You are presented with two cash flow options: Option Near, a $5,000 annuity for three years, with the first cash flow one year from today, or Option Far, a $5,000 annuity for six years with the first cash flow ten years from today
Assuming an interest rate of 7.0%, which set of cash flows has a greater present value?
A) Option Near has a greater PV of $13,121.58 vs. Option Far PV of $12,963.41.
B) Option Far has a greater PV of $13,121.58 vs. Option Near PV of $12,963.41.
C) Option Far has a greater PV of $30,000 vs. Option Near PV of $15,000.
D) Option Near and Option Far have the same PV of $12,963.41.
Answer: A
Explanation: A) Although this problem is not directly addressed in the text, its intended effect is to reinforce the idea of present value. In this kind of problem, the student must find a present value in the future, and then discount that renamed future value back to the present value at time zero.
Option Near: PV = PMT × = $5,000 × = $13,121.58.
Option Far: PV = PMT × / (1 + r)n = $5,000 × / (1.07)9 = $12,963.41.
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