Asked by theresa betty on May 12, 2024
Verified
Calculate the present value of a growing annuity given the following information: current cash flows: $90,000; cash flow growth rate = 2%; timeframe = 20 years; required rate of return = 5%.
A) $1,319,886
B) $1,329,886
C) $1,339,886
D) $1,349,886
E) $1,359,886
Present Value
The valuation now of money anticipated in the future or continuous cash flows, when calculated with a specified return rate.
Growing Annuity
A series of periodic payments that grow at a constant rate per period for a specified number of periods, used in financial calculations to determine the present value of such payments.
Cash Flow Growth Rate
This rate indicates the year-over-year percentage increase or decrease in a company's cash flow, used to assess the firm’s financial health and operational efficiency.
- Work out the contemporary and forthcoming monetary worth of lump sum investments, fixed-term annuities, and indefinite financial allocations.
- Analyze the impact of growth rates in annuities and perpetuities on their present and future values.
Verified Answer
DB
Daphne BazileMay 17, 2024
Final Answer :
A
Explanation :
The present value of a growing annuity can be calculated using the formula: PV = C * [(1 - ((1 + g) / (1 + r))^t) / (r - g)], where C is the current cash flow, g is the growth rate, r is the required rate of return, and t is the timeframe. Plugging in the given values: PV = $90,000 * [(1 - ((1 + 0.02) / (1 + 0.05))^20) / (0.05 - 0.02)] = $1,319,886.
Learning Objectives
- Work out the contemporary and forthcoming monetary worth of lump sum investments, fixed-term annuities, and indefinite financial allocations.
- Analyze the impact of growth rates in annuities and perpetuities on their present and future values.