You can choose any one of the following prizes. If your discount rate is 9% (ann

Question

You can choose any one of the following prizes. If your discount rate is 9% (annual compounding), which is the most valuable prize, i.e. has the greatest present value?

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

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

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

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

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

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

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

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

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

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

Explanation / Answer

Solution:

Present value for all the options:

A) present value factor will be 1/(1.09^10) = .4224

hence the present value = 25000*.4224 = $10560

B)

C) Perpetual = 1000/.09 = $11111

d) Lump sum payment of 10000 today will remain 10000>

e) 500 *.917 + 525/.09-.05 *.8416

458.7+11047

=$11506

Hence the answer is Option E

Year Cash Discount Present value 1 2800 0.917431193 2568.807339 2 2800 0.841679993 2356.703981 3 2800 0.77218348 2162.113744 4 2800 0.708425211 1983.590591 5 2800 0.649931386 1819.807882 Net present value 10891.02354

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