Question

You are analyzing the following two projects and have developed the following information.

Project A | Project B

Year | Cash flow | Cash flow

0 | -$50,000 | -$50,000

1 | $31,000 | $42,000

2 | $26,000 | $21,000

3 | $27,000 | $18,000

5. What is the crossover rate of the two projects?

6. Project A and B are mutually exclusive. Which project(s) should be chosen if the required return is 8%? Why?

7. Project A and B are independent. Which project(s) should be chosen if the required return is 8%? Why?

Answer 1

Crossover rate of the two projects;-

NPV of Project A = 31000/(1+r) + 26000/(1+r)^2 + 27000/(1+r)^3 - 50000

NPV of Project B = 42000/(1+r) + 21000/(1+r)^2 + 18000/(1+r)^3 - 50000

To determine crossover rate, NPV of both project should be compared i.e, NPV of project A = NPV of Project B

-> 31000/(1+r) + 26000/(1+r)^2 + 27000/(1+r)^3 - 50000 = 42000/(1+r) + 21000/(1+r)^2 + 18000/(1+r)^3 - 50000

-> by mutipling (1+r)^3 & dividing 1000 on both sides,

we get 31*(1+r)^2 + 26*(1+r) + 27 - 50*(1+r)^3 = 42*(1+r)^2 + 21*(1+r) + 18 - 50*(1+r)^3

-> 31*(1+2r+r^2) + 26*(1+r) + 27 = 42*(1+2r+r^2) + 21*(1+r) +18 - 50*(1+r)^3 + 50*(1+r)^3

-> 31+62r+31r^2+26+26r+27 = 42+84r+42r^2+21+21r+18

-> 0 = 42+84r+42r^2+21+21r+18-31-62r-31r^2-26-26r-27

-> 0 = -3+17r+11r^2 : 0 = 11r^2+17r-3 By solving this equation we will get r i.e. crossover rate

Project A and B are mutually exclusive. Which project(s) should be chosen if the required return is 8%?

Year	Project A cashflow	Project B cashflow	Present value factor @ 8%	Discounted cashflow A	Discounted cashflow B
0	$        (50,000)	$ (50,000)	1.0000	$      (50,000)	$       (50,000)
1	$         31,000	$       42,000	0.9259	$       28,704	$        38,889
2	$         26,000	$       21,000	0.8573	$       22,291	$        18,004
3	$         27,000	$       18,000	0.7938	$       21,433	$        14,289
NPV	$      22,428	$      21,182

Project A should should be chosen because it gives more NPV than project B.

Project A and B are independent. Which project(s) should be chosen if the required return is 8%? Why?

Both the project can be selected because it gives positive NPV. Now also since NPV of project A is more than NPV of project B, we 1st select project A & then project B.