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# Highest Present Value

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A financial planner has offered you three possible options for receiving cash flows. You must choose the option that has the highest present value.

(1) \$1,000 now and another \$1,000 at the beginning of each of the 11 subsequent months during the remainder of the year, to be deposited in an account paying a 12 percent nominal annual rate, but compounded monthly (to be left on deposit for the year).

(2) \$12,750 at the end of the year (assume a 12 percent nominal interest rate with semiannual compounding).

(3) A payment scheme of 8 quarterly payments made over the next two years. The first payment of \$800 is to be made at the end of the current quarter. Payments will increase by 20 percent each quarter. The money is to be deposited in an account paying a 12 percent nominal annual rate, but compounded quarterly (to be left on deposit for the entire 2-year period).

Which one would you choose?
a. Choice 1.
b. Choice 2.
c. Choice 3.
d. Any one, since they all have the same present value.
e. Choice 1, if the payments were made at the end of each month.

#### Solution Preview

The net present value (NPV) calculations have been done with a financial calculator (HP 10BII).

Choice 1a is an annuity due. Switch the calculator from End to Begin mode and input
N = 12 (number of payments)
I = 12%/12 = 1% (monthly interest rate)
PMT = \$1000 (monthly payment)
FV = 0
Solve for PV = \$11,367.63 (note that the calculator returns present value as a negative number)

(Switch calculator back to End mode.)

Choice 2b is a lump sum at the end of the year. Discount that to the present using semi-annual compounding
N = 2 ...

#### Solution Summary

The solution examines the highest present values of three possible options.

\$2.19