Growing/Shrinking Perpetuities
Alysha has been offered two perpetuities: Grow and Shrink. Grow promises her $200 in one year and an annual cash flow that will increase by 4 percent per year forever. Shrink, in contrast, promises her $2,000 in one year but the annual cash flow will decline by 2 percent forever. If her opportunity cost is 6 percent per year and both annuities cost $2,000, which annuity offers her the greater value?
Homework Answers
Grow
PV of perpetual annuity = Annuity/(r-g)
= 93/(6%-5%)
= 9300
Grow exceeds cost by 9300-990= 8310
Shrink
PV of perpetual annuity = Annuity/(r-g)
= 990/(6%+3%)
= 11000
Shrink exceeds cost by 11000-990= 10010
Shrink offers the greater value
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