Question

1. Given the following set of cash flows for a project, calculate the Payback, Discounted Payback and Accounting Rate of Return. Assume a cost of capital of 10%. Assuming that this is an independent project, should the project be accepted? Why or why not?

Year                Cash Flow                 Net Profit                   Depreciation

0                    -$125,000

1                    $22,000                     $15,000                      $10,000

2                    $58,000                     $43,000                      $25,000

3                    -$30,000                   $24,000                      $21,000

4                    $35,000                     $28,000                      $18,000

5                    $28,000                     $20,000                      $15,000

6                    $60,000                      $52,000                      $11,000

And now Construct an NPV profile for the project above and explain what you find.

Answer 1

NPV Profile

	Net Cash Flow	Cumulative Net Cash Flow	Discounting Formula	Discounted Cash Flow	Cumulative Discounted Cash Flow
0	-125,000	-125,000	-125,000 / (1.10)^0	-125,000	-125,000
1	22,000 + 15,000 - 10,000 = 27,000	-98,000	27,000 / (1.10)^1	24,545.45	-100,454.55
2	58,000 + 43,000 - 25,000 = 76,000	-22,000	76,000 / (1.10)^2	62,809.92	-37,644.63
3	-30,000 + 24,000 - 21,000 = -27,000	-49,000	-27,000 / (1.10)^3	20,285.50	-57,930.13
4	35,000 + 28,000 - 18,000 = 45,000	-4,000	45,000 / (1.10)^4	30,735.61	-27,194.52
5	28,000 + 20,000 - 15,000 = 33,000	29,000	33,000 / (1.10)^5	20,490.40	-6,704.12
6	60,000 + 52,000 - 11,000 = 101,000	130,000	101,000 / (1.10)^6	57,011.87	50,307.75

Formula : Net Cash Flow = Cash Flow + Net Profit - Depreciation

Note : All figures in the table are in Dollars.

Payback Period

Payback Period is defined as the number of years taken by an investment to start yielding positive cumulative Net Cash Flows i.e when the Project reaches / exceeds its Break-even Point. In this Project, that number lies between 4 and 5.

Payback Period for fractional years = Last Negative Year + (Cumulative Cash Flow of last Negative Year / Total Cash Flow of consecutive Year)

The Cumulative Net Cash Flows were last negative in Year 4 (-4,000). The Total Cash Flow for the consecutive year is in Year 5 (33,000).

Payback Period = 4 + (4,000 / 33,000) = 4.12

Hence, the Payback Period for this Project is 4.12 years.

Discounted Payback Period

Discounted Payback Period is defined as the number of years taken by an investment to start yielding positive cumulative Discounted Cash Flows i.e when the Project reaches / exceeds its Break-even Point after taken Time Value into consideration. In this Project, that number lies between 5 and 6.

Discounted Payback Period for fractional years = Last Negative Year + (Cumulative Cash Flow of last Negative Year / Total Cash Flow of consecutive Year)

The Cumulative Net Cash Flows were last negative in Year 4 (-4,000). The Total Cash Flow for the consecutive year is in Year 5 (33,000).

Discounted Payback Period = 5 + (6,704.12 / 57,011.87) = 5.12

Hence, the Discounted Payback Period for this Project is 5.12 years

Accounting Rate of Return (ARR)

ARR is the average rate of return an asset is expected to earn over its average cost of investment.

Accounting Rate of Return = Average Annual Profit / Average Investment

Average Annual Profit = (15,000 + 43,000 + 24,000 + 28,000 + 20,000 + 52,000) / 6 = 30,333.33

Average Investment = (125,000 + 30,000) / 2 = 77,500

Therefore, Accounting Rate of Return = 30,333.33 / 77500 = 39.14%

Net Present Value (NPV)

NPV is defined as the summation of all Cash Flows discounted to Year 0.

The NPV for this Project is $50,308 (approximately)