A new machine will cost $25,000. The machine is expectedto last 4 years and have no salvage value. If the interest rate is 12%, determine the return and the risk associated with the purchase. The following projections have been made.
Scenario 1 2 3
probability 0.3 0.4 0.3
annual savings $7000 $8500 $9500

Expected Value = Probability P1 * Expected Value E1 + Probability P2 * Expected Value E2 + Probability P3 * Expected Value E3 + ....... Probability Pn * Expected Value En

Here

P1 is 0.3 and E1 is $7000

P2 is 0.4 and E2 is $8500

P3 is 0.3 and E3 is $9500

By putting values, we have

Expected Annual Savings = 0.3 * $7,000 + 0.4 * $8,500 + 0.3 * $9,500 = $8,350

The above amount would be for first four years, hence it must be discounted using the annuity formula to calculate the present value of four annual receipts.

Annuity = [1 - (1 + r)^-n] / r

By putting values, we have:

Annuity = $8,350 * [1 - (1 + 12%)^-4] / 12%

And

Expected NPV = ($25,000) + $8,350 * [1 - (1 + 12%)^-4] / 12%

= $361.87

Requirement 2. Probable Return Percentage

Return Percentage = NPV / Investment = $361.87/ $25,000

= 1.45%

Requirement 3. Associated risk

As we know that

Minimum return = Minimum annual savings – Uniform annual costs

Here

Minimum annual savings are $7,000

Uniform Annual Costs were $8,350

By putting values, we have:

Minimum return = $7,000 – $8,350 = -$1,350 per year

Requirement 4. Risk Amount Percentage

Risk Amount percentage = Minimum Return / Uniform annual costs * 100

Risk Amount percentage = $1,350 / 8,350 * 100 = 16.17%