Question

Suppose you will receive payments of $8,000, $2,000, and $8,000 in 1, 4, and 9 year(s) from now, respectively. What is the total present value of this stream of payments if the interest rate is 9%? Enter your response below rounded to 2 decimal places.

Answer 1

Solution :

As per the information given in the question we have

Payment received in 1 year from now = Payment received in year 1 = $ 8,000

Payment received in 4 years from now = Payment received in year 4 = $ 2,000

Payment received in 9 years from now = Payment received in year 9 = $ 8,000

Discount rate = 9 %

Thus the Present value of stream of payments

= [ $ 8,000 * PVIF(9 %, 1) ] + [ $ 2,000 * PVIF(9%,4) ] + [ $ 8,000 * PVIF(9%,9) ]

= [ $ 8,000 * ( 1 / ( 1 + 0.09 ) ¹ ) ] + [ $ 2,000 * ( 1 / ( 1 + 0.09 ) ⁴ )] + [ $ 8,000 * ( 1 / ( 1 + 0.09 ) ⁹ )]

= [ $ 8,000 * ( 1 / ( 1.09 ) ¹ ) ] + [ $ 2,000 * ( 1 / ( 1.09 ) ⁴ )] + [ $ 8,000 * ( 1 / ( 1.09 ) ⁹ )]

= ( $ 8,000 * 0.917431 ) + ( $ 2,000 *0.708425 ) + ( $ 8,000 * 0.460428 )

= $ 7,339.449541 + $ 1,416.850422 + $ 3,683.422236

= $ 12,439.722200

= $ 12,439.72 ( when rounded off to two decimal places )

Thus the Present value of stream of payments at 9 % discount rate = $ 12,439.72