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

Answer:

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

Explanation:

1. Present value of investment X

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

Formula:

           $PV=C\times [\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}]$

Substitute and compute:

        $PV_1=\ 4,200\times [\dfrac{1}{0.05}-\dfrac{1}{0.05(1+0.05)^8}]$

        $PV_1=\ 27,145.49$

2. Present value of investment Y

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

Formula:

           $PV=C\times [\dfrac{1}{r}-\dfrac{1}{r(1+r)^t}]$

Substitute and compute:

        $PV_2=\ 6,200\times [\dfrac{1}{0.05}-\dfrac{1}{0.05(1+0.05)^5}]$

        $PV_2=\ 26,409.81$

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