Question

Lakia is considering adding toys to her gift shop. She estimates that the cost of inventory will be $7,500, and remodeling expenses and shelving costs are estimated at $1,800. Toy sales are expected to produce net cash inflows of $2,300, $2,900, $3,500, and $4,600 over the next four years, respectively. Should Lakia add toys to her store if she assigns a 3-year payback period to this project? Why or why not?

a) Yes; the payback period is 3.13 years.

b) No; the payback period is 3.13 years.

c) Yes; the payback period is 2.91 years.

d) No; the payback period is 3.60 years.

e) Yes; the payback period is 3.60 years.

Answer 1

After calculating the cumulative net cash inflows and comparing them to the initial investment, it is determined that the payback period is approximately 3.13 years (option b), which exceeds Lakia's 3-year payback period criterion. Therefore, she should not add the toys to her store.

Step-by-step explanation:

The question is evaluating whether Lakia should add toys to her gift shop based on a 3-year payback period. First,

let’s calculate the cumulative net cash inflows for each year:

• Year 1: $2,300
• Year 2: $2,300 + $2,900 = $5,200
• Year 3: $5,200 + $3,500 = $8,700
• Year 4: $8,700 + $4,600 = $13,300

The total initial investment is the sum of inventory costs and remodeling expenses, which equals $7,500 + $1,800 = $9,300. By comparing the cumulative cash inflows to the initial investment, we find that the payback period is reached between year 3 and year 4.


However, after 3 years, the cumulative cash inflow is only $8,700, which is less than the initial investment of $9,300. Therefore, the payback period is more than 3 years. To precisely calculate the payback period, we need to determine how much of the year 4 inflow ($4,600) is needed to cover the remaining $600 (since $9,300 - $8,700 = $600).

To cover $600 in year 4, it will take $600 / $4,600 * 12 months = 1.57 months. Hence, the payback period is 3 years and 1.57 months, or approximately 3.13 years.

Since Lakia assigns a 3-year payback period and the calculated payback period is beyond this (3.13 years), she should not add toys to her store based on this criterion.

The correct answer would be: b) No; the payback period is 3.13 years.