Question

An investment project costs $12,500 and has annual cash flows of $3,100 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 5 percent? c. What is the discounted payback period if the discount rate is 21 percent?

Answer 1

a) In case discount rate is 0% , the discounted payback period is equal to the normal/regular payback period

Discounted payback period = 12500/3100 = 4.0322 years

b) The calculations of discounted cashflows and cumulative discounted cashflows is as given below

Year	Cashflow	Discounted Cashflow	Cumulative Discounted Cashflow
0	-12500	-12500.00	-12500.00
1	3100	2952.38	-9547.62
2	3100	2811.79	-6735.83
3	3100	2677.90	-4057.93
4	3100	2550.38	-1507.55
5	3100	2428.93	921.38
6	3100	2313.27	3234.65

The cumumulative cashflows turned positive at the end of 5 yeas. So, the discounted payback period is between 4 to 5 years .At the end of 4 years, the amount to be recovered is $1507.55

So, discounted payback period (for 5% discount rate)

= 4+ unrecovered amount at the end of 4th year/ discounted cashflow in 5th year

=4+1507.55/2428.93 = 4.62 years

c)  

The calculations of discounted cashflows and cumulative discounted cashflows is as given below

Year	Cashflow	Discounted Cashflow	Cumulative Discounted Cashflow
0	-12500	-12500.00	-12500.00
1	3100	2561.98	-9938.02
2	3100	2117.34	-7820.67
3	3100	1749.87	-6070.81
4	3100	1446.17	-4624.63
5	3100	1195.18	-3429.45
6	3100	987.76	-2441.69

The cumumulative cashflows never turn positive in this case. It is a negative NPV project

So, the project has a payback period greater than the life of the project. i.e. the project never pays back the complete amount.

Thus, we cannot determine the discounted payback period in this case. (as it is a negative NPV project)