Question

The Whenworth Corporation is trying to choose between the following two mutually exclusive design projects:

Year Cash Flow (I) Cash Flow (II)

0 –$85,000 –$51,000

1 34,900 12,300

2 45,000 32,500

3 28,000 23,500

a-1. If the required return is 10 percent, what is the profitability index for each project?

a-2. If the company applies the profitability index decision rule, which project should it take?

b-1. If the required return is 10 percent, what is the NPV for each project?

b-2. If the company applies the net present value decision rule, which project should it take?

Answer 1

Solution :

a-1. If the required return is 10 percent, the profitability index for each project is

Project I = 1.0583 ; Project II = 1.0921

a-2. If the company applies the profitability index decision rule, the company should take Project II with the higher Profitability Index.

b-1. If the required return is 10 percent, the NPV for each project is

Project I = $ 4,954.1698 ; Project II = $ 4,697.2201

b-2. If the company applies the net present value decision rule, the company should take Project I with the higher Net Present Value

Please find the attached screenshot of the excel sheet containing the detailed calculation for the solution..

File Home Insert Page Layout Data Help ? Formulas D Review E View F Tell me what you want to do G H I AB J K L M N O P 1 (2) (3) Calculation of Net Present Value and Profitability Index of Project Sl.No. Particulars Amount Year PV Factor @ Discounted Cash (1) 10% Flows (3) (4)=(1) * (3) 1 Cash outflow Year O $ 85,000.00 1.0000 $ 85,000.0000 Total of Cash Outflows (A) $ 85,000.0000 3 Cash Inflow Year 1 $ 34,900.00 0.9091 $ 31,727.2727 4 Cash Inflow Year 2 $ 45,000.00 2 0.8264 $ 37,190.0826 5 Cash Inflow Year 3 $ 28,000.00 0.7513 $ 21,036.8144 Total of discounted cash Inflows (B) $ 89,954.1698 Net Present Value of the Project = (B) - (A) = (C) 4,954.1698 Profitability Index - (B)/(A) 1.0583 Calculation of Net Present Value and Profitability Index of Project II Sl.No. Particulars Amount Year PV Factor @ Discounted Cash (1) (2) 10 % Flows (4)=(1) * (3) 1 Cash outflow Year 0 $ 51,000.00 1.0000 $ 51,000.0000 Total of Cash Outflows (A) $ 51,000.0000 3 Cash Inflow Year 1 $ 12,300.00 0.9091 $ 11,181.8182 4 Cash Inflow Year 2 $ 32,500.00 2. 0.8264 $ 26,859.5041 5 Cash Inflow Year 3 $ 23,500.00 0.7513 $ 17,655.8978 Total of discounted cash Inflows (B) $ 55,697.2201 7 Net Present Value of the Project = (B) - (A) = (C) $ 4,697.2201 | Profitability Index - (B)/(A) 1.0921 1