Question

SoPretty is a kid’s jeans manufacturer and the management are considering expanding their factory next year to add an adult line. In order to facilitate the expansion, the management identified two types of equipment at different price points. The firm requires a minimum rate of return on their investment of 8%. In addition, it should not take longer than 3.5 years for the firm to recover its initial investment. The cashflows of both types of equipment (project A and project B) are given below. If both projects are mutually exclusive, which one would you recommend to the management based on the IRR, the payback period and the discounted payback ratio

Years	Project A:   Cash Flows
0	($20,000)
1	$9,000
2	($1,000)
3	$10,000
4	$4,000
5	$6,000

Years	Project B:   Cash Flows
0	($22,000)
1	$10,000
2	($1,000)
3	$9,000
4	$6,500
5	$7,000

Answer 1

Please find the below table for better understanding

IRR is high for project B

2. Payback period is in how many years they can retain their money back on their investment.

For Project A, they receive 18,000 in 3 years and the remaining 2000 in 4th year (20000-18000)

4th year=2000/4000=0.5 years

In total project A, payback period=3.5 years

For project B, they receive 18,000 in 3 years and the remaining 2000 in 4th year

4th year=2000/6500=0.307 years

In total project B takes 3.307 years.

3. Discounted payback period: Cashflows should be discounted back at 8%. Please find in the table for discounted cashflows.

For Project A, they receive 18,354.44 in 4 years and the remaining 1645.56 in 5th year (20000-18354.44)

5th year=1645.56/4083.5=0.403 years

In total project A, discounted payback period=4.403 years

For project B, they receive 20,324.10 in 4 years and the remaining 1675.9 in 5th year

5th year=1675.9/4764.8=0.351 years

In total project B takes 4.0351 years.

==>IRR is higher than required rate of 8% and payback period of 3.307 years lower than 3.5 years for project B. Hence, they should accept project B.