Question

An investment project costs $17,400 and has annual cash flows of $4,300 for six years.

a. What is the discounted payback period if the discount rate is 5 percent?

4.64, 4.73, 4.55, 4.99

b. What is the discounted payback period is the discount rate is 18 percent?

never, 1.02, 3.98, 3.35

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)]

= 4+(2152.41/3369.16)

= 4.64 years

Answer = 4.64

Note:

	Cash Flow	Discounting Factor ( 5%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-17,400	1	-17,400.00	-17,400.00
1	4,300	0.952380952381	4,095.24	-13,304.76
2	4,300	0.907029478458	3,900.23	-9,404.54
3	4,300	0.863837598531	3,714.50	-5,690.03
4	4,300	0.822702474792	3,537.62	-2,152.41
5	4,300	0.783526166468	3,369.16	1,216.75
6	4,300	0.746215396637	3,208.73	4,425.48

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)]

=Never

Answer = never

Note:

There are no positive Cumulative Cash Flow till the end of year 6 and hence the Discounted Payback Period is never.

	Cash Flow	Discounting Factor ( 18%)	Present Value (Cash Flow * Discounting Factor)	Cumulative Cash Flow (Present Value of Current Year+ Cumulative Cash Flow of Previous Year)
0	-17,400	1	-17,400.00	-17,400.00
1	4,300	0.847457627119	3,644.07	-13,755.93
2	4,300	0.718184429762	3,088.19	-10,667.74
3	4,300	0.608630872679	2,617.11	-8,050.63
4	4,300	0.515788875152	2,217.89	-5,832.73
5	4,300	0.437109216230	1,879.57	-3,953.16
6	4,300	0.370431539178	1,592.86	-2,360.31