Question

An investment project costs $16,700 and has annual cash flows of $3,200 for six years.

a. What is the discounted payback period if the discount rate is zero percent?

b. What is the discounted payback period if the discount rate is 3 percent?

c. What is the discounted payback period if the discount rate is 22 percent?

Answer 1

Discounted Payback Period =

( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]

a. Discounted Payback Period = 5 + ( 700 / 3200)

= 5.21875 years

= 5.22 years

Hence the correct answer is 5.22 years

Note:

	Cash Flow	Discounting Factor ( 0%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-16,700	1	-16,700.00	-16,700.00
1	3,200	1.00	3,200.00	-13,500.00
2	3,200	1.00	3,200.00	-10,300.00
3	3,200	1.00	3,200.00	-7,100.00
4	3,200	1.00	3,200.00	-3,900.00
5	3,200	1.00	3,200.00	-700.00
6	3,200	1.00	3,200.00	2,500.00

b. Discounted Payback =

= 5 + ( 2044.93700097749 / 2679.94962138769)

= 5.763050538 Years

Hence the correct answer is 5.76 years

Note:

	Cash Flow	Discounting Factor ( 3%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-16,700	1	-16,700.00	-16,700.00
1	3,200	0.970873786408	3,106.796116505	-13,593.203883
2	3,200	0.942595909134	3,016.306909228	-10,576.896974
3	3,200	0.915141659353	2,928.453309930	-7,648.443664
4	3,200	0.888487047916	2,843.158553330	-4,805.285111
5	3,200	0.862608784384	2,760.348110029	-2,044.937001
6	3,200	0.837484256684	2,679.949621388	635.012620

c. Discounted Payback Period =

= Never

Note:

	Cash Flow	Discounting Factor ( 22%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-16,700	1	-16,700.00	-16,700.00
1	3,200	0.819672131148	2,622.950819672	-14,077.049180
2	3,200	0.671862402580	2,149.959688256	-11,927.089492
3	3,200	0.550706887361	1,762.262039554	-10,164.827453
4	3,200	0.451399088001	1,444.477081602	-8,720.350371
5	3,200	0.369999252459	1,183.997607870	-7,536.352763
6	3,200	0.303278075786	970.489842517	-6,565.862921