Question

6. A firm is considering investing in a project with the following cash flows:

Year	1	2	3	4	5	6	7	8
Cash flow (OMR)	1,000	1,500	2,000	1,750	1,500	1,000	1,000	500

The initial investment is OMR 7,250. The firm has a required rate of return of 8 per cent.

Calculate:

1. The payback period;   
2. The discounted payback;
3. The net present value.   

Answer 1

1. A firm is considering investing in a project with the following cash flows:

Year	1	2	3	4	5	6	7	8
Cash flow (OMR)	1,000	1,500	2,000	1,750	1,500	1,000	1,000	500

The initial investment is OMR 7,250. The firm has a required rate of return of 8 per cent.

Calculate:

1. The payback period;   
2. The discounted payback;
3. The net present value.   

Solution:

1. The Payback Period:

Given:

Initial Investment = OMR 7,250.

To Calculate:

The Payback Period:

Formula:

The Payback Period = Years before full recovery + ( Unrecovered cost at start of the year / Cash flow during the year of exceeding full recovery)

Tabulation of Calculation of The Payback Period:

Year	Cash Flow (OMR)	Cumulative Cash Flow
1	1,000	OMR 1,000
2	1,500	OMR 2,500
3	2,000	OMR 4,500
4	1,750	OMR 6,250
5	1,500	OMR 7,750
6	1,000	OMR 8,750
7	1,000	OMR 9,750
8	0,500	OMR 10,250

Formula:

The Payback Period = Years before full recovery + (Unrecovered cost at start of the year / Cash flow during the year of exceeding full recovery)

Here:

Year Before Full Recovery = 4^th Year

Cumulative Cash Flow of Year Before Full Recovery = OMR 6,250

Unrecovered Cost at Start of the Year = Initial Investment – Cumulative Cash Flow of Year Before Full Recovery

Therefore, Unrecovered Cost at Start of the Year = OMR 7,250 - OMR 6,250 = OMR 1,000

Cash flow during the Year of Exceeding Full Recovery i.e. in the 5^th Year = OMR 1,500

On putting the values in the formula, we get,

The Payback Period = 4 + (1000/1500)

= 4 + 0.666 = 4.67 Years

The Payback Period = 4.67 Years

Ans a: The Payback Period = 4.67 Years

2. The Discounted Payback Period:

Given:

Initial Investment = OMR 7,250.

Required Rate of Return or Discount Rate = 8 percent.

To Calculate:

The Discounted Payback Period:

Formula:

Discounted payback period = Years before full recovery + (Unrecovered cost at start of the year / Discounted Cash flow during the year of exceeding full recovery)

Tabulation of Calculation of Discounted Payback Period:

Year	Cash Flow (OMR)	PV Factor @ 8 % = (1 / (1+Discount Rate/100)) ^ Number of Years	Present Value of Cash Flows i.e. Discounted Cash Flows = Cash Flows × PV Factor	Cumulative Cash Flow
1	1,000	0.926	OMR 0,926.00	OMR 0,926.00
2	1,500	0.857	OMR 1,285.50	OMR 2,211.50
3	2,000	0.794	OMR 1,588.00	OMR 3,799.50
4	1,750	0.735	OMR 1,286.25	OMR 5,085.75
5	1,500	0.681	OMR 1,021.50	OMR 6,107.25
6	1,000	0.630	OMR 0,630.00	OMR 6,737.25
7	1,000	0.583	OMR 0,583.00	OMR 7,320.25
8	0,500	0.540	OMR 0,270.00	OMR 7,590.25

Formula:

Discounted payback period = Years before full recovery + (Unrecovered cost at start of the year / Discounted Cash flow during the year of exceeding full recovery)

Here:

Year Before Full Recovery = 6^th Year

Cumulative Cash Flow of Year Before Full Recovery = OMR 6,737.25

Unrecovered Cost at Start of the Year = Initial Investment – Cumulative Cash Flow of Year Before Full Recovery

Therefore, Unrecovered Cost at Start of the Year = OMR 7,250 - OMR 6,737.25 = OMR 512.75

Cash flow during the Year of Exceeding Full Recovery i.e. in the 7^th Year = OMR 0,583.00

On putting the values in the formula, we get,

The Discounted Payback Period = 6 + (512.75 / 583.00)

= 6 + 0.879= 6.88

The Discounted Payback Period = 6.88 Years

Ans b: The Discounted Payback Period = 6.88 Years

3. The Net Present Value:

Given:

Initial Investment = OMR 7,250.

Required Rate of Return or Discount Rate = 8 percent.

To Calculate:

The Net Present Value:

Formula:

Net Present Value = Total Present Value of Cash flows – Initial Investment

Present Value of Cash Flows = Cash Flow of the Year / (1 + Discount Rate / 100) ^ Number of Year

Tabulation of Calculation of The Net Present Value:

Year	Cash Flow (OMR)	Present Value of Cash Flow = Cash Flow / (1 + Discount Rate / 100) ^ Number of Years
1	1,000	(1,000) / (1 + 0.08) ^ 1 = 0,926.00
2	1,500	(1,500) / (1 + 0.08) ^ 2 = 1,285.50
3	2,000	(2,000) / (1 + 0.08) ^ 3 = 1,588.00
4	1,750	(1,750) / (1 + 0.08) ^ 4 = 1,286.25
5	1,500	(1,500) / (1 + 0.08) ^ 5 = 1,021.50
6	1,000	(1,000) / (1 + 0.08) ^ 6 = 0,630.00
7	1,000	(1,000) / (1 + 0.08) ^ 7 = 0,583.00
8	5,00	(0,500) / (1 + 0.08) ^ 8 = 0,270.00
Total		Total of Present Value = OMR 7,590.25
		Net Present Value = Total of Present Value – Initial Investment NPV = OMR 7,590.25 - OMR7,250 The Net Present Value = OMR 340.25

Ans c: The Net Present Value = OMR 340.25