Question 350094: please help me!
Suppose you expect to receive $1,000 per year for each of the next 15 years, except that you will not receive any payments in years 3 and 5.
What is the present value of this amount if the discount rate is 12% per year?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! We'll assume you start from year 0.
The present value of 15 years worth of payments would be $6,810.864489.
This includes payments for years 3 and 5.
You need to subtract them.
The present value for a $1,000 payment in year 3 is equal to $711.7802478.
The present value for a $1,000 payment in year 5 is equal to $567.4268557.
Subtract both these payments from the present valueof $6,810.864489 and you have your answer.
The answer would be $5,531.657386
I used a financial calculator, but you'll get the same result by use of the present value of payments equation and the present value of a future value equation.
For the 15 years of payments, use the present value of payments equation.
For the present value of the missing payments, use the present value of a future value equation.
A cash flow analysis, using the same technique, would show the following result:
year payment present value of payment
0
1 $1,000.00 $892.86
2 $1,000.00 $797.19
3 $1,000.00 $711.78
4 $1,000.00 $635.52
5 $1,000.00 $567.43
6 $1,000.00 $506.63
7 $1,000.00 $452.35
8 $1,000.00 $403.88
9 $1,000.00 $360.61
10 $1,000.00 $321.97
11 $1,000.00 $287.48
12 $1,000.00 $256.68
13 $1,000.00 $229.17
14 $1,000.00 $204.62
15 $1,000.00 $182.70
sum of payments and present value of payments from year 1 through year 15 are shown below.
$15,000.00 $6,810.86
missing payments and present value of apyments that need to be subtracted are shown below.
3 $1,000.00 $711.78
5 $1,000.00 $567.43
total minus missing payments and present value of missing payments is shown below.
$13,000.00 $5,531.66
the formulas you would use are shown below:
PRESENT VALUE OF A PAYMENT
PV = present value
PMT = payment per time period
i = interest rate per time period
n = number of time periods
PRESENT VALUE OF A FUTURE AMOUNT
PV = Present Value
FA = Future Amount
i = Interest Rate per Time Period
n = Number of Time Periods
Using these formulas, I was able to duplicate the answer.
You should be able to also.
Write if you have questions.
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