A project manager is using the payback method to make the fi

A project manager is using the payback method to make the final decision on a project that has the cash flows as shown in the table below. The company has a 10 % required rate of return. YearlCash Flow 0 -S100,000 1S20,000 2 50,000 3 S50,000 4 S25,000 5 S500,000 i) What is the non-discounted payback period of the project? (2 marks) (ii) What is its discounted payback period? (3 marks)

Solution

The information regarding cash flow can be used to calculate both the discounted and non-discounted payback period in the following way:

Non-discounted Cash Flow:

Year

Cash Flow ($)

Balance ($)

0

-100,000

-

1

20000

(-80000)

2

50000

(-30000)

3

50000

+20000

4

25000

+45000

5

500,000

+545,000

It can be seen that there is a positive cash flow from year 3 which means that somewhere between the 2^nd and 3^rd year, the initial cost of $100,000 is recovered. Thus, in order to find the fraction of year required to recover the initial cost, the formula is:

years before full recovery + (unrecovered amount at the start of the period/cash flow during the period)

= 2+(-(-30000)/ 50000)) = 2.6 years.

Discounted cash Flow:

Year

Cash Flow ($)

Discounted Cash Flow ($)

Cumulative Discounted Cash Flow ($)

0

-100,000

-

-

1

20000

18181.81

18181.81

2

50000

41322.31

59504.12

3

50000

37565.74

97069.86

4

25000

17075.33

114,145.19

5

500,000

310,460.66

424605.85

The formula of discounted cash flow’s present value is:

PV = FV/(1+i)^n where n is the year and i is the rate of return = 10% or 0.10.

For example, PV1 = 20000/(1+0.1)^1 = 18181.81

The formula for payback period with discount = years before full recovery + (unrecovered amount at the start of the period/cash flow during the period)

Full recovery of $100,000 is made in year 4 which means the year before full recovery is 3.

Therefore discounted payback period = 3+ (100,000-97069.86)/ 17075.33 = 3.17 years.

Year	Cash Flow ($)	Balance ($)
0	-100,000	-
1	20000	(-80000)
2	50000	(-30000)
3	50000	+20000
4	25000	+45000
5	500,000	+545,000