Dime a Dozen Diamonds makes synthetic diamonds by treating carbon.
Each diamond can be sold for $100.
The materials cost for a standard diamond is $30. The fixed costs
incurred each year for factory upkeep
and administrative expenses are $200,000. The machinery costs $1
million a year and is depreciated
straight-line over 10 years to a salvage value of zero.					
					
a. What is the accounting break-even level of sales in terms of number
of diamonds sold?
					
b. What is the NPV break-even sales assuming a tax rate of 35 percent,
a 10-year project life and a discount
rate of 12 percent?					
					
					
Solution					
					
Problem 8-9 					
Instructions					
					
In part a, enter the formula to calculate the break-even point. In
part b, enter the formulas to calculate
all the unknown items (you will know that your formulas are correct if
the NPV is approximately equal to 0.
					
a. What is the accounting break-even level of sales in terms of number
of diamonds sold?
					
Accounting break-even point		#VALUE!	diamonds		
					
b. What is the NPV break-even sales assuming a tax rate of 35 percent,
a 10-year project life and a discount
rate of 12 percent?					
					
Number of diamonds	5,978				
Annuity factor	5.650 				
Revenue	FORMULA				
Variable Expenses	FORMULA				
Depreciation	FORMULA				
Fixed expenses					
Cash Flow	FORMULA				
Present value of cash flow	$0.00 				
Net present value	($1,000,000.00)				

A project has fixed costs of $1,000 per year, depreciation charges of
$500 a year, revenue of $6,000 a year, and
variable costs equal to two-thirds of revenues.						
						
a. If sales increase by 5 percent, what will be the increase in pretax
profits?
						
b. What is the degree of operating leverage of this project?						
						
c. Confirm that the percentage change in profits equals DOL times the
percentage change in sales.
						
						
Solution						
						
Problem 8-21 						
Instructions						
						
Enter formulas to solve this problem.						
						
a. If sales increase by 5 percent, what will be the increase in pretax
profits?
						
	Before	After				
Revenue		FORMULA				
Variable costs	0 	0 				
Fixed costs	1,000 					
Depreciation	500 					
Pretax profit	($1,500)	$0 				
						
b. What is the degree of operating leverage of this project?						
						
Degree Operating Leverage		FORMULA				
						
c. Confirm that the percentage change in profits equals DOL times the
percentage change in sales.
						
Percentage change in profits		-100%				
DOL x % change in sales		0%				
						
	Having heard about IPO underpricing, I put in an order to my broker
for 1,000 shares of every IPO he can
	get me. After 3 months, my investment record is as follows:						
							
	IPO	Shares 	Price per				
	return	Allocated to Me	Share	Initial			
	A	500	$10 	7%			
	B	200	20 	12%			
	C	1,000	8 	-2%			
							
	a. What is the average underpricing of this sample of IPOs?						
							
	b. What is the average initial return on my "portfolio" of shares
purchased from the four IPOs I bid on?
	Calculate the average initial return weighting by the amount of money
invested in each issue.
							
	c. Why have I performed so poorly relative to the average initial
return on the full sample of IPOs? What
	lessons do you draw from my experience?						
							
							
	Solution						
							
	Problem 14-7 						
	Instructions						
							
	Enter formulas to calculate the requirements of this problem.						
							
	a. What is the average underpricing of this sample of IPOs?						
	Average underpricing	FORMULA					
							
	b. What is the average initial return on my "portfolio" of shares
purchased from the four IPOs I bid on?
	Calculate the average initial return weighting by the amount of money
invested in each issue.
							
		Investment	Initial				
		(Shares x price)	Return	Profit			
	A	FORMULA	7%	FORMULA			
	B	FORMULA	12%	FORMULA			
	C	FORMULA	-2%	FORMULA			
	Total	$0 		$0 			
							
	Average return	FORMULA					
							
	c. Why have I performed so poorly relative to the average initial
return on the full sample of IPOs? What
	lessons do you draw from my experience?

Diamonds:

a. The accounting breakeven point is where revenues equal the sum of
variable costs, fixed costs, and depreciation.

Annual depreciation is calculated using the straight-line method,
which means the machinery's depreciation equals $1 million/10 or
$100,000.

Revenues equal the quantity sold multiplied by the selling price.  The
variable costs equal the material's cost multiplied by the quantity
sold.

Therefore, if Q is the quantity sold, then 100Q = 30Q + 200,000 +
100,000, making Q = 4285.71 or 4286 whole diamonds.

b. The net present value is calculated by taking each year's cash
flow, discounting it using the discount rate, and subtracting the
initial investment.  Each year's cash flow is calculated by
subtracting fixed costs, variable costs, and depreciation from that
year's revenue, multiplying the result by (1 - tax rate), and then
adding back the depreciation because it is not a cash flow.

Each year's revenue equals 5978*$100= $597,800
Each year's variable expenses equal 5978*$30= $179,340
Each year's fixed expenses equal $200,000
Each year's depreciation equals $100,000
Initial investment equals $1 million

Therefore, each year's cash flow equals [$597,800 - $179,340 -
$200,000 - $100,000] (1 -0.35) + $100,000 = $176,999.

NPV = annual cash flow{[(1+ 0.12) ^ 10 -1]/[0.12 (1+ 0.12)^ 10]} -
initial investment = $176,999 * 5.6502 - $1 million = $83.83

Project question:

a.  Pretax profits are equal to revenue minus variable costs minus
fixed costs minus depreciation.

With sales at a level of $6,000 per year, pretax profits are $6,000 -
(2/3)$6000 - $1000 - $500 = $500.
A 5% increase in sales results in pretax profits of $6,000(1.05) -
(2/3)$6000 (1.05) -$1000 -$500= $600.

Therefore, the increase in pretax profit is $100.

b.  Degree of operating leverage is calculated by dividing the
percentage change in pretax profit by the percentage change in
revenue.

The percentage change in pretax profit is $100/$500*100 = 20%.  The
percentage change in revenues was 5%.  Therefore, the degree of
operating leverage equals 20%/5%, or 4.

c.  Percentage change in profits = degree of operating
leverage*percentage change in revenue = 4*20% = 5%.

IPO Underpricing:

Question a.: the average underpricing would be the average of the
returns, which is equal to (7% + 12% + -2%)/3 = 5.67%

Question b.: the average return achieved would be the average of the
returns weighted by the number of shares purchased. This is equal to
[500 (7%) + 200 (12%) + 1000 (-2%)]/(500 + 200 + 1000] = 2.29%

Question c.: "This underpricing does not imply that any investor can
expect to become wealthy by purchasing unseasoned stock from the
underwriters, for if the issue is attractive, the underwriters will
not have enough stock to go around."

"Suppose that you could always be sure of getting your fair share of
any issue that you applied for without having to ingratiate yourself
with the investment banker. Does that mean that you could make
handsome profits on average by applying for an equal amount of each
issue? Unfortunately, no. If an issue is cheap, it is also likely to
be oversubscribed; if it is dear, it is likely to be undersubscribed.
So you will receive a small portion of the cheap issues and a large
proportion of the dear ones."

Principles of Corporate Finance, fourth edition, by Brealey and Myers,
McGraw-Hill, Inc., 1991, pages 345-346

This phenomenon is exactly what has happened to this investor. The
larger amount of poorly performing shares purchased relative to the
smaller amounts of the better performing shares decreased the weighted
average return by over 50% from the one that would have been achieved
with equal amounts of shares.

Sincerely, 

Wonko