The discounted payback method Newland City Council has investigated the possibility of investing in a new project, and the following information has been obtained:

Question

The discounted payback method

Newland City Council has investigated the possibility of investing in a new project, and the following information has been obtained:

	£000	£000
Total cost of project		500
Expected net cash flows:
Year 1	20
2	50
3	100
4	200
5	300
6	[latex]\underline{30} [/latex]	[latex]\underline{700} [/latex]
Net return		[latex]\underline{\underline{200} }[/latex]

Required:

Assuming a rate of interest of 8%, calculate the project’s overall return using the following methods:

(a) payback
(b) discounted payback.

Accepted Answer

(a) Payback method

Year	Net cash flow	Cumulative net cash flow
	£000	£000
0	(500)	(500)
1	20	(480)
2	50	(430)
3	100	(330)
4	200	(130)
5	300	170
6	30	200

Calculation:

After 4 years the total cash flows received = £370,000 (£20,000 + 50,000 + 100,000 + 200,000).
The £30,000 still necessary to equal the original cost of the investment (£500,000 - 370,000) will be met part way through Year 5, i.e. (£130,000 ÷ 300,000) × 12 months = 5.2 months. So the payback period is about 4 years and 5 months (41 months), assuming that the net cash flows accrue evenly throughout the year.

(b) Discounted payback

Year	Net cash flow	Discount factors	Present value at 8% [Column (2) × Column (3)]	Cumulative present value
(1)	(2)	(3)	(4)	(5)
	£000		£000	£000
0	(500)	1.0000	(500)	(500)
1	20	0.9259	19	(481)
2	50	0.8573	43	(438)
3	100	0.7938	79	(359)
4	200	0.7350	147	(212)
5	300	0.6806	204	(8)
6	30	0.6302	19	11

Calculation:

Using the discounted payback method, the project would recover all of its original cost during Year 6. Assuming that the net cash flows accrue evenly, this would be about the end of the fifth month because (£8000 ÷ 19,000) × 12 months = 5.1 months. The, therefore, discounted payback period is about 5 years 5 months (65 months).

Question 19.2: The discounted payback method Newland City Council has inves...

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