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Homework answers / question archive / Consider the mixed streams of cash flows shown in the following table
Consider the mixed streams of cash flows shown in the following table.
YearA Cash Flow StreamB Cash Flow Stream1$50,000$10,0002$40,000$20,0003$30,000$30,0004$20,000$40,0005$10,000$50,000Totals$150,000$150,000YearA Cash Flow StreamB Cash Flow Stream1$50,000$10,0002$40,000$20,0003$30,000$30,0004$20,000$40,0005$10,000$50,000Totals$150,000$150,000
Find the present value of each stream using a 15% discount rate.
Compare the calculated present values and discuss them in light of the undiscounted cash flows totaling $150,000 in each case.
First let us sum up the cash flows of both streams. The non discounted cash flows of both streams would add up to $1,500,000:
Now let's compute the present value of each stream using a 15% discount rate. Here we'll use the technique of discounting, or converting future sums into present sums. We'll do this by multiplying the cash flows received at the end of each year by the present value factor at 15% for the years 1, 2, 3, 4, and 5. These factors, as given in the present value table, are 0.870, 0.756, 0.658, 0.572, and 0.497.
Now let's compare the computed values.
The non-discounted cash flows of both the streams add up to $1,500,000. Since both the streams appear to have an equal value, we'll be indifferent when it comes to choosing stream A or stream B. This is because we're ignoring the time value of money.
The time value of money means that the value of a unit of money will be different in different time periods. For example, the present value of a dollar received in the future will be less than the value of a dollar today. Given a positive rate of interest (which is 15% here), the present value of the dollars received in the future will always be lower. For instance, $50,000 received at the end of year 1 will be equal to: 50,000 * 0.870 = $43,500.
According to our calculations, the present value of stream A is $109,890, whereas the present value of stream B is $91,290. This means that stream A has a higher value, so we'll choose stream A.