Investment X offers to pay you $6,900 per year for 9 years, whereas Investment Y offers to pay...

Present value of the investment X

From the question the values are-

• Periodic cash flow (P) = $6900 /Year
• Interest rate (r) = 21% /Year
• Time (n) = 9 Year

Lets put all the values in the formula to calculate present value of the cash flow:

{eq}Present\ value\ of\ annuity\ = \$6900\left [ \dfrac{1 - (1 + 0.21)^{-9}}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$6900\left [ \dfrac{1 - (1.21)^{-9}}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$6900\left [ \dfrac{1 - 0.1798587899}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$6900\left [ \dfrac{0.8201412101}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$6900* 3.9054 {/eq}

{eq}Present\ value\ of\ annuity\ = \$26947.26 {/eq}

So the present value of the cash flow will be $26947.26

Present value of the investment Y

From the question the values are-

• Periodic cash flow (P) = $9300 /Year
• Interest rate (r) = 21% /Year
• Time (n) = 5 Year

Lets put all the values in the formula to calculate present value of the cash flow:

{eq}Present\ value\ of\ annuity\ = \$9300\left [ \dfrac{1 - (1 + 0.21)^{-5}}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$9300\left [ \dfrac{1 - (1.21)^{-5}}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$9300\left [ \dfrac{1 - 0.3855432894}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$9300\left [ \dfrac{0.6144567106}{0.21}\right ] {/eq}

{eq}Present\ value\ of\ annuity\ = \$9300* 2.926 {/eq}

{eq}Present\ value\ of\ annuity\ = \$27211.8 {/eq}

So the present value of the cash flow will be $27211.8