Question

An investment project has annual cash inflows of $6,400,$7,500,$8,300 for the next four years, respectively, and $9,600, and a discount rate of 20 percent. What is the discounted payback period for these cash flows if the initial cost is $9,500?

A)1.30 years
B)0.80 years
C)2.55 years
D)1.80 years
E)3.60 years

Answer 1

The discounted payback period for the cash flows is approximately 2.18 years.

Step-by-step explanation:

The discounted payback period is the time it takes for the project's discounted cash inflows to recover the initial cost. To calculate the discounted payback period, we need to find the present value of each cash inflow using the discount rate of 20%. Here's how to do it:

1. Year 1: Present value = $6,400 / (1 + 0.20)^1 = $5,333.33
2. Year 2: Present value = $7,500 / (1 + 0.20)^2 = $5,000
3. Year 3: Present value = $8,300 / (1 + 0.20)^3 = $4,583.33
4. Year 4: Present value = $9,600 / (1 + 0.20)^4 = $4,000

Now, we can calculate the discounted payback period:

• Year 1: Remaining investment = $9,500 - $5,333.33 = $4,166.67
• Year 2: Remaining investment = $4,166.67 - $5,000 = -$833.33
• Year 3: The investment is recovered partially between Year 2 and Year 3, so we calculate the payback period as 2 + ($833.33 / $4,583.33) = 2.18 years

Therefore, the discounted payback period for these cash flows is approximately 2.18 years.