Question

In: Finance

For the following two projects, determine the Payback Period Discounted Payback Net Present Value Profitability Index...

For the following two projects, determine the

  1. Payback Period
  2. Discounted Payback
  3. Net Present Value
  4. Profitability Index (Benefit-Cost Ratio)
  5. Internal Rate of Return
  6. Modified Internal Rate of Return

           

Project A

Project B

Year

Net Income

Cash Flow

Net Income

Cash Flow

0

(15,000)

(19,000)

1

5,000

6,000

3,000

4,000

2

5,000

6,000

5,000

6,000

3

5000

6,000

7,000

8,000

4

5,000

6,000

11,000

12,000

Risk Index

1.80

.60

The firm’s cost of capital ko is 15% and the risk free rate Rf is 10%. The firm assesses risk and assigns a risk index to determine a risk adjusted discount rate. An index of 1.0 would be assigned to an average risk project.

To determine risk adjusted rates the firm uses the following equation:

Risk Adjusted Rate (RADR) = Rf + [Risk Index (ko – Rf)

Task: Rank the projects in accordance with each method of analysis.

Solutions

Expert Solution

Project A :

Year Cash Flow Cummulative Cashflow Discounting factor = 1/ ( 1+ r)^n Present value Cummulative present value
1 6000 6000 0.840336134 5042.016807 5042.016807
2 6000 12000 0.706164819 4236.988913 9279.00572
3 6000 18000 0.593415814 3560.494885 12839.5006
4 6000 24000 0.498668751 2992.012508 15831.51311
Total 15831.51311

Risk adjusted rated for Project A = 10 + 1.8* ( 15 - 10) = 19%

Payback period = 2 + ( 15000-12000) / 6000 = 2.5 years

Discounted payback period = 3 + ( 15000 - 12839) / 2992.01 = 3.72 years

Net present value = present value of cash inflows - initial investment = 15831.51 - 15000 = 831.51

Profitability index = Present value of cash inflows / initial invetsmnet = 15831.51 / 15000 = 1.055

Project B :

Year Cash Flow Cummulative Cashflow Discounting factor = 1/ ( 1+ r)^n Present value Cummulative present value
1 4000 4000 0.884955752 3539.823009 3539.823009
2 6000 10000 0.783146683 4698.8801 8238.703109
3 8000 18000 0.693050162 5544.401298 13783.10441
4 12000 30000 0.613318728 7359.824732 21142.92914
Total 21142.92914

Payback period = 3 + ( 19000 - 18000) / 12000 = 3.08 years

Discounted payback period = 3 + ( 19000 - 13783) / 7359.82 = 3.71 years

Net present value = 21142.93 - 19000 = 2142.93

PI = 21142.93 / 19000 = 1.113

jeff jeffy answered 2 years ago
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