Quantitative Decision Making

Quantitative Decision Making

TASKS

Using the information presented in scenario 1 and tables 1 and 2, calculate the expected value of annual unit demand (EVD) and the expected unit variable cost (EVC) to determine the expected unit profit contribution (EVP) and total expected profit contribution (EVT). Note: unit profit contribution = price - variable cost.

Scenario 1

profit

prob.

 

2516

0.25

629

1730

0.3

519

2160

0.45

972

 

mean

706.6667

 

var

55826.33

Scenario 2

profit

prob.

1440

0.2

288

2980

0.15

447

1945

0.4

778

2556

0.25

639

mean

538

var

46194

Using the EVT value found above and the proportionate value for annual fixed costs, determine the cake's net expected contribution to annual profit before tax.

First, find the dollar value of debt and equity. For example, for wd = 20%, the dollar value of debt is:

d = wd V = 0.2 ($2,659,574) = $531,915.

We can then find the dollar value of equity:

S = V - D

S = $2,659,574 - $531,915 = $2,127,659.

We repeat this process for all the capital structures.

wd Debt, D Stock Value, S

0%$0$2,500,000

20%$531,915$2,127,660

30%$817,439$1,907,357

40%$1,086,957$1,630,435

50%$1,315,789$1,315,789

The firm issues debt, which changes its WACC, which changes value. The firm then utilize debt income to repurchase stock. The stock price alteration following debt is issued, but does not change during actual repurchase (or arbitrage is possible). The stock price after debt is concern but earlier than stock is repurchased reveal shareholder wealth, which is the sum of the stock and the cash paid in repurchase.

For example, to locate the stock price for wd = 20%, let D0 and N0 signify debt and outstanding shares earlier than the recap. D - D0 is equal to cash that will be used to repurchase stock. S + (D - D0) is the wealth of shareholders' after the debt is issued but immediately before the repurchase. We can express the stock price per share prior to the repurchase, P, for wd = 20%, as:

P = [S + (D - D0)]/N0.

P = [$2,127,660 + ($531,915 - 0)] / 100,000

P = $26.596 per share.

The number of shares repurchased is:

# repurchased= (D - D0) / P

# rep.= ($531,915 - 0) / $26.596

= 20,000.

The amount of left over shares after the repurchase is:

# remaining = N = S / P

N= $2,127,660 / $26.596

= 80,000.

With reference to scenario 2 and tables 3 and 4, calculate the net expected values of annual profit for the Knightsbridge and Covent Garden projects.

We can relate this same method to all the capital structures under consideration.

# Shares # Shares Wd P Repurch. Remaining

0% $25.00 0100,000

20% $26.6020,000 80,000

30% $27.2530,000 70,000

40% $27.1740,000 60,000

50% $26.3250,000 50,000

Evaluate the absolute risk of annual profits for the investment alternatives.

Old: = = 44.44%.

New: = = 47.17%.

The change would also increase the breakeven point:

Old:QBE = = = 40 units.

New:QBE = = 45.45 units.

Evaluate the relative levels of risk associated with the two projects.

though, one could gauge working leverage in other ways, say by degree of operating leverage:

Old:DOL = = = 5.0.

New:The new DOL, at the expected sales level of 70, is

= 2.85.

The difficulty here is that we have altered both output and sales price, so the DOLs are not really ...