Question

Considering two mutually exclusive projects. The crossover rate between these two projects is ___ percent and Project ___ should be accepted if the required return is less than the crossover rate.

Year	Project A			Project B
0		−$27,000			−$27,000
1		10,000			18,100
2		10,000			8,000
3		18,000			10,120

11.75%; A

11.75%; B

17.19%; B

18.64%; A

17.19%; A

Answer 1

Answer> Cross over rate is also known as weighted average cost of capital. In order to calculate the cross over rate, we will subtract the cash flows of project A and B for each year and solve it for NPV = 0. Let the crossover rate be r

Hence,

A B A-B PV

0 -27000 -27000 0 0

1 10000 18100 -8100 -8100/(1+r)

2 10000 8000 2000 2000/(1+r)^2

3 18000 10120 7880 7880/(1+r)^3

Now the difference in NPV should be zero for the cross over rate, hence

-8100/(1+r) + 2000/(1+r)^2 + 7880/(1+r)^3 = 0

since r cannot be negative, 1+r cannot be zero, hence removing 1+r from the denominator,

-8100 + 2000/(1+r) + 7880/(1+r)^2 = 0

(1+r)^2 * -8100 + (1+r)*2000 + 7880 = 0

8100(r^2 + 2*r + 1) - 2000*(1+r) = 7880

8100*r^2 + 16200*r +8100 - 2000 -2000*r =7880

8100*r^2 + 14200*r +6100 =7880

8100*r^2 + 14200*r -1780 = 0

On solving this, we get r = 0.1175

Hence r = 11.75%

now, calculating npv of each projects

Project a

10000/(1.1175) + 10000/(1.1175)^2 + 18000/(1.1175)^3 - 27000 = 8948.54 + 8007.65 + 12898.22 -27000 = 2854.41

Project b

18100/(1.1175) + 8000/(1.1175)^2 + 10120/(1.1175)^3 - 27000 = 16196.87 + 6406.12 + 7251.67 -27000 = 2854.66

Hence, if the required rate of return is less than the crossover rate, Project B should be selected, because it has a better cash flow in the 1st year, thus investment security is higher.

Hope this answers your question.