Question

Consider the following two mutually exclusive projects:

  

Year	Cash Flow (A)	Cash Flow (B)
0	–$250,000	–$35,000
1	15,000	17,000
2	40,000	11,000
3	55,000	20,000
4	340,000	15,000

  

The required return on these investments is 14 percent.

  

Required:
(a)	What is the payback period for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

  

	Payback period
Project A	years
Project B	years

  

(b)	What is the NPV for each project? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g.,32.16).)

  

	Net present value
Project A	$
Project B	$

  

(c)	What is the IRR for each project? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

  

	Internal rate of return
Project A	%
Project B	%

  

(d)	What is the profitability index for each project? (Do not round intermediate calculations. Round your answers to 3 decimal places (e.g., 32.161).)

  

	Profitability index
Project A
Project B

(e)	Based only on the projects' NPV and IRR, which project should you finally choose?

Answer 1

a)

Project A:

Cumulative cash flow for year 0 = -250,000

Cumulative cash flow for year 1 = -250,000 + 15,000 = -235,000

Cumulative cash flow for year 2 = -235,000 + 40,000 = -195,000

Cumulative cash flow for year 3 = -195,000 + 55,000 = -140,000

Cumulative cash flow for year 4 = -140,000 + 340,000 = 200,000

140,000 / 340,000 = 0.41

Payback period of project A = 3 + 0.41 = 3.41 years

Project B:

Cumulative cash flow for year 0 = -35,000

Cumulative cash flow for year 1 = -35,000 + 17,000 = -18,000

Cumulative cash flow for year 2 = -18,000 + 17,000 = -1,000

Cumulative cash flow for year 3 = -1,000 + 11,000 = 10,000

1,000 / 11,000 = 0.09

Payback period of project B = 2 + 0.09 = 2.09 years

b)

Project A:

NPV = Present value of cash inflows - present value of cash outflows

NPV = -,250,000 + 15,000 / (1 + 0.14)¹ + 40,000 / (1 + 0.14)² + 55,000 / (1 + 0.14)³ + 340,000 / (1 + 0.14)⁴

NPV = -250,000 + 282,367.3236

NPV = $32,367.32

Project B:

NPV = Present value of cash inflows - present value of cash outflows

NPV = -,35,000 + 17,000 / (1 + 0.14)¹ + 11,000 / (1 + 0.14)² + 20,000 / (1 + 0.14)³ + 15,000 / (1 + 0.14)⁴

NPV = -35,000 + 45,757.058

NPV = $10,757.06

c)

Project A:

IRR is the rate of return that makes NPV equal to 0

NPV = -,250,000 + 15,000 / (1 + R)¹ + 40,000 / (1 + R)² + 55,000 / (1 + R)³ + 340,000 / (1 + R)⁴

Using trial and error method, i.e., after trying various values for R, lets try R as 18.04%

NPV = -,250,000 + 15,000 / (1 + 0.1804)¹ + 40,000 / (1 + 0.1804)² + 55,000 / (1 + 0.1804)³ + 340,000 / (1 + 0.1804)⁴

NPV = 0

Therefore , IRR of project A is 18.04%

Project B:

IRR is the rate of return that makes NPV equal to 0

NPV = -,35,000 + 17,000 / (1 + R)¹ + 11,000 / (1 + R)² + 20,000 / (1 + R)³ + 15,000 / (1 + R)⁴

Using trial and error method, i.e., after trying various values for R, lets try R as 28.20%

NPV = -,35,000 + 17,000 / (1 + 0.282)¹ + 11,000 / (1 + 0.282)² + 20,000 / (1 + 0.282)³ + 15,000 / (1 + 0.282)⁴

NPV = 0

Therefore , IRR of project B is 28.20%

d)

Project A:

Profitability index = Present value / initial investment

Present value was found during calculation of NPV

Profitability index = 282,367.3236 / 250,000

Profitability index = 1.13

Profitability index of project A is 1.13

Project B:

Profitability index = Present value / initial investment

Present value was found during calculation of NPV

Profitability index = 45,757.058 / 35,000

Profitability index = 1.31

Profitability index of project B is 1.31

e)

When projects are mutually exclusive, we should always choose the project with higher NPV.

Project A should be chosen