Question

Calculate the discounted payback period for the following cash flows.

Investment = $300,000

Salvage Value = 0

Service Life = 4 Years

MARR = 5%

n	Cash Flow	Cost of Capital	Balance
0	-300,000
1	100,000
2	150,000
3	125,000
4	100,000

Answer 1

Discounted payback period: It is the method to calculate the period in which capital investment of the project will be recovered. Since after recovering capital investments cost returns on the project can be evaluated.

In discounted payback method time value of money also plays an important role. All the benefits from future years will be discounted to calculate its present value.

Present value = Future value of benefits * present value factor

Present value factor = 1 / ( 1+ rate of return)^{number of years.}

For year 1 = 1 / ( 1+ .05)¹ = 0.952

Years	Cash flow	Present value factor	Present value	Cumulative cash flow	Cost of capital	Balance
0	-300000	1	-300000	0	300000	300000
1	100000	0.952	95200	95200	300000	204800
2	150000	0.907	136050	231250	300000	68750
3	125000	0.864	108000	339250	300000	-39250
4	100000	0.823	82300	421550	300000	-121550

In the above table we can see that in the year 2 only $68750 is remaining to recover from $300000

In the year 3 total cash inflow is $108000 in which $68750 is for recovery of cost of capital.

Payback period is between year 2 and year 3

Additional amount remaining to recover ( $68750) should be recover from next year cash flow ($ 108000)

= ($68750 / $108000)

= 0.64 or approx 8 months ( 12* .64)

Hence total payback period = 2 years and 8 months.

The negative figures in the year 3 and 4 in the balance section of table shows the return after recovering the cost of investment.