The answer to a and c are 80 units, but I cannot figure out how to get b and d M

Question

The answer to a and c are 80 units, but I cannot figure out how to get b and d

Modern Artifacts can produce keepsakes that will be sold for $60 each. Nondepreciation fixed costs are $1,400 per year, and variable costs are $30 per unit. The initial investment of $5,000 will be depreciated straight-line over its useful life of 5 years to a final value of zero, and the discount rate is 12%.

a. What is the accounting break-even level of sales if the firm pays no taxes? (Do not round intermediate calculations. Round your answer to the nearest whole number.) Acounting break-even level of sales units 80

b. What is the NPV break-even level of sales if the firm pays no taxes? (Do not round intermediate calculations. Round your answer to the nearest whole number.) NPV break-even level of sales units

c. What is the accounting break-even level of sales if the firm’s tax rate is 20%? (Do not round intermediate calculations. Round your answer to the nearest whole number.) Acounting break-even level of sales units 80

d. What is the NPV break-even level of sales if the firm’s tax rate is 20%? (Do not round intermediate calculations. Round your answer to the nearest whole number.) NPV break-even level of sales units

Explanation / Answer

b. If the firm pays no taxes, the NPV break even should be 93 units approx

d. If the firm pays taxes @ 20%, the NPV break even should be 96 units approx

A NPV break-even occurs when the Net Present Value of the project equals zero.

A project which simply breaks even on an accounting basis will always have a negative NPV.

NPV equals zero when present value of cash inflows = present value of cash outflows= $ 5,000

Contribution per unit is $ 30.

PVIF of an annuity can be looked in the A 4 Tables. At 12% discount rate, the PVIFA for 5 years is 3.605.

Hence the annual discounted cash flows are $5,000/3.605 = $ 1387 approx

Let the sales level for NPV break even be x. Then total contribution is 30x

Therefore, 30x- 1400 =1387. x is 93 units approx. if the firm does not pay tax. Depreciation is not considered as it is non-cash expense.

However, if the firm pays tax, the equation is modified to include depreciation and tax effect.

(30x -1000-1400) x 80% + 1000 = 1387 Solving for x, you find that the sales level needed for NPV break even is 96 units approx. Depreciation considered here. First it is deducted to arrive at earnings before tax and then added back after deducting tax to arrive at cash flow after tax,

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