FINANCE 251 Practice Exam Questions #2

1.    Suppose you win $10 million in a lottery. You have a choice of how you will receive your  winnings. The first choice is to receive a certain lump sum today. The second choice is to receive a certain amount at the end of five years. Describe how you will evaluate your choices to make your decision?

In order to make the correct choice, one has to make the comparison on the same plane. That is, you calculate the future value of the lump sum invested today at your opportunity cost and compare it to the future value under your second choice. Or you discount the future value of the amount in your second choice to its present value and compare it to the lump sum in your first choice. Either of the two approaches would allow you to select the choice that provides you the highest amount.

2.    Calculate both the Payback Period and Discounted Payback Period for the following project cash flows.

Year                         0               1                  2                  3               4              5

Discounted CF                      –5,000 1,363.64   1,239.67    1,126.97   1,024.52 931.38

Cumulative discounted CF –5,000 –3,636.36 –2,396.69 –1,269.72 –245.20   686.18

The payback period is three years plus 500/1500 = 13 of the fourth year’s cash flow, or 3.33 years.

The discounted payback period is between four and five years. The discounted payback period is four years plus 245.20/931.38 = 0.26 of the fifth year’s discounted cash flow, or 4.26 years.

3.    An investment of $100 generates after-tax cash flows of $40 in Year 1, $80 in Year 2, and

$120 in Year 3. The required rate of return is 20 percent. The net present value is closest to:

 1.202+1201.203=$58.33

4.   An investment of $20,000 will create a perpetual after-tax cash flow of $2,000. The required rate of return is 8 percent. What is the investment’s profitability index?

ThepresentvalueoffuturecashflowsisPV=2,0000.08=25,000TheprofitabilityindexisPI=PVInvestment=25 ,00020,000=1.25ThepresentvalueoffuturecashflowsisPV=2,0000.08=25,000

The profitability index is PI=PVInvestment = 25,00020,000 = 1.25

5.    Explain two circumstances under which the NPV and IRR could provide different decisions.

The IRR and NPV methods can produce different accept/reject decisions if a project either has

unconventional cash flows or the projects are mutually exclusive. Unconventional cash flows could follow several different patterns. It could be a positive initial cash flow followed by negative future cash flows, or both positive and negative cash flows, or, a cash flow stream that looks similar to a  conventional cash flow stream except for a final negative cash flow.

When you are comparing two mutually exclusive projects, the NPVs of the two projects will equal

each other at a certain discount rate. This point at which the NPVs intersect is called the crossover    point. Depending on whether the required rate of return is above or below this cross-over point, the ranking of the projects will be different. While it is easy to identify the superior project based on the

NPV, one cannot do so based on the IRR. Thus, ranking conflicts can arise.

A second situation involves comparison of projects with different costs. While IRR gives you a return based on the dollar invested, it does not recognise the difference in the size of the investments. NPV does!

6.    Why is depreciation and amortisation added back when calculating free cash flows generated by a project?

Depreciation and amortisation is a non-cash expense. Since we are interested in the cash flow

produced by a project or a company, then that means that the general income statement approach    to calculating profitability has "over" deducted the expenses from a cash perspective. Since this over- deduction helps to reduce the company's tax bill, it becomes necessary to add back the non-cash

expenses after taxes have been deducted from the income stream.

7.    A firm has a beta of 1.50, the annual risk-free rate of interest is currently 4%p.a., and the

required return on the market portfolio is 11%p.a. The firm estimates that its future

dividends will continue to increase at an annual compound rate consistent with that

experienced over the 2011-2014 Assume that today is the last business day in 2014 and the firm has just paid the $3.40 dividend

Year

Dividend

Estimate the value of one of the firm’s shares.

rs = 0.04 + 1.5(0.11 - 0.04) = 0.145            = 14.5%

growth rate of dividends = ($3.40/$2.70)1/3  - 1 =  8%

Po = $3.40(1.08)/(0.145 - 0.08) = $56.49

8.    Explain why diversification reduces risk.

The standard deviation of returns is generally higher on individual stocks than it is on the market.    Because individual stocks do not move in exact lockstep, much of their risk can be diversified away. This relates to correlation of their returns.

By spreading your portfolio across many investments you smooth out the risk of your overall

position.

The risk that can be eliminated through diversification is known as unique/diversifiable risk. The risk left in a diversified portfolio is systematic/nondiversifiable/market.

9.    Why is  beta thought to be a more relevant measure of risk than standard deviation for a diversified investor?

Standard deviation measures both a stock's market risk and unique risk.

However, a diversified investor is no longer concerned with unique risk, or at least not concerned over the small portion that remains after portfolio diversification.

Beta measures only the market risk of the stock, that type of risk that cannot be diversified away.   The stock's returns may be more or less volatile than the market portfolio and beta is an indication of that sensitivity.

10. A firm’s ordinary shares sell for $10.00 per share and are expected to pay a $1.00 dividend after one year. The dividend per share is predicted to grow at a constant 6% p.a. Its preference shares currently sell for $11.50 per share and pays $1.20 in dividends always. Calculate the firm's required rates of return for each of its equity components:

requity= $1/$10 + .06

= .10 + .06  = 16%

rpreferred= $1.20/$11.43 = 10.5%

11. What accounts for the difference in returns, given that these are both forms of equity?

The return on the preferred stock appears to be much safer in the eyes of investors.

While the common stock is expected to pay a $1.00 dividend and that dividend is expected to grow at a 6% rate, there is more uncertainty involved in the common equity than with the preferred

equity.

Of course, in return for the common shareholders accepting higher levels of risk, they have more opportunity for gain.

A firm’s target capital structure comprises of 50% shares and 50% long-term debt. These percentages are calculated using the market value of shares and debt.

Debt: The firm can sell a 10-year, $1,000 par value, 10 percent annual coupon rate bond for $1,010. Debt issuance will cost 2 percent of the face value of each bond.

Shares: The firm's shares are currently selling for $15 per share. The firm’s next dividend will be $2 per share and paid in one year’s time. Its annual dividend per share is expected to grow at 5% in

each year indefinitely. New shares must be priced $3 below the current market price in order to sell and the firm must pay another $1 per share in flotation costs.

The firm has a tax rate of 28 percent.

12. What is the firm's cost of debt before tax?

I + $1,000 − Nd                                                             $100 + ($1,000 - $990) / 10                          101

Td  =      Nd  + $1,000                                                   ($990 + $1,000) / 2                                    995

2

=            approx 10.15%

13. What is the firm's after-tax cost of debt?

10.15% * (1 – 28%)         =             7.3%

14. What is the firm's cost of equity?

re                   =            (D1/ net P0) + g

=            ($2 / [$15 -$3 - $1]) + 5%

=            23.18%

15. What is the firm’s weighted average cost of capital?

50% x 10.15% x (1-28%)               +             50% x 23.18%    =     15.24%

A firm is attempting to select the best group of independent projects competing for the firm's fixed capital budget of $5,000,000. Any unused portion of this budget will earn less than its 15 percent

cost of capital. A summary of key data about the proposed projects follows.

16.  Use the NPV approach to select the best group of projects.

Choose Projects 2, 4 and 5, since this combination maximizes NPV at $430,000

and requires $5,000,000 initial investment.

17.  Use the IRR approach to select the best group of projects.

Choose Projects 2 and 3, since this combination maximizes the return

and requires $5,000,000 initial investment.

18. Which projects should the firm implement? Explain why and discuss any qualifications.

Projects 2, 4 and 5

because NPV decision increases wealth and is better than IRR

A firm is evaluating two mutually exclusive projects that have unequal lives. The firm must evaluate the projects using the annualized net present value approach and recommend which project they

should select. The firm's cost of capital has been determined to be 18 percent, and the projects have the following initial investments and cash flows:

19. Based on the projects annualized net present values, which should the firm choose?

ANPV of Project W: $22,540/3.127 = $7,208

ANPV of Project Y: $16,900/2.174 = $7,774

Select Project Y, highest ANPV.

A firm retails goods in NZ. It is concerned about managing its cash efficiently. It’s annual sales

amount to $40 million and its COGS is $30 million. All sales are on credit as are all purchases. On

average, its inventories have an age of 80 days; its Accounts Receivables are collected in 50 days and Accounts Payables are paid 40 days after they arise. There is no change to it’s level of inventory at

the start and end of the year. It’s WACC is 20%.

20. Explain the “Operating Cycle” and calculate the firm’s Operating Cycle.

It’s Operating Cycle is the time from the beginning of the production process to collection of cash from the sale of the finished product.

OC         =            AAI                       +            ACP

=            80 days +            50 days

=            130 days

21. Calculate the firm’s Cash Conversion Cycle and explain what this means.

CCC       =             OC                        –           APP                      (or    =    AAI + ACP – APP)

=            130 days             –           40 days

=            90 days

The firm’s Operating Cycle is, on average 130 days. It doesn’t actually pay cash out to its supplies for 40 days after it receives the raw materials so the time between paying cash out to suppliers and

receiving it back in from customers is, on average, 90 days.

22. Calculate the annual average amount of resources (debt and equity) needed to support he firm’s Cash Conversion Cycle.

The resources the firm has invested in this CCC (assuming a 365 day year) are:

Inventory

+ A/R

– A/P

=

=

=

=

(80 / 365) (50 / 365) (40 / 365)

funding / resources needed

=

=

=

=

$6,575,342

$5,479,452

($3,287,671) 

$8,767,123

Note: A/R uses the Sales amount in this example, as shown in class. The other question in this practice set uses the alternative approach of Cost of Sales.

23.  Discuss how the firm’s management might be able to reduce/manage its Cash Conversion Cycle.

Turn over inventory as quickly as possible / minimise amount of inventory on hand

Collect A/R as quickly as possible – without losing sales due to high-pressure collection techniques or giving away too much with heavy discounts for early payment

Pay A/P as slowly as possible – without damaging Kiwi’s credit rating or upsetting suppliers

24. The finance manager at the firm is considering offering a 10% cash discount for payments made within 10 days. The firm’s sales volume is 100,000 units per annum. It’s finance manager expects that changes to its credit terms will result in an increase in sales to 110,000 units, that 50% of customers will take the discount and that the Average Collection Period will drop to 30 days. In addition, the finance manager believes that bad debts will fall from 2% of annual sales to  1%. State whether the firm should make this change to its collections policy and explain why or why not? (Show all workings).

Additional profit contribution from sales = 10,000 units x ($400 - $300) = - Cost of cash discount = 44,000,000 x 50% x 10% =

+ reduced bad debt expense

$1,000,000

($2,200,000)

Original bad debts $40m x 2% =

New bad debts $44m x 1% =

+ marginal investment in A/R saving

Original investme1(n)10(t =)000(100)x(0)$(0)4(0)30(00) x 50 =

New investment = =

Required return on investment

Benefit of reduced marginal investment Net Profit from implementing new plan

$800,000

$440,000              $360,000

$5,479,452

$3,616,438              $1,863,014

20%

$372,602 ($467,398)

Since there would be a net reduction in profits the project should be rejected

25.  How much value would be added to a firm that could permanently reduce its collection period by 5 days if its total annual sales on credit were $1,000,000 and its cost of capital is 10% p.a.?

interest saving = $1,000,000 x 5/365 x 10%

= $1,370

PVinterest saving            = $1,370 ÷ 10%

= $13,700 (assuming a perpetuity)

26. Calculate the implied annual cost of trade credit for firms that do not take advantage of cash discounts, based on terms of sale of 3/20, net 60.

The cash discount is 3% and customers who choose not to take the discount receive an extra 60 - 20 = 40 days of credit.

[3% / 97%] x [365 / 40]

= 28.22%

27.  If the firm’s cost of capital is 15%, should it instead accept the offer? Explain why.

Accept the offer because it is a valuable discount  i.e. costly to give up

28. A firm currently makes all sales on credit and offers no cash discount. The finance manager is considering offering a 2% cash discount for payments made within 15 days. The firm’s current Average Collection Period is 60 days, sales are 40,000 units, selling price is $45 per unit and variable costs $36 per unit. The firm expects that changes to its credit terms will result in an increase in sales to 42,000 units, that 70% of customers will take the discount and that the Average Collection Period will drop to 30 days. If the firm’s WACC is 25% should it make this change to its collections policy? (Show all workings)

Note: This question uses COGS rather than Sales to calculate A/R – either approach is acceptable

A mirror manufacturer, is currently selling 2,000 mirrors per annum, has fixed operating costs of

$25,000 p.a. and fixed financing costs of $5,000 p.a. Its sale price is $50 per mirror, and its variable   operating cost is $25 per mirror. Assume that the firm lowers the variable component of its costs in  exchange of a higher fixed cost by reducing its workforce and purchasing a mirror plating machine.   This exchange results in a reduction in the variable operating cost per unit from $25 to $20 and an    increase in the fixed operating costs from $25,000 to $30,000. Assume also that the purchase of the plating machine is financed by a loan which increases the company’s fixed financial costs from

$5,000 to $10,000. The company tax rate is 28%.

29. What is the firm’s (accounting) break-even sales units, degree of operating leverage (DOL),    degree of financial leverage (DFL) and, degree of total leverage (DTL) before the new plating machine purchase?

B/E units = FC/CM = $25,000/($50-$25) = 1,000 units

Alternatively, using formulae:

DOL@base Q  = QP(x)I(C)T = 2,000(),000 = 2

DFL@ base EBIT  = EBIT −I − (PDx  = 25,000 − 5,000 − 0 = 1.25

DTL@ base Q  = 2,000x(50(2)2(0)5(0)25(50)00(25)5,000 − 0 = 2.5

30. What is the firm’s (accounting) break-even sales units and degree of total leverage (DTL) after the assembly machine purchase?

B/E units = FC/CM = $30,000/($50-$20) = 1,000 units

DTL@ base Q  =  = 3.0

31.  If the firm expects production/sales to fall to 1,200 units and this level to remain constant in the future, is the assembly machine acquisition a good idea? Justify your answer.

Probably not a good idea to acquire new machine.

Company is only profitable after 1000 units output is reached. anything higher is profitable Profits & losses are “magnified” 2.5x under old structure but 3x with new structure

So for instance a 25% revenue decrease sees profits decrease over 75% instead of 62.5% This would magnify the firm’s losses even more if

A firm is a publicly listed forestry company with 200 million shares currently trading at $5.00 per

share. The firm needs to raise an additional $200 million capital and the CFO is considering doing this through a renounceable rights issue at a subscription price of $4.00 per share.

32.  How many existing shares will be required to acquire one right?

Total new shares needed: $200,000,000 ÷ 4 = 50 million shares

# shares required for each right: 200 million ÷ 50 million = 4 i.e. a 1-for-4 rights issue.

33. What would be the theoretical value of one right for the firm?

R = N x (Pcum – S) / (N + 1)

= 4 x ( $5.00 - $4.00) / (4+1)

= $4.00 /5 = $0.80

34. What would be the best estimate of the firm’s share price on the ex-rights date?

V = R / N

V = $0.40 / 4 = $0.20

and

Pex = Pcum – V

Pex = $5.00 – $0.20 = $4.80

35. Demonstrate what would happen to the wealth of a shareholder who owned 1,000 of the  firm’s shares before the rights issue if they i) exercised their rights; ii) Sold their rights and; iii) allowed their rights to lapse.

Wealth Prior to Rights Issue  =  1,000 shares @ $5.00

i)Wealth if rights are exercised = 1,250 shares @ $4.80 Less outlay on new shares = 250 shares @ $4.00

ii)Wealth if rights are sold = 1,000 shares @ $4.80 Plus proceeds on sale of rights = 250 @ $0.80

= $5,000

= $6,000

= ($1,000)

= $5,000

= $4,800

= $   200

= $5,000

iii)Wealth if rights are left to lapse 1,000 shares @ $4.80 =$4,800