(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.
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 ...
The solution examines the highest present values of three possible options.
Discounting Methods: The concept of discounting should be used in order to keep track of real costs for the purpose of planning.
Calculate the present value of the estimated benefit stream at all three discount rates. Explain the effect of higher and lower discount rates.
Hopeful House, a nonprofit orgnanization serving the Big City community, is considering building a playground. It needs to rationally convince the Community Chest that its project is worthy of a special grant by calculating the present value of future benefits. The financial manager estimates future benefits of the playground at $10,000 that will be realized at the end of a four year period. Further, he recommends using a discount rate of 9%. His executive director thinks that his discount rate is too high and she recommends using 8%. The Community Chest associate, however, insists both rates are too low and wants them to use 10%. Calculate the present value of the estimated benefit stream at all three discount rates. Explain the effect of higher and lower discount rates.
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