
 TWO ASSET PORTFOLIO
 Portfolio return
Where,
= Expected return on Asset A
= Weightage (in percentage) of the asset in the portfolio. This also reflects the market value of
the asset at the time of the decision
It is important to note the dates when you are calculating the return or beta.
 Portfolio risk

Affected by the following factors;



Individual asset risk
Respective weightages
Relationship between returns of portfolio assets

= correlationship coefficient of return of assets (Relationship between return of
portfolio assets. Following maximum values are possible with their relevant interpretation;
Values
+1
0
-1
Interpretations
Perfect positive correlationship (high volatility) or direct
relationship between portfolio assets
No relationship between portfolio assets
Perfect negative correlationship (low volatility) or inverse
relationship between portfolio assets
 CONCEPT OF EFFECIENCY / INEFFECIENCY OF ASSETS IN RELATION TO EACH OTHER
 Inefficient:
 Efficient:
as compared to others
as compared to others
 Political answer
Both assets are efficient since risk
risk orientation / attitude;


return. Decision would depend on the investor’s risk profile /
Risk averse – low risk / low return
Risk taker – high risk / high return
Page 36 of 108
INVESTMENT APPRAISAL
PORTFOLIO THEORY
 However, where the risk and return are proportional for more than one security, the decision
should be taken on the basis of percentage of return per percent of risk borne by the investor.
(1/Coefficient of variation)
 COVARIANCE

Replacing this in the portfolio risk formula we obtain;
 THREE ASSET PORTFOLIO



Portfolio Beta
Weighted average of individual security β’s of the asset in the portfolio
Page 37 of 108
INVESTMENT APPRAISAL
CAPITAL ASSET PRICING MODEL (CAPM) THEORY
 The model is mainly a tool to calculate the cost of equity (Ke)
 The model assists in absolute decision making
 The model identifies the fair return from an asset as opposed to the earlier models which identified
the return being required. The model therefore, identifies the true and fair return that is required
from a particular investment by an equity investor.
Risk
Specific
(Unsystematic)
Market
(Systematic)
Business
Financial
 SPECIFIC / UNSYSTEMATIC RISK
 Can be avoided through diversification since it is individual investment specific risk
 Unsystematic risk of the entire market is ‘0’
 Investors do not get any return for this risk
 SYSTEMATIC RISK
 Associated with the environment in which the entity operates
 Investor receives consideration for this risk
 Business risk – associated with the activities undertaken by the entity
 Financial risk – associated with the gearing of a company
 PRINCIPAL ASSUMPTION (IN ADDITION TO THAT OF THE MMT)
 Linear relationship between market return and individual security return
 All securities have correlation with the market return
 EQUATION
Where,
=
= Risk free return
= Market rate of return
 SHARE PRICE USING CAPM RETURN
Using the CAPM return, share price for any given future date can be calculated. The share price today x
(1 + CAPM return) will give the future share price of the share. However, if there is dividend yield, the
price will be cum dividend and to arrive at ex-dividend price, which is what is actually required, the
dividend will be deducted from this share price.
Page 38 of 108
INVESTMENT APPRAISAL
CAPITAL ASSET PRICING MODEL (CAPM) THEORY

 Measures the relationship between the systematic risk of a security and risk of market as a whole
 Denotes the change in the return of a security resulting from a unit change (1% change) in market
return
OR
 ALPHA ( )
Alpha value
+ve
-ve
0
Interpretation
Actual return > CAPM return – Company is undervalued
Actual return < CAPM return – Company is overvalued
Actual return = CAPM return
 Assuming CAPM to be a realistic model,
abnormality.
= 0, therefore, if it is not equal to zero, it is a short term
 Positive alpha value attracts the investors to invest in the security, and vice versa for negative alpha
value.
 LIMITATIONS
 Ignores premium on unsystematic risk which in fact exists
 No empirical evidence of linear relationship between market return and individual security return
 Determination of a single uniform risk free return involves subjectivity
 Model does not prescribe return for security which does not have any correlation with market
return ( = 0)
However, premium on such investment exists as well
 Assumes

and
to be stable over time
OF A COMPANY (LINKED WITH THE PORTFOLIO BETA)
 Company is a two asset portfolio

Equity asset

Debt asset


 As per MMT,
(MMT WITHOUT TAXES)
(MMT WITH TAXES)
= 0, since debt is risk free, therefore the above equation becomes;
Page 39 of 108
INVESTMENT APPRAISAL
CAPITAL ASSET PRICING MODEL (CAPM) THEORY
, which can be seen as
 Therefore, the above equation makes an adjustment for the business risk and the financial risk of
the company in the Beta of the company.

 COMPUTING Ke:
 For un-geared company  For a geared company  Ke calculated through CAPM model is equal to the Ke calculated through MMT, only if Rf = Kd
 POINT TO NOTE

X
X
However, if Market rate of borrowing is given, such as in cases where there is credit rating and market
rates of borrowing is given as a link with the best credit rating, the Beta debt of the company can also
then be calculated. Moreover, in such cases by substituting the Rm above in Kd formula with the
market rate of borrowing of the debt and beta debt calculated using the credit ratings, the cost of
borrowing Kd can be computed by the above formula.
 DECISION TREE
Actual price <
CAPM price
Actual price =
CAPM price
Actual price <
CAPM price
Actual return >
CAPM return
Actual return =
CAPM return
Actual return <
CAPM return
Alpha = positve
Alpha = 0
Alpha =
negative
Under valued
Fairly valued
Over valued
Should invest
Can invest
Should not
invest
Page 40 of 108
INVESTMENT APPRAISAL
RISK ADJUSTED WACC
 The method is only applicable if the D:E ratio is given.
 Identify business risks of the project i.e. Beta Asset of the industry to which the project relates.
 Identify the Financial risk or Debt : Equity Ratio of the project. In absence of information assume project
is financed in the existing Debt : Equity ratio.
 Using the Beta asset and Debt : Equity ratio calculate Beta equity (Geared) using formula
 Using Beta equity calculated above, calculate Ke using the formula;
 Using adjusted Ke and Debt : Equity ratio calculate risk adjusted WACC using the formula;
Page 41 of 108
INVESTMENT APPRAISAL
ADJUSTED PRESENT VALUE (APV)
 Using MMT,
 Applying the same on the project;
Where;


NPVg = project cash flows discounted at Keg
NPV u = project cash flows discounted at Keu and is also called BASE CASE NPV
 For APV we need;
 Cash flows
 Keu
 Adjustments for debt related tax benefit
 COMPUTING Keu
Method 1
Method 2
Use Keu of the project industry or calculate the Keu of the industry by using Keg in the
formula;
[the factor 1-t will be eliminated for world without taxes]
Use of un-geared company of the industry OR
Calculate
of the industry using
of the industry i.e. un-gearing of
formula;
Put the
using the
in the formula;
To calculate the Keu
 ADJUSTMENT TO BASE CASE NPV
Base case NPV
Financing adjustments
PV of tax benefit on interest of debt (may be subsidized)
PV of issue cost
PV of tax savings (if any) on issue cost
PV of interest savings on subsidized debt
Net Present Value / Adjusted Present Value
xxx
xxx
(xxx)
xxx
xxx
xxx
Discounted using
Pre tax Kd or Rf
 Interest on debt – tax savings

Computed for both the utilized and the spare capacity of debt created by the project

The benefit of the debt taken here is not taken in any further project in which the debt may be
utilized.
Page 42 of 108
INVESTMENT APPRAISAL
ADJUSTED PRESENT VALUE (APV)
 Subsidized debt – tax and interest savings
Method 1 (Preferable)
Tax savings on actual rate
Interest saved (before tax) due to lower rate
Total savings
xxx
xxx
xxx
The total savings are discounted using Kd
Method 2
Tax benefit @ market rate of interest
Interest savings (pre tax)
Tax benefit forgone due to lower interest rate
Total savings
xxx
xx
xx
xxx
xxx
The total savings are discounted using Kd
Method 3



Plot actual cash flows of the loan
Discount using pre tax Kd
NPV is the amount of adjustment
Page 43 of 108
INVESTMENT APPRAISAL
DECISION TREE TO USING INVESTMENT APPRAISAL TECHNIQUE
Step One: Identify a benchmark with the same BUSINESS RISK as the project
Step Two: Has the project the same FINANCIAL RISK (gearing / leverage) as this benchmark?
No
Yes
Find NPV of the project
cash flows using the
benchmark’s WACC
Un-gear the benchmark
using the benchmark’s D/E
ratio
Are you given the
PROJECT debt or debt
capacity in Rupees?
Use APV
Find base case NPV of
project cash flows at
benchmark
+
Are you given the
PROJECT D/E ratio?
Regear the ungeared
benchmark using the
project D/E ratio to
find an adjusted WACC
Adjust for financing
side effects / tax shield
Find the NPV of the
project cash flows at
the adjusted WACC.
Page 44 of 108
INVESTMENT APPRAISAL
LEASE OR BUY DECISIONS
 Decision between own investment and financing option
Feature
Own financing
Discounting
Company’s cost of
rate
capital
Cash
flows  Initial outlay for
incorporated
investment
 Residual value
benefit
 Tax shield for
depreciation
net of gain on
disposal
Lease financing
with tax shield for
lease rentals
-do

Lease rentals
Tax shield for
lease rentals
Additional
considerations
Lease financing
with tax shield for
depreciation &
interest element of
rentals
-do

Loan financing
-do-
Lease rentals
Tax shield for
depreciation
and
interest
element
of
lease rentals
Will
have
to
compute
the
Implicit rate of
return to compute
the interest element
in the lease rentals
by preparing the
repayment schedule

Initial outlay for
investment
 Tax shield for
depreciation
net of gain on
disposal
 Benefit
of
residual value
 Financing cash
flows
The
decision
between the loan
financing and the
own
capital
investment can also
be
taken
by
comparing
the
borrowing rate and
the company’s cost
of capital.
 Decision between lease financing and loan financing
Feature
Discounting rate
Lease financing with tax
shield for lease rentals
Opportunity
cost
of
capital, for ease purposes,
the borrowing rate from
the bank (in case of with
taxes, the rate is also after
tax)
Cash
flows  Lease rentals
incorporated
 Tax shield for lease
rentals
Additional
considerations
Lease financing with tax
shield for depreciation &
interest element of
rentals
-do-


Lease rentals
Tax
shield
for
depreciation
and
interest element of
lease rentals
Loan financing
-do-

Initial
outlay
for
investment
 Tax
shield
for
depreciation net of
gain on disposal
 Benefit of residual
value
Will have to compute the The cash flows are
Implicit rate of return to prepared with respect
compute the interest from the investor side.
Page 45 of 108
INVESTMENT APPRAISAL
LEASE OR BUY DECISIONS
element in the lease Moreover, the FINANCING
rentals by preparing the CASH FLOWS ARE NOT
repayment schedule
TAKEN since it is built in
the discount rate being
used.
In cases where the annual
rentals are repayable, the
cash flows will remain the
same as above. However,
post tax Kd will be
calculated by plotting the
financing cash flows of the
debt and computing its
IRR. Moreover, the annual
repayment shown in the
cash
flows
when
computing IRR will be
calculated using present
value annuity formula and
interest will be computed
by making a repayment
schedule to calculate the
tax shield thereon.
In case the outflow is to
be shown at the end of
the period, the interest
element on the loan will
have to be built in for the
period of the investment,
in order the make the
present value of the
interest and outflow at
the end of the period
equal to the outlay if done
at the start of the project.
Implicit assumption of one financing being the direct substitute of the other
By using the borrowing rate above as the discounting rate, we are assuming that the loan financing is
direct substitute of the lease financing. In case where either generates in-equivalent debt capacity for
the company, one would not be the direct substitute of the other. Therefore, the rate would not be an
appropriate rate. In such cases, a possible solution which would make the two options comparable
would be to discount the tax shield on the interest of the debt capacity of each financing option (i.e. D x
kd x t, D being the debt capacity generated, kd being the rate of borrowing and t being the rate of tax)
at the borrowing rate used for discounting the cash flows of each option.
Page 46 of 108
INTERNATIONAL INVESTMENT APPRAISAL
All the same rules apply as stated above (for normal cash flow) with the following additions:
 We make separate post tax cash flows for Local currency and Foreign currency, and convert the bottom
lines of the foreign currency cash flows in local currency using the interest rate parity / inflation rate
parity theory.
 We must never knock off Royalty Income & Royalty Expense because changes in tax rates may allow for
differing tax benefits.
 If stated that Full Bi Lateral Tax Treaty Exists than no further computation is required for tax.
 In the absence of full bi lateral tax treaties, foreign currency cash flows would be converted into local
currency cash flows and added to the cash flows made in local currency. For the combined local
currency cash flows; following rules shall apply;
Local currency tax rate: 25%
No further work required
Foreign currency tax rate: 35%
Local currency tax rate: 35%
10% tax would be provided on the foreign
Foreign currency tax rate: 25%
currency cash flows
Page 47 of 108
DIVIDEND POLICY
 TRADITIONAL THEORY / RESIDUAL THEORY / THEORY OF RELEVANCE
As per the theory, the dividend policy affects the shareholder’s wealth. Therefore, only such portion of
the divisible profits should be distributed which cannot be invested in projects yielding positive NPVs.
Illustration of Theory of Relevance
EPS or profit for distribution or Do
Ke
12
10%
Scenario I - Company pays out all profits as dividend
E (ex dividend) - Do / Ke
E (cum dividend) - E + Do
120
132
Scenario II - Payout percentage 40%
Dividend
4.8
Case a - retained profits earning at 'r' percent > 'ke'
Case c - retained profits earning at 'r' percent = 'ke'
b = 60%
b = 60%
r = 12%
Using dividend grow th model
Grow th = b x r
E = Do (1+g) / Ke - g
E (Cum dividend)
Using dividend grow th model
7.20%
184 Ex-dividend
189 Higher than before
Case b - retained profits earning at 'r' percent < 'ke'
b = 60%
r = 10%
Grow th = b x r
E = Do (1+g) / Ke - g
E (Cum dividend)
6.00%
127 Ex-dividend
132 Same as in Scenario I
Note: Bonus Dividend is only Capitalization of profit, hence is not real dividend.
r = 8%
Using dividend grow th model
Grow th = b x r
E = Do (1+g) / Ke - g
E (Cum dividend)
4.80%
97 Ex-dividend
102 Low er than before
 MM THEORY / THEORY OF IRRELEVANCE
As per the theory, shareholder is indifferent of dividend policy. Since positive NPV projects increase
shareholder wealth, hence the company should borrow & invest funds in positive NPV generating
projects to increase Shareholder wealth.
 PRACTICAL ASPECTS
Signaling Effects: dividends declared by a company serve as a signal to the shareholders of the financial
performance & future prospects. It is important to maintain a constant stream.
Cliental Effect: A shareholder makes gain in two ways
 Dividend
 Capital Gain
Page 48 of 108
DIVIDEND POLICY
We know that:
High dividend low capital gain
Low dividend  high capital gain
Corporate ------------- capital gain ------------- taxable
------------- dividend ------------- exempt/NTR
Individual ------------- capital gain ------------- exempt
------------- dividend ------------- taxable
The company can influence its cliental by way of its dividend policy, it can lead to the following
advantages:

attracts high profile clients

resist takeovers if there are large corporate entities who have invested for long term strategic
purposes rather than for short term profit making.
Page 49 of 108
SHARE / BUSINESS VALUATION TECHNIQUES
These techniques are employed;

When buying a company to identify the price at which to buy

When floating shares of a company to identify the price at which to float

Fair valuation of investments in private equity when reporting under IAS 39
Valuation
technique
Dividend Valuation
Features
Formulae / Procedure
Fair value of the company is the present Constant Dividend Model
value of all expected future cash dividends
of the company.
Suitable for mainly minority shareholders.
Dividend Growth Model
More objective / comfort on the method
since it consider the cash flows and not
Ke is also called ‘Earning Yield’
profits which is very subjective.
Earning yield
Price Earning Ratio
Suitable for companies that give cash
dividends only.
The method is very similar to the dividend
valuation method.
Earnings used for the computation of the Listed Companies
price, is the future expected earnings /
EPS.
In case of unlisted companies, the P/E Unlisted Companies
ratio of a listed company from the similar
industry is adjusted for the liquidity
preference, for which the RULE OF
THUMB states that it’s 1/3rd of the
investment value.
Net Assets
Therefore, the P/E ratio of an unlisted
company is 2/3rd of the P/E ratio of a
listed company from the same industry.
Net assets = Assets – Liabilities.
Option 1 – Net assets based on book
Points to note
values
The value of net assets would vary with
This option is not a very suitable basis
the option being used i.e. the book
since, it accounts for the historical cost of
value or the fair value.
the assets and liabilities which are not
relevant.
The net assets would not include
fictitious assets, which are mainly;
The value obtained is also called the
 Deferred tax assets / liabilities
Breakup Value of the company.
 Goodwill
 Deferred costs
Page 50 of 108
SHARE / BUSINESS VALUATION TECHNIQUES
Option 2 – Net assets based on market
values
A more preferred method since gives
almost the fair value of the share.
Super profits
This method is preferred when substantial
acquisition is to be done. Moreover, it
provides the Floor Value of the Business
Under net assets based valuation, the
inherent assumption of going concern is
ignored. This method incorporates the
assumption and helps incorporating the
goodwill of the business in the share
valuation.
Procedure
Compute the net assets of the company
based on the fair values i.e. market
values.
Compute the average industry return on
the net assets. (A)
Compute the average profits of the
company. (B)
Case I – B > A
The company is generating super profits
(i.e. B-A). Using professional judgment
identify the number of years for which
the company would generate the super
profits.
Value of the Company = Net assets (fair
value computed above) + (Super profits
x number of years estimated)*
Value per share = Value of company ÷
number of shares
* as per the method, this represents the
goodwill of the company being
acquired.
Case II – B = A or B < A
The company is not generating super
profits. Therefore,
Value of the company = Net assets (fair
value computed above)
Cash flows based
Value per share = Value of company ÷
number of shares
As per this method, the value of the Value per share = Value of company ÷
company is the present value of all future number of shares
cash flows of the company discounted at
the appropriate discount rate.
Page 51 of 108
SHARE / BUSINESS VALUATION TECHNIQUES
Free cash flow of This method uses the free cash flows of
the COMPANY
the company to compute the value of the
company.
Free cash flows available to the company,
refers to the cash available for distribution
to both the debt holders and the equity
holders.
Procedure
Developing of the cash flows is similar
to that used as per IAS 7.
Differences are:
No financing cash flows would be
incorporated. Neither dividend nor
BEWARE – IT’S DIFFERENT FROM THE
interest
payment
would
be
FREE CASH FLOWS AVAILABLE TO THE
incorporated.
EQUITY HOLDERS.
Cash flows for investing activities would
This is the British approach. An alternative
only include those investments that
method is computing the Free Cash flow
pertain to the operations (e.g.
to the equity holders, illustrated below
replacement of property plant and
and discounting it using Ke.
equipment)
The net free cash flow obtained above is
discounted using WACC. The discounted
cash flows is the market value of the
company since, the net cash flow
represents the cash flow for both the
debt and the equity holders and Market
Value of the company is E + D.
Value per share = (Value of company –
market value of Debt ) ÷ number of
shares
SUMMARISING THE METHODS
Earnings based method
Assets based method
Cash flow based method
Hybrid
Dividend
valuation Net assets based on Discounted cash flow Super profits method
method
Book value
method
Earning yield valuation
Net assets based on Free cash flow to the
market value
company method
PE ration based valuation
FREE CASH FLOW TO EQUITY
The concept is linked with the free cash flow to the company discussed above. Discounting the free cash
flow to the equity holder at Ke will give the ‘E’ of the company and when divided by the number of shares
will give the price per share. The computation is as follows;
Free cash flow to the company
xxx
Adjustment for debt related cash flows:
Interest payments
Tax savings on interest
Inference dividend
Repayment of debt / preference share capital
Issue of debt
(xxx)
xxx
(xxx)
(xxx)
xxx
Free cash flow to equity
xxx
Page 52 of 108
FOREX
GENERAL RULES
 Determination of rates – (direct / indirect, buying / selling)
 Single currency conversion (e.g. Pak / USD)

Draw a complete transaction cycle (like in picture)

Check the position of the known currency in the exchange
rate provided (whether it is in the numerator or
denominator)

Foreigner
$ = 100
$ = 100
RULE – if the known currency is in the numerator, for
conversion, the known currency will be DIVIDED by the
rate, and vice versa
Me
Bank
PKR = ?

Identify the ‘?’ currency, and check whether it is being paid or received from bank.

RULE – if the amount is being received from the bank, we will always receive the lesser amount
and vice versa. (in short we will always be at the losing end)
 Cross currency conversion
Example
U need GBP in Pakistan
Conversion directly from PKR to GBP not possible
Rates quoted as PKR / USD and GBP / USD

Check the requirement of USD for the known amount of GBP

Now check the conversion of the known USD in PKR
 All above rules apply for conversion
EXCHANGE RATE / PARITY
“It is the rate at which one currency can be exchanged or traded for another currency”
The foreign Currency buying & selling rates are referred to with the perspective of “FOREIGN EXCHANGE
DEALER” and “FOREIGN CURRENCY”.
BUYING RATE:
“The rate at which ‘foreign Exchange Dealer, buys foreign currency is BUYING RATE”.
SELLING RATE:
“The rate at which ‘Foreign Exchange Dealer’ sells foreign currency is SELLING RATE”.
Example:
CUSTOMER
1 USD
Sells
Rs.60 Accepts
Local Currency
F.E DEALER
Buys
1 USD
Gives
Rs.60
Foreign Currency
Page 53 of 108
FOREX
GENERAL RULES
CUSTOMER
F.E DEALER
1 USD Buys
Sells
Rs.60 Gives
1 USD
Accepts
Local Currency
Rs.60
Foreign Currency
 Thus, if the Customer wants of sell foreign currency, he will sell it at the ‘BUYING RATE’ of foreign
exchange dealer.
 Thus if the customer wants to buy foreign currency he will buy it at the ‘SELLING RATE’ of foreign
exchange dealer.
Example:
 An importer has to pay of one million USD abroad. How much should he expect to pay in Rupees if
bank has quoted the following rates;
BUYING
SELLING
Rs.59/USD
Rs.60/USD
Amount of payments 1,000,000 x 60 = 60,000,000.
 Importer is required to ‘buy’ USD for payment abroad and accordingly the bank will ‘SELL’ the USD.
Example:
An exporter has received £.5,000 how much should he expect to receive in Rupees if bank has quoted the
following rates.
BUYING
SELLING
Rs.117/£
Rs.117.5/£
Amount of Rs. Received 5,000 x 117 = Rs.585,000
 The exporter as received £ and now he wants to convert them into Rupees. Therefore, he will ‘SELL’
these £ and accordingly bank will ‘buy’ the same thus Bank’s buying rate will be used.
QUOTING OF CURRENCY
DIRECT QUOTE
“Local Currency per unit of Foreign Currency” e.g Rs.60/USD, Rs.117/£
Page 54 of 108
FOREX
GENERAL RULES
In, Direct Quote
Buying Rate
Selling Rate
LOWER
HIGHER
INDIRECT QUOTE
Foreign Currency per unit of Local Currency. e.g 0.0167 USD/Rs. 0.0086 £/Rs.
In, In Direct Quote
Buying Rate
Selling Rate
Higher
Lower
In foreign countries, Currencies are quoted in Indirect quote. However, in Pakistan, Currencies are quoted
in direct quote.
Example:
A Co. has received 25,000 Saudi Riyal from one of its customer. How much the Company expects it will
received Pak Rupees.
Selling
Buying
SR 0.0625/Rs
SR 0.0645/Rs
Amount to be received
=
25,000 x 1/0.0645
=
Rs.387,597
This amount will be paid to the Company by the bank.
IMPORTANT NOTE:
In case of Indirect Quote, one confusion arise about which rate to be used, the amount (Payment / receipt)
should be calculated using both rates. If Bank is purchasing the foreign Currency, then the local currency
(actual) will be lower. Similarly, if bank is selling foreign currency, then the local currency to be received by
the bank will higher.
i.e Convert Indirect quote to Direct quote and compare as if it is direct quote.
Page 55 of 108
FOREX
GENERAL RULES
Example:
A Co. has to pay 75,000 Euros to its French supplier, how much PKR it needs to pay if its bank has quoted
the following exchange rates.
Buying
Selling
Rs.73/€
Rs 74/€
€ 0.01333/Rs
€ 0.01315/Rs
Solution:
Amount to be paid
Amount to be paid.
=
75,000 x 74 = 5,550,050
Example: How much a UK Co. will receive and pay in its local currency in the following situation.
i)
It receive an amount of 150,000 French France from its customer.
ii)
It has to pay an amount of one million Yen to japanies supplier.
Spot Exchange rates are:
FF/£
9.4340
9.5380
JY/£
203.6500
205.7800
Solution:
In Direct Quote
i)
ii)
Higher rate
Lower Rate
Buying Rate
Selling rate
Amount to be received in £
150,000/9.5380
Amount to be pain in £
1,000,000/203.65
=
15,727 £
=
4,910 £
Example: A customers has a Dollar A/C at ABN Bank he wants to withdraw Rs.100,000 from its Bank
account. By what amount the bank would debit his account if the exchange rate on the day was its bank
account.
Rs / $
61
62
Solution:
Bank is buying USD by debiting the customer A/C, So in case of direct quote, lower rate ‘Bank’ buying rate.
Amount to be debited =
100,000/61
=
$1639
Direct QUOTE
Rs / $
Page 56 of 108
FOREX
GENERAL RULES
61
62
Lower
Higher
Buying Rate
Selling rate
0.01639
0.01613
Higher
Lower
Buying Rate
Selling rate
Indirect Quote
$ / Rs
CALSSIFICATION OF EXCHANGE RATES
EXCHANGE RATE
Spot Rate
Forward Rate
SPOT RATE:
“The rate at which the currency is exchanged at spot or now”
FORWARD RATE:
“The rate at which the currency is exchange in future”
Foreign Exchange Risk / Foreign Exchange Rate Risk
Foreign Currency transactions carries risk of rate fluctuation, it is called foreign exchange risk.
Hedging:
Insulating from risk of rate fluctuation. The work which we done in future, but doing now is
called Hedging.
Risk:
i)
ii)
Loss due to more payment.
Loss due to less receipt.
Page 57 of 108
FOREX
GENERAL RULES
iii)
Amount would not be fixed / determined.
 Hedging / managing the foreign currency risk / speculative tools
Following tools are available:
1. Natural hedging
2. Forwards
3. Money market hedging
4. Futures
5. Options
6. Swaps
Page 58 of 108
FOREX – HEDGING TOOLS
FORWARDS
FORWARD CONTRACT
“A contract to buy / Sell foreign Currency at an agreed rate in future”
It has no initial cost i.e no fee is charged. It is a binding contract.
1 Million USD to be
Spot Rate
3Months Forward Rate
Paid after three months
61.05
61.70
 The rate agreed today at which a currency can be bought or sold in future (at some future date) are
called ‘forward rates’
 Forwards are binding contracts which have to be honored at the maturity date
 Forwards yield 100% hedge since it eliminates completely the variation / volatility, although the initial
spread between the spot and forward rates, once lost cannot be recovered.
Example:
A Wrist Watch trader in Pakistan has paid his Swiss Supplier SF 26,000,000 on 31-12-2007 It is
October; 2007 now and banker of the Co. has quoted the following forward rate.
Rs.76
3 Month forward rate
Rs.77
How much the trader should expect to pay in PKR if he has obtained forward contract from the bank what is
actual cost of trader in PKR if on 31-12-2007 the Spot exchange rates are as follows.
a)
Rs.77
Rs.78
b)
Rs.77
Rs.75
Solution:
Amount to be paid if the trader has obtained forward contract.
26,000,000 x 77 =
Rs.2,002,000,000
CLOSE OUT OF FORWARD CONTRACT

Before maturity
 Equal offsetting contract for the remaining period
 Settle today by calculating the value of forward contract today

At maturity
 If the underlying transaction does not happen, you settle the forward at the spot rate
Also example 4.11 PBP-130 + Q # 6 Sum08
Example:
leather goods exporter expects to receive 100,000 S.R in one month time the exchange rate
quoted by the bank is as follows.
Page 59 of 108
FOREX – HEDGING TOOLS
FORWARDS
Spot
Rs./SR
15.9
16.2
Months Forward
Rs./SR
16.0
16.5
How much the exporter expects to receive in PKR, if he enter into a forward contract.
Solution:
Amount to be received under forward contract (Selling)
=
100,000 x 16
=
Rs.1,600,000
Assume that the amount to be received was not actually received. Now foreign currency under forward
contract will be sold buying at spot.
If Spot rate month end is
Rs./SR
16.5
16.90 (Buying)
What is forward close out (gain) / loss?
 100,000 SR bought to pay under forward contract (100,000 x 16.9) 169,000
100,000 SR sold under forward contract
(100,000 x 16)
Close out loss
(1,600,000)
90,000
If spot rate at month end is
15.60
Rs./SR
15.80
What is the forward close-out gain/loss?

100,000 SR bought to pay under forward contract
(100,000 x 15.80)
1,580,000
100,000 SR sold/paid to bank under
Forward Cont. (100,000 x 16)
(1,600,000)
Forward Close-Out gain
(20,000)
INTREST RATE PARITY THEORY
“If currency interest rate is higher, than this currency depreciate in future”
Page 60 of 108
FOREX – HEDGING TOOLS
FORWARDS
Note: If interest rates are annual, than forward rate determined is also for 12 months forward.
Thus, period of forward rate depends upon the period of Interest rate.
Formula:
1+ra
1+rb
=
ƒ a/b
S s/b
Where,
f a/b
ra
rb
S a/b
=
=
=
Interest rate of currency ‘a’
Interest rate of currency ‘b’
Spot rate expressed as currency ‘a’ amount of currency ‘b’
=
Forward rate expressed as currency ‘a’ per unit of currency ‘b’
 CALCULATING FORWARD RATES / FUTURE SPOT PRICE

Relative purchasing power parity theory
Sf = Future spot price

International Fisher Relation
Sf = Future spot price

So = Sport price now
Covered interest rate parity
F = forward rate

So = Sport price now
So = spot exchange rate
Uncovered interest rate parity
NOTE: In any of the formula above, Sf can be replaced with F to calculate forward rate
Page 61 of 108
FOREX – HEDGING TOOL
Example:
Spot Rate
Interest rate in Pakistan
Interest rate in USA
Req:
Rs.60/$
8% p.a
3% p.a
Compute forward rate.
Or
1+ra
1+rb
=
ƒ a/b
S s/b
1+0.08
1+0.03
=
ƒ a/b
60
ƒ a/b
=
Rs.62.9/$
Check
Rs. 60/$
8%
60 x 1.08
64.8
Rs.64.8 / 1.03 $
62.91
(1+ra)(Sa/b)
3%
1 x 1.03
1.03
(1+rb)
ƒ a/b
Example:
Spot Rate
PKR 115/£
PKR Interest Rate
10 % p.a
£ Interest Rate
Req:
8 % p.a
Compute three months forward rate:
Solution:
3 Months interest rates
PKR
10% x 3/12
2.5 %
N
£
6% x 3/12
1.5 %
N
1+ra
1+rb
=
ƒ a/b
S s/b
1+0.025
1+0.015
=
ƒ a/b
115
`
ƒ a/b
=
Rs.116.13/£
Page 62 of 108
FOREX – HEDGING TOOL
N-1
These are periodic rates. It should not be equivalent periodic rates. Because equivalent periodic
rates is used when compounding is involved. Here is no compounding.
Page 63 of 108
FOREX – HEDGING TOOL
MONEY MARKET HEDGE
“It is used when forward contract is not available”.
Receipt of Foreign Currency:
 Raise loan in FOREIGN CURRENCY
 This amount is less than the amount of receipt
 The amount borrowed should be such that after interest expense it will be equal to amount
of receipt.
 Convert the loan raised in local Currency using spot rate.
 Invest the local currency.
 Amount received in FOREIGN CURRENCY is utilized to pay the loan raised in FOREIGN CURRENCY.
 Investment of local currency is withdrawn. It includes interest income. It is the amount to be
received if we obtain a forward contract.
Check:
Compute forward rate and determine the amount of receipt. This amount and the amount
withdraw (Local Currency) should be same.
Or Compute “Effective exchange rate under Money Market Hedge”.
Amount with drawn (Local Currency)
Amount received (Foreign Currency)
 Now, compare both the above rates, they should be identical.
Example:
A Pakistani Co. is expecting to receive 50,000 can $ in one year time. Currency spot rate is Rs40/can $. The
Company has identified that interest rate in PKR is 10% and in can $ is 6%.
Req: How can that Co. arrange a money market hedge for itself and what is expected exchange rate
under this hedge.
Solution:
Amount to be borrowed in Can $ (x)
X + (X x 6%)
X
=
=
50,000
50,000/1.06 = Can $ 47,170
1.
This amount is less than 50,000 Can $ Actually it will increase to can $ 50,000 in one year
and Can $ 50,000 will be required to be paid to the Bank.
2.
Local Currency units of the amount raised.
=
47,170 x 40
=
Rs 1,886,800
Page 64 of 108
FOREX – HEDGING TOOL
3.
Amount invested in deposits etc. which will be withdrawn in one year.
=
4.
PKR 1,886,800
Amount withdrawn after one year including interest @ 10% p.a
=
1,886,800 x 1.1
=
PKR 2,075,480 (Total Receipt)
CHECK:
Effective exchange rate under Money Market Hedge
=
=
Forward Rate
2,075,480/50,000
PKR 41.51/Can $
=
Sa/b x
=
40
Rs
1 + ra
1 + rb
1 + 10%
1+6%
x
41.51 / Can $
PAYMENT OF FOREIGN CURRECNY
1.
Raise loan in LOCAL CURRENCY
 This amount is determined as the amount of foreign currency that should be bought using
this loan amount (LOCAL CURRENCY) and that foreign currency be invested so that this
grow foreign CURRENCY when withdraw should be equal to the amount required to be paid
in future date.
2.
Convert the loan raised into FOREIGN CURRENCY using spot rate.
3.
Invest the FOREIGN CURRENCY
4.
Investment in FOREIGH CURRENCY is withdrawn and paid to the supplier e.g in Foreign Country.
5.
Loan raised in LOCAL CURRENCY is repaid using the Company’s own funds. It includes interest
expense on the loan.
It is the amount to be paid, if we obtain forward contract.
CHECK:
OR
Compute forward rate and determine the amount of payment. This amount and the loan
amount paid should be same.
Compute ‘Effective Exchange Rate’ under Money Market Hedge.
Local Amount paid (Local Currency)
Amount Withdraw & paid (Foreign Currency)
Now, compare both the above rates, they should be identical.
Example:
Company ows a French Creditor € 3.5 Million in three months time. The spot exchange rate is Rs/€
75-76 Co. can borrow in PKR for 3 months @ 12% p.a and can deposit Euro for 3months @ 10%.
Page 65 of 108
FOREX – HEDGING TOOL
Req: What is cost in PKR if the company arranges a Money Market Hedge, what effective forward rate
this represents?
Example:
A UK Company ows a French Supplier 6Million French France (FF). The Current spot exchange rate is
FF/£ 7.5509
7.5548. The Company borrows and invest in £ @ 8.6% p.a and 9% p.a and can deposit and
borrow FF at the rate of 10% p.a and 12% p.a respectively. Payment is to be made after 3months. What will
be the effective exchange rate using Money Market Hedge.
Solution:
1 Amount to be borrowed in £
X + 0.01X x 3/12
=
6,000,000
X
=
5,853,659 FF
In £ 5,853,659/7.5509 =
£ 775,227
Initially Co. shall raise loan in LC convert this LC in FC using selling rate (It is lower in Indirect quote)
Total Cost loan
Loan
Interest
(775,227) + (775,227 x 8.6% x 3/12)
=
791,894
Effective Exchange Rate
= 6,000,000/791,894 = FF 7.577/£
Example:
USD A/C
An investor has USD 1Million to invest for 3months deposits rates are currently
= 6%, PKR A/C = 12%
The current spot rate is Rs/USD 62-62.2,
3months forward rates are Rs/USD 62.4-62.6
REQ:
Identify that if there is an opportunity of arbitrage gain for investor in currency.
Solution:
1.
2.
If invested in USD, the interest of USD 15,000 (1,000,000 x 6% x 3/12) would be earned.
Convert USD 1,000,000 in PKR and invest in PKR and enter into 3months forward contract.
1,000,000 x 62 =
62,000,000
Interest @ 12% for 3months
=
1,860,000
=
63,860,000
At the end of 3months, USD are bought
63,860,000/62.6
=
1,020,128
Actual amount
=
1,000,000
Interest earned
=
20,128
Arbitrage Gain:
Interest earned in USD by investing in PKR
Interest earned in USD by investing in USD
Arbitrage Gain
20,128
15,000
5,128
Page 66 of 108
FOREX – HEDGING TOOL
However, if the forward rate is computed & using the above date, then there will be NO ARBITRAGE GAIN.
ƒ a/b
=
Sa/b x
=
62
x
Rs
1 + ra
1 + rb
(1 + 12% x 3/12)
(1 + 6 % x 3/12)
62.9163 Rs/USD
Now, gain in PKR investment of 63,860,000 in USD
63,860,000/62.9163
Actual Amount
Cost earned
Gain in USD investment
Arbitrage Gain
=
1,015,000
1,000,000
=
15,000
15,000
-
=
=
=
Forward rate using the above data = 62.9163 i.e At this rate no chance of Arbitrage gain.
If actual forward rate is lower then the (Theoretical) forward rate, it means there is a chance of
arbitrage gain.
Note:
Customer:
1m $ payment after 3months
Spot
3Months forward
60 Rs/$
65.5 Rs/$
Bank: If bank gives the customer 3months forward rates of Rs.60.5/$, the bank will already purchase
forward contract of Rs.64.4/$ (e.g)
If Spot rate at that point
Rs.60.5/$
Rs.61/$
Rs.58/$
No forward Contract
Loss of 0.5
If forward Contract
Gains of 2.5
Only gain of Rs.0.1/$ irrespective of the spot rate at that time.
Page 67 of 108
FOREX – HEDGING TOOLS
FUTURES
Example:
Mr. A is required / wants to buy 90shares of MM Ltd. Now, (April 1, 2007) the sopot price of the
share of MM ltd. Is Rs.80. Future price to purchase 100 shares at April 30, 2007 is
Futures
Standardized contract size and maturity dates
These are exchange traded
Initial deposit (as a security)
No party risk as settled by the clearing house.
Marked to market losses are recovered on periodic
basis
Always settled net in cash.
Imp: It will, therefore, always have an expense on
settlement at maturity equivalent to spread
between the Buying and Selling rate (dealer
commission) as we have to buy and sell same
amount of FCY on the Maturity date @ spot rate
Future contract price at maturity date will be equal
to the price at spot rate.
Rs.80.5 share.
Forwards
Customized as per the requirement
Over the counter – negotiated
No initial deposit
Have to bear the risk of opposite party
No losses are recovered, instead all dealing at
maturity date.
Can be settled by delivery or net in cash (as in case
of close out).
Expense of spread only in case of net cash
settlement.
Since not traded in the market therefore not
relevant.
Mr. A is intended to buy shares at April 25, 2007 Spot price at April 25, 2007 are as follows.
Spot Price
Future Price
Rs.84/Share
Rs.85/Share
Risk:
More amounts will be paid to buy the shares as compared with today’s Spot rate.
LOSS ON ACTUAL TRANSACTION
Price paid to buy shares at April 25, 2007
(90 x 84)
=
Price at April 1st 2007
(90 x 80)
=
=
HEDGE STRATEGY (BOUGHT Now
7,560
7,200
360
SELL IN FUTURE)
GAIN ON FUTURE CONTRACT
Contract to sell the future Contract .
April 25,2007 Selling of future Contract
(100 x 85)
=
Contract to buy the shares under April 2007 future Contract
(100 x 80.5)
=
8,500
8,050
450
Page 68 of 108
FOREX – HEDGING TOOLS
FUTURES
NET PAYMENT
Payment under of original translation
Receipt / Gain under future contract
Net payment to buy 90 shares
=
=
=
7,560
(450)
7,110
90 Shares
100 Shares
Net Effect
Example: Mr. A holds one share of OGDCL. Spot price is Rs.110/Share on 01/03/07. He wants to sell it on
16/03/07. He is facing the risk of lowering of share price Future Contract is available at Rs.111/Share to be
settled at 31/03/07.
Spot Rate at 16/03/07
Rs.108/Share
Future Price at 16/03/07
Rs.109.5/Share
HEDGE STRATEGY
SELL
(at future Market)
Buy
01/03/07
16/03/07
Less
Original Transaction (Spot Rates)
110
108
(2)
Future Contract (Future Price)
111
109.5
1.5
(Sell Now)
(Buy Later)
Net Loss
(0.5)
Original Transaction
108
Under Future Contract
1.5
109.5
Example:
An Investor is currently looking forward to purchase 2,100 shares of OGDCL on 05/08/06. It
is 02/08/06 today and share prices of security are as follows:
Spot Price
=
Rs.164/Share
Future Price
=
Rs.166/Share
2/8/06
Page 69 of 108
FOREX – HEDGING TOOLS
FUTURES
The investor is planning to hedge against future of the security through future Contracts. Standard contract
quantity in future is 500 Shares and its Maturity date is 31/08/06
REQ: Determine how can the invest setup the future hedge and what is outcome of the hedge if prices
on the Transaction date are as follow:
Case I
Spot Price
=
Rs.165.5/Share
Future Price
=
Rs.166.8/Share
Solution:
Describe whether buy or sell in the future market. i.e Hedge Strategy buy future contract.
No. of Contracts
=
Required Quantity/Standard Qty.
Future Price
=
2,100/500 = 4.2
=
4 Contractors
We contracted to buy 4 future contracts i.e 2000 shares (4x500) of OGDCL @ Rs.166/Share on 31/08/06
Hedge Outcome: 25/08/06
Spot Market Outcome
(2,100 x 165.5)
=
347,550
[2,000 x (166.8 – 166)]
=
(1,600)
Net Outcome (Payment)
=
345,950
Target Cost (2100 x 164)
=
344,400
Actual Cost
=
345,950
Future Market Outcome
ANALYSIS:
Page 70 of 108
FOREX – HEDGING TOOLS
FUTURES
Loss
=
(1,550)
Target Cost (2,100 x 164)
=
344,400
Actual Cost at spot (2,100x165.5)
=
347,550
Loss on Spot market
=
(3,150)
Gain on future Market
=
1,600
Net Loss
=
(1,550)
=
3,150
Hedge Instruments Gain
=
1,600
Hedge Efficiency
=
or
Spot Market Outcome
Hedge Efficiency
Hedge Items
Loss
Gain/Loss on hedging Instrument
Loss/Gain on Hedging Item
=
3,150/1,600=197%
=
1,600/3,150=51%
=
51% - 197%
Spot Price
=
Rs.162/Share
Future Price
=
Rs.162.6/Share
=
340,200
[2,000 x (162.6 – 166)]
=
6,800
Net Outcome (Payment)
=
347,000
Or
Hedge Efficiency Range
CASE-II on 25/08/06
Hedge Outcome
Spot Market Outcome
(2,100 x 162)
Future Market Outcome
ANALYSIS
Page 71 of 108
FOREX – HEDGING TOOLS
FUTURES
Target Cost
=
344,400
Actual Cost (Net)
=
347,000
Net Loss
=
(2,600)
Target Cost
=
344,400
Actual Cost at Spot
=
340,200
Gain
=
4,200
Future Market Loss
=
(6,800)
Net Loss
=
2,600
Hedge Efficiency
=
6,800/4,200=162%
or
In future Contract, we are not local in future rate.
Our Purpose is to near out the target cost / target revenue.
Comparison is made with target Cost/Revenue.
 When no Gain/Loss on future net result then the Hedge is perfect.
Future Market may or may not give perfect Hedge. Its reasons are:
1. Future contract Size/Quantity is not equal to the actual Quantity.
2. Basis Risk.
Basis
=
Spot Price – Future Price on Particular Date
The Variability in Basis is called basis risk.
 If basis risks become zero, and future quantity is equal to the actual quantity, then there is perfect
Hedge.
Basis
CASE-I
CASE-II
164 – 166 =(2)
(At the beginning)
162 – 162.6 =(0.6)
(At the end)
IMPORTANT NOTES
1. Future Market is a Market for the purchase and sale of items in future through, Standard Contract.
2. The future Contract has standard quantity and has fixed standard Maturity date.
3. The price of futures contract fluctuates in random/line with the price of underlying items (Quantity,
Price, rate etc.)
4. When use for hedging, the future contract off-set the gain/loss on spot market.
5. The future Contract can be closed out any time before their Maturity date.
6. Future contract may or may not result in perfect Hedge. This is because of the tow reasons.
Page 72 of 108
FOREX – HEDGING TOOLS
FUTURES
i)
ii)
The Standard quantity under future contract may not exactly match the actual required
quantity.
Basis risk which means that Movement in future price may not exactly match the
movement in the underlying price of item.
Example: A Co. plans of Sell 67,100 shares of K Ltd. Spot price of the shares on March 3, 2007 is to
Rs.152/Share. The March end future Contracts of K Ltd. Are available 10,000 shares @ Rs.155/Share on
March 3, 2007 the Co. expects to off load the shares on March 20, 2007. The company faces the risk of price
decrease in near future and therefore, it wants to Hedge this transaction through future contracts.
REQ:
1. How Can the Co. setup future Hedge.
2. What is hedge outcome on March 20, 2007 when share prices on that day are as follows:Spot Price
=
Rs.148/Share
Future Price
=
Rs.150/Sgare
=
67,100/10,000
=
6.71 OR 7 Contracts
Solution:
1. Hedge Strategy
Sell future contracts now and buy later
No of Contracts
2. Hedge Outcome
Sell of future Contracts @ Rs.155/Sahre
10,850,000
Bought of future contracts @ Rs.150/Share
10,500,000
Gain on Future Market (155 – 50) x 70,000
350,000
Actual Net Receipt:
Spot rate Rs.148/Share (Actual Sale Price)
Gain On Future Market
9,930,800
350,000
10,280,800
ANALYSIS:
Target proceeds @ Rs.152/Share
10,199,200
Actual proceeds
10,280,800
Net Gain on the Transaction
81,600
Page 73 of 108
FOREX – HEDGING TOOLS
FUTURES
OR
Target Price
10,199,200
Actual Price
9,930,800
Loss on Cash Market
268,400
Gain on future Market
350,000
Net gain on the Transaction
81,600
BASIC RISK
Future price moves w.r.t movement in spot price
Basis =
Future Price – Spot Price
 On the date of Maturity of Future Contract, the future price and Spot Price are same and Basis is
‘Zero’.
 Normally basis decreases gradually with the time.
 It would be stated that Basis risk is constant.
 If no data is given to compute future price or future price is not given, then we assume that Basis
DECREASES GRADUALLY with time.
PRICING OF FUTURES
The basis is amortized at the effective rate over the period of the future (Cash and Carry Arbitrage Theory)
BASIS RISK
The risk that the basis does not move smoothly towards zero over the period of maturity
CLOSING OUT OF FUTURE CONTRACT (ALWAYS BEFORE MATURITY)
Although 2 options but cash-flow same because price for both options are same
 Selling the future in the market at the prevailing price
 Obtaining an equal offsetting contract
HEDGE EFFICIENCY
Here, notional profit / loss is calculated by comparing gain as calculated in transaction i.e.
1) Spot price to spot price at settlement date
2) Future price to spot price at settlement date
Page 74 of 108
FOREX – HEDGING TOOLS
FUTURES
CURRENCY FUTURE
Direct Future Hedging
Example: A US Company is expecting to pay € 2.1 Million in mid of December 2007. Current Spot rate on
18-04-2007 is $/£ 1.58–1.60 the Co. decides to hedge against adverse exchange rate movement through
future contract. Following 3 future contracts are available:
Prices ($/£)
September-07
1.552
December-07
1.5556
March-08
1.5564
Standard Quantity is £ 62,500 for all these contracts. (Future Foreign currency contracts are available)
Req:
a). How can the Co. Setup the Hedge?
b). What is actual hedge outcome if on the transaction date, rates are as follows:
Spot rate $/£ 1.612 – 1.620, Future rates:
Dec
March
Contracts $/£ 1.610
Contracts $/£ 1.625
Solution:
Hedge Strategy: Buy the future Contracts now and sells later.
No. of Contracts.
2,100,000
62,500
=
33.4 or
34
Contracts
Choose the future Contract whose maturity date is near to the Transaction date but does not before
this date i.e December Contracts.
Future Market Outcome
34 Contracts of £ 62,500 bought @ 1.5556 $/£
3,305,650
34 contract to sell at transaction date @ 1.610
3,421,250
Gain on future Market [(1.610-1.5556) x 34x62,500)]
115,600
Cash Market Outcome:
Actual payment @ 1.620
3,402,000
Gain on Future Market
(115,600)
Page 75 of 108
FOREX – HEDGING TOOLS
FUTURES
Actual Cost (Net Payment)
3,286,400
ANALYSIS
Target cost @ 1.60
3,360,000
Actual Cost
3,286,400
Net Gain
73,600
Comprising
Target Cost @ 1.6
3,360,000
Actual Payment @ 1.620
3,402,000
Loss on Cash Market
42,000
Gain on Future Market
115,600
Net Gain on Transaction
73,600
Example: A US Co. has bought goods amounting to Euro 720,000 payable in 30days time. Current Spot rate
is $/€ 0.9215 – 0.9221. A future Contract in Euro having Standard quantity of 125,000€ and Maturity after
90 days from now is available at a Price of $/€ 0.9245. What is hedge outcome after 30days if the Co.
Purchase Euro future, and on that date, the Spot rate is $/€ 0.9345 – 0.9351.
Solution:
Hedge Strategy: Buy future contract now and sell later.
No. of Contracts
=
720,000
125,000
=5.76
Or 6 Contracts
Future Market Outcome
=
Current Future
Rate
-
Current Spot Rate
=
0.9245
-
0.9221
=
0.0024 $/€
Remaining Basis after 30 Days
=
0.0024
90
Estimated Future rate after 30days
=
0.9351 + 0.0016
=
0.9367 $/€
Current Basis
Remaining Basis
X60
=.0016 $/€
Future Market Outcome
Buy 6 Future Contracts @ 0.9245
693,375
Sell 6 Future Contracts @ 0.9367
702,525
Page 76 of 108
FOREX – HEDGING TOOLS
FUTURES
Gain on Future Market
9,150
Net Payments
Actual Payment @ 0.9351
673,272
Gain on future contract.
(9,150)
664,172
ANALYSIS (Net Loss)
Target Payment @ 0.9221
663,912
Actual Payments
664,122
210
Gain on Future Market
(9,150)
Loss on Cash Market
@ 0.9221
663,912
@ 0.9351
673,272
(9,360)
Net Loss
(210)
INDIRECT FUTURE HEDGING
When in the base currency (In Which Payment is to made, i.e foreign Currency) Future Contract, are
not available, then the hedging is carried out in future contracts denominated in the currency other than
the base Currency (e.g local Currency). It is called Indirect Future Hedging.
e.g If payment is to be made in USD by a Pakistan based Company and USD Future Contract, are not
available then hedging can be made through the use of Pak-Rupee future Contracts. The Hedging through
Pak Rupee future Contracts is called Indirect Future Hedging.
Example: UK Based
Co. has to pay $ 2m in mid of Dec 2007.
Current Spot Rate
Future contract prices ($/£)
Sep 07
Dec 07
March 08
=
$/£ 1.58 – 1.6 (Indirect Quote)
1.5552
1.5556
1.5564
Spot rate on transaction date $/£ 1.612 – 1.620 future Contract price for Dec. Contracts at Transaction date
$/£ 1.610 future Contract size is £ 62,500.
Page 77 of 108
FOREX – HEDGING TOOLS
FUTURES
Req: Hedge Outcome.
Solution:
Hedge Strategy
[Buy $ (Foreign Currency) now i.e. sell £ (Local Currency) now and buy later
at the Transaction date.]
Convert it first in £ (Local Currency) using FUTURE RATE not the Current Spot Rate.
So No. of Contracts
=
=
$ 2,000,000 / 1.5556
£ 62,5000
20.57 or 21 Contracts
Future Market outcome
$
Sell 21 Contracts @ 1.5556 (i.e. USD received)
2,041,725
Buy 21 Contracts @ 1.610 (i.e. USD Paid)
2,113,125
Loss on Future Market
71,400
USD to be paid is more than USD received so to fulfill liability Further USD
71,400 purchased.
Buy USD 71,400 @ 1.612 $/£
£44,292
There is a loss of $ 71,400 (Foreign Currency) in future Market So to meet the liability Co. has purchase
foreign currency is $ 71,400 which is also the amount of loss in future Market. So Co. Pay £ 44,292 (Net Loss
in future Market).
Analysis:
Gain / Loss on Cash Market
£
Target Cost @ 1.58
1,265,823
Payment on Cash Market @ 1.612
1.240,695
Gain in Cash Market
25,128
Loss on Future Market
(44,292)
Net Loss
(19,164)
Or
Target Cost
£
1,265,823
Page 78 of 108
FOREX – HEDGING TOOLS
FUTURES
1,284,987 *
Actual Cost – Net
Net Loss
19,164
* Bought USD @ 1.612 $/£
1,240,695
Loss on Future Market
44,292
Total Cost (Payments)
1,284,987
PERMIUM / DISCOUNT
Spot Rate (Rs.61/$)
3Months Forward
3 Months
Forward
=Rs.61.20/$
Rs.60.50/$
 If Foreign Currency ($) APPRECIATES, The Local Currency DEPRECIATES.
More local currency is required when FC Appreciates that means increase in Ex-Rate (Greater to Spot rate)
 If Foreign currency ($) DEPRECIATES, the Local Currency APPRECIATES.
Less local Currency is required when FC Depreciate, that means Decrease in (Lesser than Spot rate)
Premium
Premium
Forward Rate – Spot Rate
=61.20-61
=Rs.0.20/$
Discount
Spot Rate –
Forward rate
=61-60.50
=Rs.050/$
Page 79 of 108
FOREX – HEDGING TOOLS
FUTURES
DETERMINATION OF FORWARD RATE
Direct QUOTE (Spot rate)
Premium
Discount
ADD (+)
Less (-)
Indirect QUOTE
Premium
Discount
Less (-)
ADD (+)
Page 80 of 108
FOREX
OPTIONS
General Points
There is initially no cost/no significant cost on:
Forward Contracts
Money Market Hedge
Futures Contracts
However, these are binding contracts;
OPTION:
An Option is an agreement giving its holder the right but not the obligation, to buy or sell
specific quantity of any item at specified price (called Exercise Price/ Target Price) within a
stated predetermined period.
OPTION CONTRACTS INVLOVES TWO PARTIES:
1.
2.
Holder of Option
Writer of option
OPTIONS ARE OF TWO TYPES:
1. CALL OPTIONS
2. PUT OPTIONS
CALL OPTION:
It provides option to the holder that he could buy at an exercise price at future date
or for a period.
It provides guaranteed ceiling price/maximum price.
Example:
Mr. A wants acquires 10,000 shares of SNGPL after 3months. Now April 1, 2007 the
price of each share is Rs.80.
He bought a call option with exercise price of Rs.80.50/Share.
Share price as at June 30, 2007 is,
a) Rs.79/Share
b) Rs.82/Share
Spot Price (30-06-2007)
Rs.82/Share
Rs.79/Share
Feasible to Exercise
Not Feasible to exercise since
it is available in Market at a
lower rate.
Exercise
Not Exercise
Page 81 of 108
FOREX
PUT OPTION:
It provides option to the holder that it could SELL at a fixed price at a date in future
or for a period.
IT PROVIDES GUARANTEED FLOOR OR MINIMUM PRICE.
Holder of the option has only the right exercise it, However, No OBLIGATION.
Example:
Mr. A holds 10,000 shares of PPL. Current share price is Rs.102. He buy an option to sell
these share, at Rs.101/Share for (Three) 3 months. It is now April 1, 2007.
As at June 30, 2007, Spot price of the share is as follows:
a)
Rs.109/Share
b)
Rs.95/Share
Spot Price (30-06-2007)
Rs.109/Share
Rs.95/Share
Not Feasible to exercise the
option since it could be sold
in market @Rs.109 instead of
Rs.101 (as under the option.)
Feasible Exercise
Not Exercise
Exercise
‘IN THE MONEY’ OPTION
When the option (Put or Call) is feasible to exercise, it is called that the option is in the Money’.
In the Money Option
PUT OPTION
Exercise
Price
>
Market
Price
CALL OPTION
Exercise
Price
<
Market
Price
PREMIUM ON OPTIONS:
In options, the holder pays some premium to the writer as compared to other hedging modes, i.e
the Forward Contracts, Money Market & Futures.
 The Premium is paid UP-FRONT
Page 82 of 108
FOREX
‘OUT OF THE MONEY OPTION’
When the option (Put or Call) is NOT FEASIBLE to exercise, it is called that the option is ‘Out of the Money’.
Out of the Money Option
PUT OPTION
Exercise
Price
<
CALL OPTION
Market
Price
Exercise
Price
>
Market
Price
CONCEPT OF INTRINSIC VALUE
INTRINSIC VALUE:
It is the difference of exercise price and spot price.
Example:
Exercise Price
:
Rs.40/Share
Spot Price
:
Rs.43.5/Share
Premium
=
Rs.3.2/Share
(To Purchase the Call Option)
INTRINSIC VALUE
=
43.5 – 40
=Rs.3.5/Share
For ‘In the Money’ Option:
Intrinsic value is the Difference b/w Exercise price and Spot price.
For ‘Out of the Money Options: Intrinsic Value is ‘Zero’ because holder has no obligation.
 For ‘Out of the Money’ Options:
It is always better to Sell it in the Market and earn a premium; or
Allow it to LAPSE when there is NO PREMIUM for remaining period.
 For ‘In the Money’ Options Compare intrinsic value with Premium amount:
-
If premium amount is greater than the Intrinsic value, it is better to SELL the Option,
rather than to exercise it;
Otherwise, Exercise the Option.
 PREMIUM is a Sunk Cost for:
Decision Making Purpose; &
Calculation of Intrinsic Value.
‘Out of the Money’ Option
Page 83 of 108
FOREX
If it could be sold
If it Could not be sold
SELL
LAPSE
Not Exercise
‘In The Money’ Options
Compare I.V with Premium
Intrinsic
Value
<
Premium
SELL
Not Exercise
Intrinsic
Value
>
Premium
Exercise
TIME VALUE OF OPTION
“The difference b/w intrinsic value and Premium of Option is called the value of Option.”
Example:
(CALL OPTION)
Spot
42.5
Exercise
40.0
Intrinsic Value
2.5
Premium
3.2
Time value of Option (That could be sold)
0.70
Page 84 of 108
 Most important point to note is that options are not exercised if they are out of the money.
 Currency options are always settled net in cash.
 Are not useful if not available for same maturity.
PRICING
The contracts are to be purchased at a price specified on basis of time. Price is generally quoted on basis of
Rs/$ format.
NET OPEN POSITION
Net open position (NOP) of a bank in any foreign currency at any date is the net total exposure of the bank
in that foreign currency after taking into account all on and off balance sheet transactions in that currency
contracted till date.
NOP is mainly a risk management tool imposed by the State Bank of Pakistan on all the Commercial Banks.
Regulation
The higher of Over sold / Over bought position at any given time should not
exceed 10% of the paid up capital of the bank.
NOP is merely a regulator check, and it should be kept in mind that it does not tell whether a bank will be
able to fulfill the contracts / liabilities or not. In other words, its merely a maturity schedule that illustrates
the cash flow position of the bank.
Terminology
Over sold position / short position
Over bought position / long position
Squared position
Explanation
When the liability / sale / outflow side of foreign currency
transactions are greater than the asset / purchase /
inflow side, the bank is said to be in an over sold position.
When the asset / purchase / inflow side of the foreign
currency transactions are greater than the liability / sale /
outflow side, the bank is said to be in an over bought
position.
When the purchase / asset / inflow side is equal to the
sale / liability / outflow side, the bank is said to be in a
squared position.
PROCEDURE FOR QUESTIONS

The over bought or over sold position is calculated with respect to each currency individually.

All balance sheet items are converted at the spot rates.

All off balance sheet items are converted at relevant maturity rates.

Over bought positions of all currencies are summed up to compute the total over bought position of
the bank.

Over sold potions of all currencies are summed up to compute the total over sold position of the bank.

Compute 10 percent of the paid up capital of the bank.
Page 85 of 108

Identify the higher of the over bought or over sold position in absolute terms and compare with the 10
per cent of the paid up capital.
Illustration of Net Open Position
Exam ple
A commercial bank has reported follow ing balance of USD and Euro as on 31-10-2008:
Particular
USD
Cash
Nostro Account
NFCA Deposit
Interest payable
Euro
Exchange rates as per SBP mid rate sheet on 31-10-08 are;
75
200
185
25
15
180
200
40
Purchases maturing on
30-11-2008
31-12-2008
150
125
80
130
Sales maturing on
30-11-2008
31-01-2009
80
100
125
150
USD
80.00
80.50
81.00
82.00
Spot
1 month forw ard
2 month forw ard
3 month forw ard
Euro
101.00
102.00
102.50
104.00
Forward contracts
Paid up capital
Rs. 120 M
Calculate NOP of the bank in PKR.
Solution
NOP of USD
Amount
Xchng rate
PKR
On balance sheet
65
80.00
5,200
Off balance sheet
30-11-2008
31-12-2008
30-11-2008
31-01-2009
150
125
(80)
(100)
80.50
81.00
80.50
82.00
12,075
10,125
(6,440)
(8,200)
Over bought position
NOP of EURO
Amount
Xchng rate
12,760
A
PKR
On balance sheet
(45)
101.00
(4,545)
Off balance sheet
30-11-2008
31-12-2008
30-11-2008
31-01-2009
80
130
(125)
(150)
102.00
102.50
102.00
104.00
8,160
13,325
(12,750)
(15,600)
Over sold position
(11,410)
B
Higher of A and B
(in absolute terms)
12,760
C
10% of paid up capital
12,000
D
Exceeding limit
760 Over bought position
Page 86 of 108
INTEREST RATE SWAPS
Swaps
A Swap is an agreement between two parties to exchange cash flows related to specific underlying
obligations for an agreed period of time.
Two types of swap are described here:
 Interest rate swaps
 Currency swaps.
Interest rate swaps are much more widely used than currency swaps
Interest rat swaps
Swaps can be quite complex instruments, but in this chapter, we shall concentrate on ‘plain vanilla coupon
swaps’.
A plain vanilla coupon (liability) swap is an agreement between two parties to exchange interest payments
on a notional amount of principal at regular interest payment dates throughout the life of the swap. One
party pays interest at a fixed rate and the other pays interest at a variable rate, for example the BBA LIBOR
reference rate. A swap can have a term or duration ranging anywhere between one year and 30 years.
Swaps can be used to hedge exposures to interest rate risk on long-term financial instruments, notably
bonds and medium-term bank loans.
Payments by the parties in an interest rate swap are in the same currency.
Example
A company and a bank might enter into a four-year swap agreement in which interest payments are
exchanged every six months on notional principal of 10 million. The company might undertake to pay a
fixed rate of 6% per annum (300,000 every six months) and in return the bank might undertake to pay
interest at the six-month LIBOR rate.
Payments of the floating rate interest will change every six months if the LIBOR rate has changed. In
practice, if interest payments are made by each party on the same dates, there is a net cash payment by
one party to the other. In the example above, if the six-month LIBOR rate for one interest payment period
is 7.5%, the bank would pay the company 75,000 (10 million X 6/12 X (7.5% - 6%)) if the LIBOR rate is just
5.25%, the company would pay the bank 37,500 ( 10 million X 6/12 X (6% - 5.25%)).
Reasons for using swaps
Interest rate swaps have several uses.
 A company can use swaps to manage the mix of its fixed rate and floating rate debt obligations,
without having to change the underlying loans themselves.
 If a company anticipates a rise or fall in short-term rates relative to long-term interest rates ( = a
change in the shape of the yield curve), it might use swaps to take on more floating rate and less
fixed rate debt obligations, or less floating rate and more fixed rate debt obligations.
 A swap can allow a company to borrow at an effective fixed rate when it cannot do so directly in
the bond markets because it is too small to make a bond issue.
Page 87 of 108
INTEREST RATE SWAPS
The key to understand coupon swaps is that they allow a company to swap either:
 Floating rate interest payments into fixed rate payments, or
 Fixed rate interest payments into floating rate payments.
Example
A company has a loan of 5 million on which it pays LIBOR plus 1% every six months. The loan has a
remaining term of four years. The company is concerned that interest rates are likely to rise, and it wants
to fix its debt payment obligations.
A bank specializing in swaps will agree to a four-year swap in which it receives a fixed rate of 5.5% in
exchange for paying LIBOR.
This swap will fix the company’s borrowing cost for the next four years at 6.5%, as follows.
%
Interest payable on loan
Swap
Receive (floating rate)
Pay (fixed rate)
Net interest cost
(LIBOR % + 1%)
LIBOR
(5.5)
.
(6.5)
.
The overall interest cost has been fixed at 6.5%, without having to change the variable rate loan itself.
Example
VBN plc has 20million (nominal value) of 7% bonds in issue which have a remaining maturity of 10 years.
Interest is payable every six months. The company thinks that interest rates will fall and would like to swap
its fixed interest obligations for floating rate obligations.
A bank specialising in swaps is willing to arrange a 10-years swap on 20 million in which it pays a fixed rate
of 6.15% and receives six-month LIBOR, with ‘interest payments’ exchanged every six months.
The swap allows the company to exchange a fixed rate debt obligation of 7% for a net interest cost of LIBOR
plus 0.85%.
Interest payable on bonds
Swap
Receive (fixed rate)
Pay (floating rate)
Net interest cost
%
(7%)
6.15
(LIBOR) .
(LIBOR+0.85)
These examples might illustrate how swaps allow companies to manage the balance of their fixed and
floating rate interest obligations. They can therefore be used for hedging longer-term interest rate risk.
Currency swaps
Currency swaps are similar to interest rate swaps, but the underlying obligations are in different currencies.
Other significant differences are as follows.
Page 88 of 108
INTEREST RATE SWAPS
 With a currency swaps, there is an exchange of currencies at the end of the swap, and possibly also
at the beginning of the swap. When currency is exchanged at the beginning and the end of the
swap, the same rate of exchange is used. In other words, the amounts exchanged at the start of
the swap and the amounts exchanged at the end are exactly the same.
 Interest rate payments by each party could be either at a fixed rate or at a floating rate.
Example
A US company wants to borrow Swiss francs to finance a five-year investment project in Switzerland. It
wants to borrow in Swiss francs because the profits from the project will be in francs and so it would like to
have Swiss franc debt liabilities in order to hedge its currency exposures. However, the firm is unknown in
Switzerland and could well have to pay higher interest rates than Swiss companies on the Swiss money
markets. To get round this problem the US company might be able to arrange a currency swap.
Suppose that the company needs to invest SFr13 million and the current spot rat is $1=SFr1.30
 The company could borrow in the US at either a fixed or a floating rate. Let’s suppose that it
borrows by issuing $ 10 million of bonds at a fixed rate.
 It can then arrange a five year currency swap with a specialist bank, in which it agrees to exchange
$ 10 million for SFr13 million at the start of the project.
 In the swap, the US company pays interest on SFr 13 million at either a fixed rate or a floating rate
(perhaps Swiss franc LIBOR).
 In return, the US Company will receive interest payments from the bank on US $ 10 million. Since
the bank has borrowed in the US at fixed rate, it will want to receive dollar interest at a fixed rate.
 The dollars received in the swap can be used for making interest payments on the $ 10 million
dollar bonds.
 The Swiss franc income from the investment can be used to make the payments under the swap
agreement.
 At the end of the swap, after 10 years, the US Company will pay the bank SFr13 million in exchange
for US $10 million.
Market participants are not restricted to swapping new liabilities. In a similar way to interest rate swaps,
parties can also swap existing liabilities to obtain preferred repayment currencies. Another variant on the
currency swap is where parties agree to exchange currencies at some future date at a given exchange rate.
These may be used to cover foreign exchange transaction exposure in much the same way as with a
forward foreign exchange contract.
Question 2:
a)
Manling plc
Manling plc has 14 million of fixed rate loans at an interest rate of 12% per year which are due
to mature in one year. The company’s treasurer believes that interest rates are going to fall,
but does not wish to redeem the loans because large penalties exist for early redemption.
Manling’s bank has offered to arrage an interest rate swap for one year with a company that
has obtained floating rate finance at London interbank offered rate (LIBOR) plus 1-1/8%. The
bank will charge each of the companies an arrangement fee of 20,000 and the proposed terms
of the swap are that Manling will pay LIBOR plus 1-1/2% to the other company and receive from
the company 11-5/8%.
Page 89 of 108
INTEREST RATE SWAPS
Corporate tax is at 35% per year and the arrangement fee is a tax allowable expense. Manling
could issue floating rate debt at LIBOR plus 2% and the other company could issue fixed rate
debt at 11-3/4%. Assume that any tax relief is immediately available.
Required
(i)
Evaluate whether Manling plc would benefit from the interest rate swap:
1. if LIBOR remains at 10% for the whole year.
2. if LIBOR falls to 9% after six months.
(ii)
If LIBOR remains at 10% evaluate whether both companies could benefit from the interest
rate swap if the terms of the swap were altered. Any benefit would be equally shared.
Answer:
Tutorial note: there are two ways in which to evaluate the effect of a swap:
1
Assess the effect on the overall interest rate incurred-not taking account of whether that rate is
fixed or floating.
2
Evaluate the effect on the ability of the company to raise funds with interest rates of a
particular type.
Part (i) of the question focuses on the first effect, part (ii) on the second effect.)
(i)
Evaluation of whether interest rate swap is beneficial
1
LIBOR remains at 10% for whole year
Existing commitment
Fixed rate of
12%
Commitment after the swap
(A)
(B)
Cost of fixed rate loan
Floating rate paid to the other company
10 + 1-1/2
(C)
Rate received from the other company
Net Rate incurred
Saving in interest 14m X (12% - 11-7/8%)
Arrangement fee
Increase in Cost
12%
11-1/2%
(11-5/8%)
11-7/8%
17,500
(20,000)
2,500
Therefore, swap world not be beneficial, although the final cost, after tax, is mitigated to 2,500 (1 – t) =
2,500 (1 – 0.35) = 1,625
(2)
LIBOR falls to 9% after six months Commitment after the swap
First
Six months
(A)
(B)
Cost of fixed rate loan
Floating rate paid to other company
12%
Second
six months
12%
10+1-1/2
11-1/2%
Page 90 of 108
INTEREST RATE SWAPS
(C)
Rate received from other company
9+1-1/2
(11-5/8%)
Net rate incurred
10-1/2%
(11-5/8%)
11.875%
10.875
Saving in interest:
First six months 14m X (0.12 – 0.11875) X 6/12
Second six months 14m X (0.12 – 0.10875) X 6/12
Arrangement fee
Net benefit
8,750
78,750
87,500
(20,000)
67,500
Therefore, swap is beneficial. After tax, the benefit of the swap over the year will equal 67,500 (1- 0.35) –
43,875
Note: there is a timing difference which should be taken into account i.e. the arrangement fee is
presumably payable now whereas the interest saving will accrue in one year.
(ii)
Evaluation of whether both companies can benefit – given LIBOR remains at 10%
Tutorial note:
in this example part (i) asks for a calculation of the final outcome which will depend
on what happens to the floating rate. If LIBOR falls to 9% Manling will benefit from the swap. In (i) the
other effect of the swap is for Manling to obtain funds at LIBOR + 1-7/8 from the other company, i.e. a
saving of (LIBOR + 2)-(LIBOR+1-7/8) = 1/8% on the rate at which it can otherwise obtain floating rate debt.
It is this other effect that has to be considered from the viewpoint of both companies in (b)(ii).
Cost to the other company
1
Cost of floating rate finance 10+1-1/8%
2
Fixed rate interest to Manling
3
Amount received from Manling floating rate of 10+1-1/2
Net cost of fixed rate finance
11-1/8%
11-5/8%
(11-1/2%)
11-1/4%
The other company world otherwise pay 11-3/4% for fixed rat finance, and is thus saving 11-3/4% - 11-1/4%
= ½% under the swap.
Therefore, under the present swap agreement, with LIBOR = 10%, the savings being achieved are:
1.
Manling
1/8%
2.
Other Company 1/2 %
Total saving
5/8%
It is this saving which needs to be shared equally between the two firms.
Shared equally = 5/8 / 2 = 5/16% to each company
At the moment, the other company obtains a 1 / 2 % saving compared to the 5/16% it would obtain if
savings were shared equally. It must therefore give, by way of the interest rates applied to the swap,
3/16% (1/2% - 5/16%)of additional benefit to Manling plc. This would give Manling an equal 1/8% + 3/16%
= 5/16% benefit in comparison to the finance it would otherwise obtain.
Page 91 of 108
INTEREST RATE SWAPS
Thus, the other company should either pay 3/16% more as a fixed interest charged to Manling ( making that
charge 11-5/8% + 3/16% = 11-13/16%,or receive an interest charge of 3/16% less from Manling by way of
floating rate charge – i.e. commit Manling to paying LIBOR + 1-1/2% less 3/16% - i.e. LIBOR + 1-5/16% (115/16% if LIBOR = 10%). In summary the overall finance costs for both companies under both options
become either:
Fixed rate
Floating rate
Floating rate SWAP
Fixed rate SWAP
Manling
11-1/2%
(11-13/16%)
Other company
12%
11-1/8%
(11-1/2%)
11-13/16% (bal fig)
Overall cost:
11-11/16%
11-7/16%
Or:
Manling
12%
Fixed rate
Floating rate
Fixed rate swap
Floating rate swap (bal fig)
Other company
(11-5/8%)
11-5/16%
11-1/8%
11-5/8%
(11-5/16)
11-1/16%
11-7/16%
Overall cost
Thus, the benefit to each company is:
14m X 5/16%
Less: benefit before tax
20,000
43,750
Net benefit before tax
23,750
Net benefit after tax 23,750 X (1- 0.35) =
15,437
Each company could thus benefit by 5/16% compared to its alternative finance options.
_______________________________________________________________________________________
This topic is explained further by the use of an illustrative question.
DATA FOR ILLUSTRATION
Interest rates offered by Bank Limited to two companies are tabulated below:
Fixed Rate
Variable Rate
Lockwood Plc
Thomas Plc
----------------%---------------10
11
KIBOR + 0.3%
KIBOR + 0.5%
Lockwood Plc needs debt of Rs 75 million to finance its new business which is volatile to fair valuation risk.
Whereas Thomas plc requires Rs 75 million of finance to meet the funding requirement of new order, cash
flows of which are fairly stable over next three years.
QUESTION 1 – Which rates should be preferred by the companies?
Page 92 of 108
INTEREST RATE SWAPS
Lockwood plc should accept variable rates because cash flows to be generated by the company are largely
variable as it they are subject to fair valuation risk. Thomas plc should accept fixed rate because its cash
flows are fixed in nature.
QUESTION 2 – Should the company accept swap arrangement if the swap arranger limited offers variable
rate to lock wood plc and fixed rate to Thomas plc?
Decision is based upon two things:
1.
2.
The rates offered to both companies are preferred one.
Please refer the table below:
Option
Rates preferred
Rates not preferred
Lockwood
KIBOR + 0.3%
10
Thomas
11
KIBOR + 0.5%
Total interest
KIBOR + 11.3%
KIBOR + 10.5%
Both companies will only accept the swap if the rate offered by Bank are (total) comparatively expensive. In
other words, the swap arrangement leads to cost saving to both companies which can be mutually shared.
QUESTION 3 – Compute net exposure of the companies after swap arrangement and payments to be
made to each other?
STEP 1 – Workout cost saving gross of commission
Option
Rates preferred
Rates not preferred
Lockwood
KIBOR + 0.3%
10
Thomas
Total interest
11
KIBOR + 11.3% (A)
KIBOR + 0.5%
KIBOR + 10.5% (B)
Saving (A – B) 0.8%
NOTE: ignore commission paid by both parties here
STEP 2 – Workout share of cost saving of both parties
In the absence of any cost saving ratio, assume that savings are shared in equal proportion. i.e. 0.4% by
both parties.
STEP 3 – Workout net exposure of each party
Net exposure is the preferred exposure net of savings and can be computed in the manner mentioned
below:
Lockwood Plc
Prefered exposure had the company not KIBOR + 0.3
entered in swap arrangement
Share of cost saving from swap 0.4
arrangement
Exposure net of cost saving
KIBOR – 0.1
Thomas Plc
11
0.4
10.6%
STEP 4 – Workout net payment/receipt between counterparties
Net payment/receipt is the difference between payment to bank limited and net exposure computed in
Step 3
Page 93 of 108
INTEREST RATE SWAPS
Payment to Bank limited - A
Exposure net of cost saving - B
Lockwood Plc
10
KIBOR – 0.1
Thomas Plc
KIBOR +0.5
10.6%
Net payment between counterparties (A – B)
10.1 – KIBOR
KIBOR – 10.1
Lock wood plc would (vice versa for Thomas plc)
1.
receive 10.1% and
2.
pays KIBOR
STEP 5 – Conclude the swap arrangement
Payment to Bank limited
Lockwood Plc
-10
Thomas Plc
-KIBOR -0.5
Receipt from counterparty
Payment to counterparty
10.1
-KIBOR
KIBOR
–10.1
Payment of commission *
-0.1
-0.1
Net exposure after swap
-KIBOR
-10.7%
* Always assume that respective share of commission is paid directly by each counterparty.
Page 94 of 108
FOREX – HEDGING TOOLS
INTRIST RATE SWAPS
QUESTION USED FOR ILLUSTRATION
Adventurer Ltd. a UK company, is considering a contract to supply telephone system to Blueland Telecom.
All operating cash flows would be in the local currency, the Blue, as follows;
Time from start
0 month
After 6 months
After 12 months
Cashflow (in blue)
(700,000)
(400,000)
1,800,000
Because of high inflation in Blueland, the directors of Adventurer limited are very concerned about the
foreign exchange risk. However, the only available form of cover is a currency swap at a fixed rate of 9 blues
to the pound, for 1,100,000 Blues, to take effect in full at the start of the project and to last for a full year.
The interst rate chargeable on the Blues would be 18% a year. This compares to a UK opportunity cost of
capital for Adventurer Limited of 22%. The swap will involve exchange of interest liabilities as well.
The alternative to the swap is to convert between sterling and Blues at the spot rate, currently 10 Blues to
the pound. The Blue floats freely on world currency markets. Inflation in Blueland and the UK over the year
for which the project will last is forecast to be as follows:
UK %
2
3
4
Blueland %
10
30
70
Probability
0.2
0.3
0.5
Required:
You are required to show whether or not Adventurer Limited should use the available swap. Do not
discount
receipts
and
payments
time.
Page 95 of 108
FOREX – HEDGING TOOLS
INTRIST RATE SWAPS
DATA EXTRACTED FROM THE QUESTION ABOVE
A UK based company establishes a branch in Blue Land, cash flows of would be in blue and have tabulated
below:
Period
0 month
After 6 months
After 12 months
Cashflow (in blue)
(700,000)
(400,000)
1,800,000
Country
Rate of inflation
UK
Blueland
3.3%
46%
Current spot rate is Blues 10 /£1
Step 1 – Calculate the cash flows in pound?
Period
Exchange rate
Cashflow
A*
In Blue – B
0 month
10
After 6 months
10 x (1.46/1.033)
11.89
6/12
After 12 months
10 x (1.46/1.033)
14.13
12/12
In Pounds (B / A)
(700,000)
(70,000)
=
(400,000)
(33,642)
=
1,800,000
127,389
Net cash flow in Pounds
23,747
* Exchange Rate 10 is blue / pound, thus rate of inflation would also be in inflation in Blue land / inflation in
UK
Step 2 – The company obtains are loan of £ 122,222 from a bank a rate of 10% per annum. Further, it has
entered into a currency swap thereby obtains a loan of 1,100,000 in blues at a rate of 18% per annum?
Compute net cash flow in pounds?
(Effective exchange rate of Blues 10 /£1)
PERIOD
CASHFLOW – In Blues
Opening
0 month
After 6 months
After 12 months
Inflow
-
1,100,000
500,000
-
1,800,000
Outflow
Closing
(700,000)
500,000 *
(400,000)
-
(1,298,000) *
502,000
* The company may earn short term return by investing the surplus cash.
** 1,100,000 x 18% = 198,000 + 1,100,000 = 1,298,000
Page 96 of 108
FOREX – HEDGING TOOLS
INTRIST RATE SWAPS
PERIOD
CASHFLOW – IN POUNDS
Opening
Inflow
0 month
-
After 6 months
-
After 12 months
-
122,222 *
Outflow
Closing
(122,222)
-
502,000/14.13
= 35,527
-
35,527
* The interest payment and along with principal repayment shall be paid by counterparty of the swap
arrangement, the company shall pay interest and principal of loan in blues.
INTEREST RATES FUTURES
Calculate rate of interest on short term interest futures of 96.40? (Par value of 100)
Market interest rate would be = 100 – 96.40 = 3.6%
NOTE: Short term interest futures are quoted at discount to par value
Calculate rate of interest on 9% long term interest futures of 118? (Par value of 100)
I = 100 x 9% = 9
Kd = I / MV = 9 / 118 = 7.6%
Page 97 of 108
MERGERS AND ACQUISITIONS
GENERAL RULES
The topic covers the following three aspects;
 Valuation of the target company
 Determining the share exchange ratio after taking into account the synergies
 Assessing the effect on the share prices of the target and predator companies upon announcement
of merger / acquisition
VALUATION OF TARGET COMPANY
The valuation of the target company may be required due to certain planned restructurings using or more
of the following methods;





P/E multiples
Dividend valuation models
Free cash flows model
Berliner method
Super profits (dual capitalization) method
While calculating the value of the target company using the free cash flows method, the discount rate
should reflect the systematic risk of the target company’s industry. The cash flows of the target company
will be discounted using the WACC of the target company, after taking into account any post-merger
changes in the equity beta or the gearing levels.
DETERMINING THE SHARE EXCHANGE RATIO
The share exchange ratio will be calculated using the post-merger values of the predator and the target
companies, depending upon the manner in which the two companies have decided to share the benefits of
synergies. The predator company, at the maximum, can give all the benefit of synergies to the shareholders
of the target company.
The shareholders of the target company will only accept the bid, if the value of the bid is at premium over
the current share price. Further, the shareholders of the predator are likely to welcome the bid, if it
increases the value of their shares, which will only occur if some of the benefit of synergies accrues to the
predator company.
EFFECTS ON THE SHARE PRICES OF THE TARGET AND PREDATOR COMPANIES
The share price of the predator company will move to reflect the impact of synergies / restructuring costs.
The share price of the target company will move to reflect the share exchange ratio.
Page 98 of 108
MERGERS AND ACQUISITIONS
ILLUSTRATIVE EXAMPLE OF ABOVE
DATA USED FOR ILLUSTRATIONS BELOW
Prodco Ltd is contemplating a bid for the share capital of Nordik Ltd. The following statistics are available:
Prodco Ltd Nordik Ltd
Number of shares
Share price
Latest equity earnings
14 million
Rs. 8.40
Rs. 11,850,000
45 million
Rs. 1.66
Rs. 9,337,500
Prodco Ltd's plan is to reduce the scale of Nordik Ltd's operations by selling off a division which accounts for
Rs. 1,500,000 of Nordik Ltd's latest earnings, as indicated above. The estimated selling price for the division
is Rs. 10.2 million.
Earnings in Nordik Ltd's remaining operations could be increased by an estimated 20% on a permanent
basis by the introduction of better management and financial controls.
Prodco Ltd does not anticipate any alteration to Nordik Ltd's price / earnings multiple as a result of these
improvements in earnings.
To avoid duplication, some of Prodco Ltd's own property could be disposed of at an estimated price of
Rs.16 million. Redundancy costs are estimated at Rs. 4.5 million.
Page 99 of 108
MERGERS AND ACQUISITIONS
ILLUSTRATIVE EXAMPLE OF ABOVE
Page 100 of 108
MERGERS AND ACQUISITIONS
ILLUSTRATIVE EXAMPLE OF ABOVE
Case 1
Calculate the effect on the current share price of each company, all other things being equal, of a tw o for nine share offer by Prodco Limited.
Calculation procedure
Compute price earning ratio
Prodco Ltd
Number of shares
Share price
Latest equity earnings
Earnings per share
Price earning ratio
Nordik Ltd
14,000,000
8.50
11,850,000
0.85
10.04
45,000,000
1.66
9,337,500
0.21
8.00
A
B
C
D = C/A
E = B/D
Compute the restructuring benefits
Assets sold - Prodco
Redundancy cost - Prodco
Sale proceeds - Nordik
16,000,000
(4,500,000)
10,200,000
Total restructuring benefits
21,700,000
Compute the value of the merged company
Valuation of Nordik Limited
Existing earnings
Less: closing of division
Revised earnings
Increase in earning
Revised increased earning
9,337,500
(1,500,000)
7,837,500
20%
9,405,000
F
Revised value
75,240,000
FxE
Valuation of Prodco Limited
Existing value
119,000,000
130,500,000
Value of merged company
Value of Nordik
Value of Prodco
Restructuring benefits
75,240,000
119,000,000
21,700,000
Total value
215,940,000
G
Compute the number of shares to be issued by Prodco
Number of share of Nordik
Sw ap ratio
Number of share to be issued
45,000,000
2/9
10,000,000
H
Compute the share price of Prodco (Predator) after the merger
Total value of merged company
Existing number of shares
Number of shares issued
Revised num ber of shares
215,940,000
G
The share price of the predator w ould reflect the impact of synergies
/ restructuring costs
14,000,000 Of Prodco
10,000,000
H
24,000,000
I
Price per share
9.00
J = G/I
Compute the share price of Nordik (Target) after the merger
Value of Prodco
Sw ap ratio
Value of Nordik
9.00
J
2.00
J * 2/9
2/9
The share price of the target compnay w ould move to reflect the
sw ap ratio
Alternative method
Total value of merged company
Existing number of shares
Number of shares if all issued
by the target company
Revised total shares
Value of share
215,940,000
G
45,000,000
63,000,000 14M /2 *9
108,000,000
K
2.00
G/K
Page 101 of 108
MERGERS AND ACQUISITIONS
ILLUSTRATIVE EXAMPLE OF ABOVE
Case 2
Calculating the sw ap ratios
Case 2a - Gain or benefit of the m erger given as percentage of share price
Calculate the sw ap ratio if Prodco w ishes to give Nordik Ltd shareholders a 10%
gain on the existing value of their shares.
Calculation procedure
Existing share price
Rs
1.66
Increase in share price given
10%
Revised share price
Rs
1.83
Computing the swap ratio
Total value of merged company
Revised share price
215,940,000
Rs
1.83
A
B
Total number of shares required
Existing number of shares
New shares required to be issued
118,258,488
45,000,000
73,258,488
C = A/B
D
E = C-D
New shares to be issued against
(Shares of Prodco Limited)
14,000,000
sw ap ratio
5.23
F
E/F
Therefore, 1 for 5 shares is the sw ap ratio
Case 2b - Gain or benefit of the m erger given as am ount of benefit to be shared
Calculate the sw ap ratio if Prodco w ishes to give Nordik Ltd shareholders 50% of the
synergical benefit to Nordik Limited
Calculation procedure
Restructuring benefits
21,700,000
50% of the benefits
10,850,000
Revised value of Company
Nordik Ltd
Existing value
Share of restructuring benefits
Revised value of the com pany
74,700,000
10,850,000
85,550,000
Original number of shares
45,000,000
Revised share price
Rs
1.90
Prodco Ltd
119,000,000 Existing earnings x PE ratio
10,850,000
129,850,000
A
14,000,000
Rs
9.28
B
C = A/B
Value of merged company
215,940,000
215,940,000
D
Revised number of shares required
Existing number of shares
New shares required to be issued
113,586,207
45,000,000
68,586,207
23,281,941
14,000,000
9,281,941
E = D/C
F
G = E- F
14,000,000
45,000,000
H
4.90
4.85
New shares to be issued against
Sw ap ratio
G/H or H/G
Therefore, in both cases sw ap ratio is 5 for 1 share
Page 102 of 108
MERGERS AND ACQUISITIONS
PROCEDURE FOR QUESTION SUMMARISED
CASE I – COMPUTATION OF POST ACQUISITION SHARE PRICE FOR A GIVEN SWAP RATIO
 Calculate the value of the merged company being the sum of the existing value of both the companies
and the synergical benefits.
 Calculate the revised number of shares of the issuing company, being the sum of existing number of
shares and new number of shares computed using the swap ratio on the target company.
 Calculate the share price of the share issuing company by dividing the value of the merged company by
the revised number of shares.
 Use swap ratio to compute the share price of the acquired company.
CASE 2 – COMPUTATION OF SWAP RATIO
 Calculate the total value of the merged company being the sum of the existing value of
both the companies and the synergical benefits.
 CASE 2A – SHARING IS GIVEN AS A PERCENTAGE INCREASE IN THE SHARE PRICE OF
THE ACQUIRED COMPANY
 Compute the existing share price of the acquired company.
 Increase it by the factor of increase given.
 Use the revised price for further computation.
 CASE 2B – SHARING OF BENEFITS IS GIVEN IN AMOUNT TERMS
 Compute the revised value of the company i.e. the sum of the existing value and the share of
synergical benefits attributable to the company.
 Compute the revised share price of the existing number of shares by dividing the revised value of
the company by the existing number of shares.
 Use the revised price for further computation.
 Calculate the number of shares required to be issued against the existing shares of the
acquired company using the following formula;
 Calculate the swap ratio by using the value of the ‘x’ computed above. (Divide the larger number of
shares with the smaller number of shares.)
Page 103 of 108
RIGHT ISSUES AND THEORATICAL EX-RIGHT PRICE COMPUTATION
RIGHT ISSUE
Raising of a new capital by giving existing shareholders the right to subscribe to new shares in proportion to
their current holdings. These shares are usually issued at a discount to the market price.
ISSUE PRICE
Theoretically, there is no upper limit to an issue price but practically, it would never be set higher than the
prevailing market price of the shares, otherwise shareholders will not be prepared to buy as they have
purchased more shares at the existing market price anyway. Similarly, there is no lower limit to an issue
price theoretically, but in practice it can never be lower than the nominal value of the shares.
UNDERWRITING
Underwriting avoids the possibility that the entity will not sell all of the shares it is issuing, and so receive
less funds than it expects. The underwriting costs can potentially be avoided through deep discounted right
issue. In such and issue, the issue price is set at a large discount to the current market price so reducing the
possibility of shareholders not taking up their rights.
SELECTION OF AN ISSUE QUANTITY
Normally the issue price is decided first, and the issue quantity later. The effect of the additional shares on
the earnings per share and dividend cover needs to be considered.
TERMS OF AN ISSUE
Once the issue price and the quantity of the issue has been set, the terms of the issue (1 for every 4 shares
held) can be calculated.
THEORATICAL EX-RIGHTS PRICE (TERP)
Value of right
The value of a right is the theoretical gain a shareholder can make from taking up their rights. The value of a
right will be the difference between the theoretical ex-rights price and the issue price of the shares. If a
shareholder decides not to take up the rights to a rights issue, the rights may be sold to another investor.
Computing TERP
Case 1 – Funds from the right issue earn at the existing rate of return
This is the normal case and same as addressed in IAS 33 – Earnings per Share. The formula for computation
of TERP in such a case is as follows;
Where,
– Pre-issue share price
– New-issue price
– Number of old shares
– Number of new shares
- Total number of shares
Page 104 of 108
RIGHT ISSUES AND THEORATICAL EX-RIGHT PRICE COMPUTATION
Case 2 – Funds from the right issue earn at rate different from the existing return
In such a case a yield adjusted TERP needs to be calculated. Formula for the same is as follows;
Where,
– Pre-issue share price
– New-issue price
– Yield on ‘old’ shares
– Number of old shares
– Number of new shares
- Total number of shares
-Yield on ‘new’ capital
Where the new funds are expected to earn a return above the rate generated by existing funds, there will
be less dilution of the market price than suggested by the original TERP calculation.
Page 105 of 108
RIGHT ISSUES AND THEORATICAL EX-RIGHT PRICE COMPUTATION
ILLUSTRATION OF THE ABOVE
DATA BEING USED
Molson Plc has a paid-up ordinary share capital of Rs.2,000,000 represented by 4m shares of Rs.0.50 each.
Earnings after tax in the most recent year were Rs.750,000 of which Rs.250,000 was distributed as dividend.
The current price / earnings ratio of these shares, as reported in the financial press, is 8.
The entity is planning a major investment that will cost Rs.2,025,000 and is expected to produce additional
after tax earnings over the foreseeable future at the rate of 15% on the amount invested.
The necessary finance is to be raised by a rights issue to the existing shareholders at price 25% below the
current market price of the entity’s shares.
Requirements;
i.
Current market price of the shares already in issue;
ii.
The price at which the rights issue will be made;
iii.
The number of new shares that will be issued;
iv.
The price at which the shares of the entity should theoretically be quoted on completion of the
rights issue (i.e. ex-rights price), ignoring incidental costs and assuming that the market accepts the
entity’s forecast of incremental earnings.
SOLUTION
Requirement I – current market price of the shares
Market price per share = P/E ratio x Earnings per share
8 x 0.19
PKR
1.52
Current year earnings
Number of shares
Earnings per share
750,000
4,000,000
PKR
0.19
A
B
A/B
Requirement II – Price at which right issue will be made
Current market price x 75%
Rs.1.52 x 75% = Rs.1.125
Requirement III – Number of new shares that will be issued
Investment requirements / Price at which right issue is to be made = Number of new shares
Rs.2.025M / Rs.1.125 = 1.8M shares
Requirement IV – TERP
= Rs.1.453 per share
Note – the price / earnings ratio is given as 8. This would imply an earnings yield of (1/8) = 12.5%. this is
assumed to be the yield or rate of return on existing funds.
Page 106 of 108
FOREIGN CURRENCY SWAPS
Page 107 of 108
PRUDENTIAL REGULATIONS
PROVISIONING OF NON-PERFORMING LOANS AND ADVANCES
SPECIFIC PROVISIONING
General formula
Prov = (A - B) * C
Where,
A = Amount of the Loan
B = Benefit allow ed as per rules
C = Relevant rate
Determination of Benefit (COM PONENT B)
A)
Liquid Security
Benefit of liquid security can be taken for any loans of any class and category. Liquid Security generally include:
1
2
3
B)
Pledge of shares and certificates (listed shares only)
Lien over deposit accounts
LC margins, etc
Forced Sale Value - Property m ortgaged - Im m ovable property
1) Consumer Loans
Available only in case of house loans
for residential property
@ 30% of FSV
Available for 3 years
No restriction on the date of Valuation report
2) Corporate Loans
Available for :
a) Residential property
b) Commercial property
C)
@ 30% of FSV
Available for 3 years
Valuation date w ithin 1 year of classification
Forced Sale Value - Pledged property - Movable property
1) Consumer Loans
No provision
2) Corporate Loans
Available for :
a) Residential property
b) Commercial property
@ 30% of FSV
Available till under pledge.
Valuation done by Mucaddam on Closing Date
Under possession of bank's mucaddam
Determination of rate (COM PONENT C)
No. of
Provision % age Required
days from
Corporate
Consumer
due date Laon facilities
Bills
Secured
Unsecured
90
25%
0%
25%
25%
180
50%
100%
50%
100%
1 year
Classification of loans
Provided @ 25%
Provided @ 50%
Provided @ 100%
100% Provided
100% Provided
Sub-Standard
Doubtful
Loss
Page 108 of 108