Investment X offers to pay you $5,500 per year for nine years, whereas Investment Y offers to pay you $8,000 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 22 percent?

$31,985.20

Investment X offers to pay you $5,500 per year for nine years, whereas Investment Y offers to pay you $8,000 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 22 percent?

To find out which cash flow stream has the higher present value, we need to calculate the present value of both investments using the given discount rates.

1. At a discount rate of 5 percent:
To calculate the present value for each cash flow stream, we can use the formula for the present value of an annuity:

PV = C * [(1 - (1 + r)^(-n)) / r]

For Investment X:
C = $5,500 (annual payment)
r = 5% (discount rate)
n = 9 (number of years)

PV(X) = $5,500 * [(1 - (1 + 0.05)^(-9)) / 0.05]
≈ $5,500 * 7.0246
≈ $38,635.29

For Investment Y:
C = $8,000 (annual payment)
r = 5% (discount rate)
n = 5 (number of years)

PV(Y) = $8,000 * [(1 - (1 + 0.05)^(-5)) / 0.05]
≈ $8,000 * 4.3295
≈ $34,635.48

Therefore, at a discount rate of 5 percent, Investment X has a higher present value than Investment Y.

2. At a discount rate of 22 percent:
Following the same formula as above:

For Investment X:
C = $5,500 (annual payment)
r = 22% (discount rate)
n = 9 (number of years)

PV(X) = $5,500 * [(1 - (1 + 0.22)^(-9)) / 0.22]
≈ $5,500 * 5.0759
≈ $27,927.43

For Investment Y:
C = $8,000 (annual payment)
r = 22% (discount rate)
n = 5 (number of years)

PV(Y) = $8,000 * [(1 - (1 + 0.22)^(-5)) / 0.22]
≈ $8,000 * 3.2322
≈ $25,857.60

Therefore, at a discount rate of 22 percent, Investment X still has a higher present value than Investment Y.

In summary, regardless of the discount rate, Investment X has a higher present value than Investment Y.