Question

An investment project has annual cash inflows of $4,392, $3,276, $4,222, and $3,268 for the next four years, respectively, and a discount rate of 15%.

What is the discounted payback if the initial investment is $5,500? (Round answer to 2 decimal places. Do not round intermediate calculations)

Answer 1

Initial investment = $5,500

Payback period is the time period required to cover the initial investment back. Discounted payback period takes in to account the time value of money of future cash inflows.

Time	Cash inflows(in $)	PVF(15%,n)	PV of cash inflows(in $)	Cumulative value of cash inflow(in $)
1	4392	0.870	3821.04	3821.04
2	3276	0.756	2476.656	6297.696
3	4222	0.658	2778.076	9075.772
4	3268	0.572	1869.296	10945.068

Note : It is assumed that all the cash flows are evenly distributed through out the year.

Discounted payback period = 1 + 1678.96 / 2476.656

( As the initial investment is $5500, we need to cover this cost, we will take year corresponding to the cumulative value which is less than or equal to 5500, here it is 1 year. In 1 year 3821.04 $ will be covered, we will be needing $1678.96 (5500 - 3821.04) more to cover full initial cost. As the cash flows are evenly distributed, remaining 1678.96 $ will be covered from 2nd year inflows of amount 2476.656$) . Hence 1678.96 / 2476.656 is taken.

= 1 + 0.68 (approx)

= 1.68 years (approx)

Hope it helps!