Question

Consider the following two mutually exclusive projects:

Year	Cash Flow (A)	Cash Flow (B)
0	–$245,000	–$53,000
1	34,000	31,900
2	49,000	21,800
3	51,000	17,300
4	325,000	16,200

The required return on these investments is 13 percent.

a.	What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
b.	What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
c.	What is the IRR for each project? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
d.	What is the profitability index for each project? (Do not round intermediate calculations and round your answers to 3 decimal places, e.g., 32.161.)
e.	Based on your answers in (a) through (d), which project will you finally choose?

Answer 1

a. Payback period is the time that it takes for a firm to recover its initial investment in a project. To calculate the payback period, first compute the cumulative cash flow for each project Cumulative cash flow in a particular year is the sum of all cash flows up until that year For example, the cumulative cash flow in year 3 will be the sum of cash flows in years 0 1, 2, and 3. The cumulative cash flows for both projects are shown below: Cumulative cash flow Calculation Year Project A 245000 0 -245000 1 34000 -211000 -245,000+34,000 49000 -162000 -211,000+49,000 3 51000 -111000 -162,000+51,000 325000 214000 -111,000+325,000 Cumulative cash flow Calculation Project B -53000 -53000 --53,000+31,900 -21,100+21,800 31900 21100 21800 700 17300 18000 =700+17,300 16200 34200 =18,000+16,200 Now, the payback period will be that point in time where the cumulative cash flow for each project is zero. This is because at that point, the initial investment is equal to the sum of cash inflows For project A, the payback period must lie after year 3 as the cash flow in becoming positive after that. To calculate the exact point where the cumulative cash flow is zero, use the following formula:

Amount of investment left to be recovered after year 3 Payback period =3+ Cash fow in year 4 111,000 =3+ 325,000 = 3.34 years Therefore, the payback period for project A is 3.34 years For project B, the payback period is after year 1. Calculate the exact payback period for project B as follows Amount of investment left to be recovered after year 1 Payback period =1+ Cash fow in year 2 21,100 =1+ 21,800 =1.97 years Therefore, the payback period for project B is |1.97 years

Next compute the NPV, IRR, and the profitability index of each project in excel as follows: C D Required return 1 13% 2 Project A Project B Year 0 245000 -53000 5 1 34000 31900 6 2 49000 21800 7 51000 17300 8 4 325000 16200 =NPV($C$1,D5:D8) + D4 =NPV($C$1,C5:C8) +C4 =IRR(C4:C8) 10 b NPV 11 c IRR IRR(D4:D8) | =(D10-D4)/-D4 Profitability index =(C10-C4)/-C4 12 d. The output is as shown below A 1 Required return 13% 2 Project B Year Project A 4 245000 -53000 34000 5 31900 6 49000 21800 7 51000 17300 8 4 325000 16200 10 b 14,228.22 NPV 58,136.83 11 c IRR 20.54% 27.38% 12 d Profitability index 1.24 1.27 Solely based on a. and d., Project B would be chosen as it has a better payback period and a better profitability index LO