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# Dime a Dozen Diamonds - Accounting Break-Even Level and NPV Break-Even Level

(See attached files for full problem description)

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?

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.

Fill in the table below for the following zero coupon bonds. The face value of each bond is \$1,000.

Yield to
Price Maturity Maturity
\$300 30 ?
\$300 ? 8%
? 10 10%

Use the RATE, NPER, and PV functions to solve for the unknowns in the table below.

Yield to
Price Maturity Maturity
\$300 30 FORMULA
\$300 FORMULA 8%
FORMULA 10 10%

Here are the cash flows for two mutually exclusive projects:

Project C0 C1 C2 C3
A (\$20,000) \$8,000 \$8,000 \$8,000
B (\$20,000) 0 0 \$25,000

a. At what interest rates would you prefer project A to B?

b. What is the IRR of each project?

Use the MS Excel NPV function to calculate the NPVs for both projects in the profile below. In part B use
the IRR function.

#### Solution Summary

The solution has three problems - calculation of accounting and financial break-even level, finding various unknowns in a bond equation and constructing an NPV profile. All these questions are addressed and calculated in three attached Excel files.

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