Question

Investment X offers to pay you $4,200 per year for eight years, whereas Investment Y offers to pay you $6,100 per year for five years.

Which of these cash flow streams has the higher present value if the discount rate is 5 percent?

Answer 1

• The cash flow stream from investment X has higher present value than the the cash flow stream from investm Y.

Step-by-step explanation:

1. Present value of investment X

• Annual payment: C = $4,200
• Number of years: t = 8
• Rate: r = 5%
• PV₁ = ?

Formula:

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

Substitute and compute:

`PV_1=\$ 4,200* [(1)/(0.05)-(1)/(0.05(1+0.05)^8)]`

`PV_1=\$ 27,145.49`

2. Present value of investment Y

• Annual payment: C = $6,100
• Number of years: t = 5
• Rate: r = 5%

Formula:

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

Substitute and compute:

`PV_2=\$ 6,200* [(1)/(0.05)-(1)/(0.05(1+0.05)^5)]`

`PV_2=\$ 26,409.81`

Hence, the cash flow stream from investment X has higher present value than the the cash flow stream from investm Y.