You can choose any one of the following prizes. If your discount rate is 10% (an

Question

You can choose any one of the following prizes. If your discount rate is 10% (annual compounding), which is the most valuable prize, i.e. has the greatest present value?

A. A perpetual stream of annual payments of $1,000 starting in one year.

B. A perpetual stream of annual payments starting at $500 in one year and increasing at 5% per year thereafter.

C. A lump sum payment of $25,000 at the end of 10 years.

D. Five annual payments of $2,800 - the first payment occurs one year from today.

E. A lump sum payment of $10,000 today.

Explanation / Answer

A. Present value = $1000 / .10 = $10000

B. Present Value = Cash flow at year one / (rate of return - growth rate) = $500 / (.10 - .05) = $10000

C. Present Value = Future Value / (1+r)^n = 25000 / (1+.10)^10 = $9639

D. Present Value = [2800/ 1.10] + [2800/(1.10)^2] + [2800/(1.10)^3] + [2800/(1.10)^4] + [2800/(1.10)^5] = $10614

E. Present Value = $10000

The most valuable price is D. Five annual payments of $2,800 - the first payment occurs one year from today since it has the highest present value.

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