What is the Present Value of a total loss with an annual impact of $50,000 over 5 years at a discount rate of 5%?

What is the Present Value of a total loss with an annual impact of $50,000 over 5 years at a discount rate of 5%?

• A. $35,345
• B. $216,473
• C. $44,316
• D. $19,983

Answer: (B)

To calculate the Present Value (PV) of a total loss with a consistent annual impact over several years, we can use the formula for the Present Value of an annuity. The formula is: \[ \text{PV} = C \times \frac{1 - (1 + r)^{-n}}{r} \] where: - \( C \) is the annual cash flow (in this case, the annual impact), - \( r \) is the discount rate, and - \( n \) is the number of years. In this situation: - The annual impact (\( C \)) is $50,000, - The discount rate (\( r \)) is 5% or 0.05, - The number of years (\( n \)) is 5. Substituting these values into the formula gives: \[ \text{PV} = 50000 \times \frac{1 - (1 + 0.05)^{-5}}{0.05} \] Calculating the components step by step: 1. Calculate \( (1 + 0.05)^{-5} \): - \( (1.05)^{-5} \approx 0.783

To calculate the Present Value (PV) of a total loss with a consistent annual impact over several years, we can use the formula for the Present Value of an annuity. The formula is:

[ \text{PV} = C \times \frac{1 - (1 + r)^{-n}}{r} ]

where:

• ( C ) is the annual cash flow (in this case, the annual impact),

• ( r ) is the discount rate, and

• ( n ) is the number of years.

In this situation:

• The annual impact (( C )) is $50,000,

• The discount rate (( r )) is 5% or 0.05,

• The number of years (( n )) is 5.

Substituting these values into the formula gives:

[ \text{PV} = 50000 \times \frac{1 - (1 + 0.05)^{-5}}{0.05} ]

Calculating the components step by step:

1. Calculate ( (1 + 0.05)^{-5} ):

• ( (1.05)^{-5} \approx 0.783