# Investment X offers to pay you $4,500 per year for 9 years, whereas Investment Y offers to pay... ## Question: Investment X offers to pay you$4,500 per year for 9 years, whereas Investment Y offers to pay you $6,600 per year for 5 years. If the discount rate is 6%, what is the present value of these cash flows? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) If the discount rate is 16%, what is the present value of these cash flows? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) ## Present Value of Annuity: An annuity is a regular stream of cash flows for a definite time period. We need to calculate the present value of annuity because it gives the maximum amount an investor will pay today for the future cash flows. The underlying concept is of time value of money that a dollar in hand is more valuable than a dollar to be received in the future. ## Answer and Explanation: . Answer 1. • Annual Cash Flow =$4,500
• Time = 9 Years
• Rate = 6% = 0.06

The present value is calculated as follows -

• Present Value of Annuity = {eq}P * [ 1 - ( 1 + r ) ^ -n / r ] {/eq}
• Present Value of Annuity = {eq}4500 * [ 1 - ( 1 + 0.06 ) ^ -9 / 0.06 ] {/eq}
• Present Value of Annuity = {eq}$30,607.62 {/eq} . • Annual Cash Flow =$6,600
• Time = 5 Years
• Rate = 6% = 0.06

The present value is calculated as follows -

• Present Value of Annuity = {eq}P * [ 1 - ( 1 + r ) ^ -n / r ] {/eq}
• Present Value of Annuity = {eq}6600 * [ 1 - ( 1 + 0.06 ) ^ -5 / 0.06 ] {/eq}
• Present Value of Annuity = {eq}$27,801.60 {/eq} . Answer 2. . • Annual Cash Flow =$4,500
• Time = 9 Years
• Rate = 16% = 0.16

The present value is calculated as follows -

• Present Value of Annuity = {eq}P * [ 1 - ( 1 + r ) ^ -n / r ] {/eq}
• Present Value of Annuity = {eq}4500 * [ 1 - ( 1 + 0.16 ) ^ -9 / 0.16 ] {/eq}
• Present Value of Annuity = {eq}$20,729.45 {/eq} . • Annual Cash Flow =$6,600
• Time = 5 Years
• Rate = 16% = 0.16

The present value is calculated as follows -

• Present Value of Annuity = {eq}P * [ 1 - ( 1 + r ) ^ -n / r ] {/eq}
• Present Value of Annuity = {eq}6600 * [ 1 - ( 1 + 0.16 ) ^ -5 / 0.16 ] {/eq}
• Present Value of Annuity = {eq}\$21,610.34 {/eq}