Question

An investment project has annual cash inflows of $3,900, $4,800, $6,000, and $5,200, for the next four years, respectively. The discount rate is 15 percent. What is the discounted payback period for these cash flows if the initial cost is $6,600? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

6,582.18

Explanation:

this exercise can be solve by calculating the present value of each payment, and at the end substrating that sum from the initial payment, but there must be carefull because there is said to use a discount rate, so lets first remember how to calculate present and future values with discount rates:

$PV=P*(1-d)^{n}$

where P is the payment value, and

$FV=P*(1-d)^{-n}$

so applying this to the given values, we have:

$PV=3,900*(1-15\%)^{1}+4,800*(1-15\%)^{2}+6,000*(1-15\%)^{\\3}+5,200*(1-15\%)^{4}$

$PV=13,182.18$

so the discounted payback is given by:

dp=13,182.18-6,600

dp=6,582.18