Tutorial Suggested Answers

Topic 1: Overview of Financial Management (Chapter 1)

Non-text Question 1.1

Explain why is that the assumed objective of the firm for finance is to maximise shareholder wealth.

Answer:

• practical, a single objective leads to clearer decisions;

• the contractual theory;

• survival in a competitive world;

• it is better for society;

• counters the tendency of managers to pursue goals for their own benefit;

• they own the firm.

Non-text Question 1.2

Explain the link between managerialism and the agency problem.

Answer:

Large corporations usually have a separation of ownership and control. This may lead to managerialism where the agent (the managers) takes decisions primarily with their         interests in mind rather than those of the principals (the shareholders).

This is a principal–agent problem.

Non-text Question 1.3

Suggest some solutions to mitigate the agency problem.

Answer:

There are a number of ways of seeking to optimise managerial behaviour in order to encourage  goal  congruence  between  shareholders  and  managers.  One  way  is  for shareholders to monitor the actions of managers. There are several potential monitoring devices that could be used, but they will all incur costs in terms of both time and money. These devices include:

• independently audited accounting statements;

• government regulation; the legal system;

• cash dividends;

• reputation;

The costs of monitoring must be weighed against the benefits accruing from a decrease in suboptimal managerial behaviour.

Alternatively, shareholders can try and incorporate clauses into managerial contracts which are intended to reduce the agency problem and encourage goal congruence. Such clauses may formalise constraints, incentives and punishments. In this way, agency costs are reduced. An optimal contract is one which minimises agency costs, while reflecting the needs of individual companies. For example, if monitoring is difficult or costly, the

contract could include bonuses for good performance.

It is also possible to discuss here the following points:

• the right of shareholders to appoint and remove directors;

• incentives (performance-related pay, share options, etc.);

• the right of shareholders to sell their shares in the capital markets;

• competition in the market for managerial control.

Non-Text Question 1.4 - Financial decisions and the goal of the firm

Three types of financial decisions are – the investment decision, the financing decision and the dividend decision.   Describe each in detail, and explain how these decisions relate to the corporate objective.

A N S W E R

The investment decision relates to the manner in which funds raised in capital markets are employed in productive activities. The objective of such investments is to generate future cash flows, thus providing a ‘return’ to investors.  The capital budgeting or project evaluation function is the process by which the investment decision is undertaken. Maximising the future cash flows generated will maximise the value of the firm and the wealth of owners.

The financing decision relates to the mix of funding obtained from capital markets; that is, the mix of debt and equity issued by the firm to  fund its operations. Obtaining the most appropriate sources of finance, taking into account the cost of finance and the risk, will maximise the value of the firm and therefore the wealth of owners.

The dividend decision relates to the form in which the returns generated by the firm are passed on to equity holders. There is a substantial body of theory that indicates that an appropriate dividend policy can also maximise firm value and owner wealth.

Topic 1 Time Value of Money (Chapter 5)

Non-Text Questions

1.1

Joe bought a house for $208,000 and sold it for $256,000 4 years later. What is his annual return in percent?

208,000 ( 1 + r)^4  = 256,000                        r = 0.0533

r = (FV/PV) ^ 1/n]  – 1 = (256/208) ^ 1/4]  – 1 = 0.0533 (5.33% pa)

1.2

a.   The rate of interest is 0.6667% per month. What is the nominal rate?   Simple/nominal interest rate p.a. = m x r  = 12 x 0.6667%  = 8.0% p.a.

c.   What is the Effective interest rate?

Answer  = (1 + r)m – 1  = (1 + 0.006667)12 – 1  = 8.3004%

m = number of compounding period a year.

1.3

What is the Effective return for continuous discounting where interest is earned over a year and the rate of 6% pa?  e = 2.7182

Answer  = e r x t – 1 = e0.06 x 1 – 1  = 6. 1837%

1.4

You receive $1,000 every year for 13 years except for years 3 and 5. What is the present value of the receipts? Discount rate = 11%.

Full Annuity:   CALC:  n = 13   r = 11%   PV = ?   PMT = $1,000   FV = 0 PV = - $6,749.87

Subtracting PV of missing PMT:   PV = $6,749.87 - $1,000 / (1 + 0. 11)3 - $1,000 / (1 + 0. 11)5

PV = $6,749.87 - $731.19 - $593.45 = $5,425.23

1.5. John House has taken a 20-year, $250,000 mortgage on his house at an interest rate of 6% per year. What is the value of the mortgage after the payment of the fifth annual  installment?

Hint: a loan repayment involves an annuity. So the annuity formula is used. Here, we need to find the pv of the loan as at t=5, ie 15 more years to go. But we do not know the pmt. So, we make use of the original loan amount with t=20 to find pmt first. This is step 1. Then we          substitute the found pmt into the same equation but now t=15. This is step 2.

Answer: Step 1:   I = 6%; N = 20;  PV = 250,000;  FV  = 0 ;  Compute PMT = 21,796. 14 Step 2:   I = 6%; N = 15 ;  PMT = 21,796. 14;  Compute   PV  = 211,689. 53

1.6 Mr. Hopper is expected to retire in 30 years and he wishes accumulate $1,000,000 (FV)  in his retirement fund by that time.  If the interest rate is 12% per year, how much should Mr. Hopper    put into the retirement fund each year in order to achieve this goal?

Response: Future value annuity factor = [(1. 12^30 - 1]/(0. 12) = 241.3327; payment = 1,000,000/241.3327 = 4143. 66

(1+ r)n −1

FV         = PMT                                                             PMT = 4143. 66 per year

r

1.7    A deposit of $1300 earns $339.45 interest in 3 years. Interest is compounded monthly at 0.6465% per month. What is the effective rate (per year)?

Effective rate = (1 + 0.006465)^12 – 1 = 0.0804= 8.04% pa

1.8       9% (nominal rate) compounded quarterly is equivalent to what effective rate?

Effective rate = (1 + [0.09/4])^4 – 1 = 0.0931 = 9.31% pa

1.9       A customer deposits $1,000 in a savings account earning 6% per annum. The

value of the account in one year if the bank uses daily compounding will be _______. ANS = $1000 x [ 1 + 0.06/365]^365 =  $1,061.83

1.10 Find the discount factor (DF) for an interest rate of 9% and 10 periods.

ANS =  1 / [1.09]^10 = 0.4224

1.11 The one-year discount factor is 0.905, and the two-year interest rate is 10.5%. What is the two-year annuity factor?

ANS =  0.905 + 1/ [1. 105^2] = 1.724

1.12 The three-year annuity factor is 2.6243. The four-year annuity factor is 3.3872. What is the four-year discount factor?

ANS = 3.3872 – 2.6243 = 0.7629

1.13  You deposited $100 in a bank that pays interest at 5 percent per annum. How much interest would you have earned in the seventh year?

ANS = FV at year 7 – FV at year 6 = $140.71 – $134.01 = $6.70

1.14 AA Autos is selling a car for $100,000. It suggests that you pay a $15,000 deposit now, followed by payments of $4,000 per month for 25 months. What is the present value of the total interests are you paying AA Autos?

Ans = $15,000

Topic 2: Stock and Bond Valuation (Chapters 6 and 7)

Bond Valuation

Non – text question 2. 1

A bond has par value $1,000, semi-annual payments, has 13 years to maturity , yields 7.8% p.a. and priced at $1,140.60 today.

What is the coupon rate?

n = 13 x 2 = 26   r = 7.8% / 2 = 3.9%   PV= Price == $1,140.60

PMT = ?   FV = $1,000 PMT = $47.70 per period

Since coupon interest = coupon rate x par value

Coupon Rate pa = Coupon interest pa / Par = 47.70 x 2 / 1,000 = 9.54%

Non – text question 2.2

Acetate Inc. issued a $10,000 bond at the coupon rate of 8% payable annually. Now, the bond has a remaining life of 25 years’ time.

(a) Five years later, you bought Acer’s bond when the market interest rate for a new Acer bond is 12%. How much did you pay?

PV = Bond price = PMT { [ 1 – ( 1 + i )-n ] / i } + Par / (1 + i) ^ n PMT=800; n=20; Par=10,000; I=12. PV= ?

Your purchase price was $7,012.22

(b) 6 years after your bond purchase, interest rates (for bonds of similar risk as Acer’s bonds) fell to 6%. What is the value of the bond?

PMT=800; Par=10,000; I=6.; n=14 . PV=?

The value of the bond is $11,859.00

Non – text question 2.3 (zero coupon Bonds)

A ZCB has par value $1,000, based on annual discounting, has 5 years to maturity , and priced at $790.09 today. What is the yield?

790.09 (1 + r) ^ 5 = 1000 ➔ r = 0.0482 (4.82% pa)

Share Valuation Non-Text Question 2.4

Pegasus Holidays plc has the following earnings and dividends for the last three years:

Year Profit after taxation (£)  Dividend per share (pence)

2009 4,800,000

2008 5,629,000

2007 3,080,000

16p

18.8p

14.4p

The nominal value of an ordinary share is 50p each. Five years ago the company gained its Full Listing on the London Stock Exchange and 15 million shares were issued at that time. From 2008 the total number of ordinary shares in issue has been 21m. The market capitalisation of Pegasus Holidays is currently £31,080,000.

Mkt cap = no. of shares x share price

Pegasus Holidays’ after tax profit is expected to rise by 6% each year for the next four      years and 5% thereafter. The equity cost of capital has been estimated to be 14% per year. Dividends are assumed to grow at the same rate as profits.

Required:

(i) Using the dividend  valuation model (DDM) , determine whether the shares of Pegasus Holidays are currently undervalued.  Show your calculations

(ii) Briefly discuss whether the dividend valuation model should be relied upon to indicate the value of a company share.  Suggest alternatives that could be used.

ANSWER  - Use the supernormal growth model

(i)  From now to  year 4 (note D0=16p)

YR Growth     Div per share  14% DR          PV

1    6%             16.96p             0.877               14.87

2    6%             17.98p             0.769               13.83

3    6%             19.06p             0.695               12.87

4    6%            20.20p             0.592 11.95

53.52p

D5= D4 x 1.05

PV of P4 = 20.20 x 1.05 x 0.592      = 21.21 x  0.592   = 139.5p

0.14 - 0.05                           0.09

Based on the  dividend valuation model, company’s shares should be valued : [PVs of D1 to D4] + PV of P4 = 53.52p + 139.5p = 193p (Target price)

Current market price is 31,080,000 21,000,000

= 148p     (lower than the fair value of 193p)

Thus, based on the dividend valuation model, Pegasus’ shares are currently undervalued.

(ii)

•  Consider the  assumptions of the model used like constant Ke and growth rate. Are these valid?  Ke = Re

The DDM (no growth) gives Value = D1/ Ke

The DDM (constant growth) gives Value = Di/( Ke – g)

Ke is not constant. Ke changes with the level of debt. Students to discuss proposition II of MM’s perfect market view and imperfect market  view of capital structure.

Growth rate is also not constant. Students to discuss periods of supernormal growth where growth rate can exceed Ke.

•    Does the model capture the market worth of quoted companies like those which pay little or no dividends?

No, the DDM does not capture the value of these quoted companies.

Since these are quoted firms, it is more relevant to use relative valuation methods like the price-earnings approach, the price-book approach, the dividend yield approach or the       earnings yield approach.

Alternative Share Valuation approaches based on comparative analysis

1.   Price-Earnings Ratio approach – to describe the approach and the advantage over       DDM, being useful for firms that do not pay dividends. To provide examples (tech-based firms).

2.   Price-Book  Ratio approach – to describe the approach and the advantage over DDM, being useful for capital-intensive firms. To provide examples (shipbuilders, car-makers).

3.   Multiple over cash flow approach – to describe the approach and the advantage over DDM, being useful for firms with high level of cash sales. To provide examples             (supermarkets, fast food chains).

Topic 3: Working Capital Management (Textbook Chapters 19 and 20)

Non-Text Questions: Credit policy and cash discounts

3.1 (Cash discount)

A firm intends to offer a 1.5% discount to customers who pay within 30 days of the sale of the product. It is expected that 40% of customers will take up the offer. The rest of the customers will continue to pay within 45 days. The expected level of sales is $15 million.

The earlier payment will decrease bad debts from $160,000 to $100,000 per year, and administration costs by half from $30,000 per year. The bank overdraft rate is 9% pa.

Make a recommendation if the firm should proceed with the cash discount.

This benefit is so small that it is unlikely it can be justified. Further investigation of likely costs and benefits is called for.

Source: Adaptedfrom Watson and Head, 2009, Corporate Finance: Principles and Practice, 5th edition, FT/Prentice Hall.

Non-text Question 3.2 - Credit period extension

Microbiotics currently sells all of its frozen dinner cash on delivery but believes it can increase sales by offering supermarkets 1 month of free credit. The prices per carton is $50, and the cost per carton is $40.

a.        If unit sales will increase from 1,000 cartons to 1,060 per month, should the firm offer the credit? The interest rate is 1 percent per month (simple interest), and all customers will pay their bills.  Interest rate per year = 1% x 12 = 12%.

Contribution  = (Selling price – cost)/selling price)

= (50 – 40)/50 = 0.20 (20%)

Increase in contribution = (1060 – 1000) x $50 x 12 x 0.2 = $7,200 p.a

Projected debtors

= Annual credit sales x debtor period / 12 = 1,060 x 50 x 12 x 1 / 12 = $53,000 Current debtors = 0

Cost of additional debtors = $53,000 x 0.12 = $6,360 p.a

Net benefit = $7,200 – 6,360 = $840 per year (offer the credit)

b.       What if the interest rate is 1.5 percent per month?

Interest rate per year = 1.5% x 12 = 18%.

Cost of additional debtors = $53,000 x 0.18 = $9,540 p.a.

Net benefit = $7,200 - $9,540 = ($2,340) per year (do not offer the credit)

Source: Brealey, Myers and Marcus (2007), Fundamentals of Corporate Finance

Non-Text Question 3.3

Describe the three elements of the working capital cycle.

Describe management techniques that can be used to influence the different components of the working capital cycle.

Comment on whether or not techniques to manage changes to the elements of the cycle will necessarily be for the overall corporate good.

Answer

No single item (debtors, creditors and stocks) can be adjusted without repercussions and without affecting other parts of the working capital.

The minimisation of the debtors’ period should, take into account the potential detrimental side effects of some of the minimisation tactics. Adjustments to debtors will require the firm to think about the effects on the behavior of the clients, whether they will buy lesser or not buy at all. There is always a potential conflict of interest between the collection department  and the  sales  department. Example,  decreasing  debtors through  discounts would lead to a loss in profits as sales decrease. Good collection policy balances conflicting goals. The company wants cordial relations with its customers. It also wants them to pay their bills on time.

Next, trade credit represents temporary borrowing from suppliers until invoices are paid, thereby becoming an important method of financing. Firms may be tempted to view trade creditors as a cheap source of finance, especially when it is interest-free. Having a debtors collection period shorter than the trade collection period, may be taken as a sign of efficient working capital management. However, trade credit is not free. The loss of valuable cash discounts is the penalty for delaying payments to suppliers. Further too long a creditor period frustrates suppliers to the extent that stocks received may be of an inferiority quality and/ or delayed.

So, for the creditors’ period the focus will be on managing to maximise rather than minimise the period. Examples of detrimental side effects for reduction of the creditors’ period, for example, could be that suppliers start missing supply deadlines, sending poorer quality products or taking less care in their actions concerning the manufacture and supply of the quantities and types of the products required. There will be negative feedback from your production department.

Lastly,  the  minimisation  of the  stock  period  should  take  into  account  the  potential detrimental  side  effects.  Too  low  a  level  may  results  in  stockouts  and  customer dissatisfaction. Too high results in funds tied up as inventory. Adjustment / reduction of inventory requires the production efficiency to increase  inventory through increase usage of equipment and hiring of more workers.

Working capital adjustments must be dealt with holistically and firms should consider the non –monetary factors as well. Often, these factors, including relationships with customers, suppliers and its staff, could be adverse in achieving the intended outcomes from the optimising techniques described above.

Topic 4: Portfolio Theory: Risk and Return

Textbook Chapter s 11 and 12

Non-Text Questions 4.1

a.Find the expected return for each project.

Project A’s Expected return = (0.3 × 0.27) + (0.4 × 0. 18) + (0.3 × 0.05)

= 0.081 + 0.072 + 0.015 = 0.168 i.e. 16.8%

Project B

Expected return = (0.3 × 0.35) + (0.4 × 0. 15) + (0.3 × 0.20)

= 0.105 + 0.06 + 0.06 = 0.225 i.e. 22.5%

a.      Find the proportion of funds in each project to achieve an expected portfolio return of 20%.

Hence, 44% of the portfolio should be invested in Project A and 56% in Project B.

(c) Calculate the correlation coefficient between projects A and B.

Correlation coefficient = Covariance Between A and B / [Std D. of A x Std D of B]

First find the Standard Deviations

n

i=1

Then find the covariance:

N

Cov(X, Y ) = pn (xn −x )(yn − y )

n =1

d) Find the portfolio risk.

p  = (W2x).(x)2  + (W2y).(y)2  +  2.Wx.Wy.x.y. x,y

where covariance = 43.50

Non-Text Question 4.2

Non-Text Question 4.3

Sales Ltd is an unquoted company that operates four divisions, all focused on single activities as shown in the table below.  Sale identifies a proxy quoted company for each

activity in order to calculate cut-off rates for new investment.

Division Proxy Beta Assets employed ($m)

C

E

R

P

Total

0.7

1.1

0.8

0.6

3

8

4

5

20

The risk free rate is 7% and the market risk premium is 8%.