Question

5. Calculate the ARR for each. 6. Which plan would you choose and why?

Answer 1

1. Plan A NPV = -7,740,000-600,000+ (4,000,000-2,450,000)[1/(1.1) + 1/(1.1)^2 + 1/(1.1)^3 + 1/(1.1)^4 + 1/(1.1)^5 + 1/(1.1)^6 + 1/(1.1)^7 + 1/(1.1)^8 + 1/(1.1)^9]

= -8,340,000 + 1,550,000(5.795) = 642,250

Plan B NPV = -6,680,000-500,000+ (3,500,000-2,350,000)[1/(1.1) + 1/(1.1)^2 + 1/(1.1)^3 + 1/(1.1)^4 + 1/(1.1)^5 + 1/(1.1)^6 + 1/(1.1)^7 + 1/(1.1)^8 + 1/(1.1)^9] + 1275000

=-7,180,000+1,150,000(5.795) + 1,275,000/(1.1)^9 = 24974.63 = 24975

2. profitability index = 1 + (NPV/Initial Investment)

PI(Plan A) = 1 + (642250/8340000) = 1.077

PI(Plan B) = 1+ (24975/7180000) = 1.0034

3. Let IRR of Plan A = x

-7,740,000-600,000+ (4,000,000-2,450,000)[1/(1+x) + 1/(1+x)^2 + 1/(1+x)^3 + 1/(1+x)^4 + 1/(1+x)^5 + 1/(1+x)^6 + 1/(1+x)^7 + 1/(1+x)^8 + 1/(1+x)^9] = 0

=> -8,340,000 + 1,550,000(1/x ( 1- (1/1+x)^9) ) = 0

=> 1/x ( 1- (1/1+x)^9) = 5.3806

using approximation, the IRR = 11.72%. Excel can be used to calculate this. Otherwise, there will be a 9 degree equation which is solvable only using approximation.

Let IRR of Plan B = x

-6,680,000-500,000+ (3,500,000-2,350,000)[1/(1+x) + 1/(1+x)^2 + 1/(1+x)^3 + 1/(1+x)^4 + 1/(1+x)^5 + 1/(1+x)^6 + 1/(1+x)^7 + 1/(1+x)^8 + 1/(1+x)^9] = 0

=> -7,180,000 + 1,150,000(1/x ( 1- (1/1+x)^9) ) = 0

=> 1/x ( 1- (1/1+x)^9) = 6.243

using approximation, the IRR = 8.02%. Excel can be used to calculate this. Otherwise, there will be a 9 degree equation which is solvable only using approximation.[Salvage value is not considered as mentioned in question]

4. Payback period = Initial inv / annual cash flow

Plan A PP = 8,340,000 / 1,550,000 = 5.38 years

Plan B PP = 7,180,000 / 1,150,000 = 6.243 years

Plan A is best for the organization.