
Explanation:
First, calculate Stone's expected post-retirement spending. A 20% reduction on her current $70,000 spending means she will spend 80% of it:
New spending = $70,000 * (1 - 0.20) = $56,000.
The present value of a perpetuity is calculated by dividing the annual cash flow by the yield rate (PV = C / r):
Investment required = $56,000 / 0.07 = $800,000.
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Q.52 Amelia Stone plans to retire next year and is considering an investment that would help to ensure her future financial stability. On average, Stone spends $70,000 annually. After retirement, she plans to relocate to the countryside, a move that should cut her living expenses by 20%. She was approached by her broker with the idea to start investing in perpetuities. Specifically, he suggested a perpetuity that would yield 7% per year. Assuming the mentioned reduction of costs, how much should Stone invest in the perpetuities to meet her new spending needs?
A
$800,000
B
$8,000,000
C
$560,000
D
$5,600,000