Question

An investment project costs $20,500 and has annual cash flows of $4,300 for six years. Required : (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 19 percent?

Answer 1

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

Year	0	1	2	3	4	5	6
Cashflow(in $)	(20,500)	4,300	4,300	4,300	4,300	4,300	4,300
PVF @0%	1	1.000	1.000	1.000	1.000	1.000	1.000
Discounted Cashflow (Cash flow * PVF)	(20,500)	4,300	4,300	4,300	4,300	4,300	4,300
Cumulative Cashflow(in $)	(20,500)	(16,200)	(11,900)	(7,600)	(3,300)	1,000	5,300

Discounted Payback Period = A + (B/C)

where

A -  last time period where the cumulative discounted cash flow was negative

B - absolute value of the CCF at the end of that period A

C - value of the DCF in the next period after A

Discounted Payback Period = 4+3300/4300

= 4.767 years

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

Year	0	1	2	3	4	5	6
Cashflow(in $)	(20,500)	4,300	4,300	4,300	4,300	4,300	4,300
PVF @3%	1	0.971	0.943	0.915	0.888	0.863	0.837
Discounted Cashflow (Cash flow * PVF)	(20,500)	4,175	4,053	3,935	3,820	3,709	3,601
Cumulative Cashflow(in $)	(20,500)	(16,325)	(12,272)	(8,337)	(4,516)	(807)	2,794

Discounted Payback Period = 5+807/3601

= 5.224 years

(c) What is the discounted payback period if the discount rate is 19 percent?

Year	0	1	2	3	4	5	6
Cashflow(in $)	(20,500)	4,300	4,300	4,300	4,300	4,300	4,300
PVF @19%	1	0.840	0.706	0.593	0.499	0.419	0.352
Discounted Cashflow (Cash flow * PVF)	(20,500)	3,613	3,037	2,552	2,144	1,802	1,514
Cumulative Cashflow(in $)	(20,500)	(16,887)	(13,850)	(11,298)	(9,154)	(7,352)	(5,838)

When the discount rate is 19%, the investment does not payback in 6 years.

Average discounted payback per year is 2443.67 ((3613+3037+2552+2144+1802+1514)/6), if continues it payback between 8 and 9

Discounted Payback Period = 8+(951/2443.67)=

= 8.389 years