Question

You are considering two investment options. In option A, you have to invest RM6000 now and RM1000 three years from now, In option B, you have to invest RM1500 now, RM1500 a year from now, and RM1000 three years from now. In both options, you will receive four annual payments of RM3000 each. (You will get the first payment a year from now.) Which of these options would you choose based on (a) the conventional payback criterion, and (b) the present worth criterion, assuming 10% interest?

Based on conventional payback period method, choose either (A/B/Both)
PW Option A   Format : 5866.8
PW Option B   Format : 6935.44
Based on PW analysis method, choose Option (A or B)

Answer 1

Note: Cash Outflows are preceded by a negative (-) sign

Cumulative Net Cash Flow is just the running total of cash flows at the end of each year. Payback will occur when the cumulative net cash flow becomes zero.

Payback period = Full years until recovery + (unrecovered cost at the beginning of recovery year/cash flow during recovery year)

Present Worth is the sum of the present values of all future cash flows discounted at a certain interest rate (which is also known as the cost of capital of a firm).

Present Worth = CF0 + CF1/(1+i)^1 + CF2/(1+i)^2 + .......... + CFn/(1+i)^n

where CF0 is the initial investment outflow and CF(1,2,3,.....n) are the Net Cash Flow for the corresponding years and "i" is the discount rate  

(a) To make a choice between Option A and B based on the Conventional Payback criterion we prepare the Cumulative Net Cash Flow table for both the options:

Cumulative Net Cash Flows in Option A

Year	0	1	2	3	4
Cash Outflow	-6000	0	0	0	-1000
Cash Inflow	0	3000	3000	3000	3000
Net Cash Flow	-6000	3000	3000	3000	2000
Cumulative Net Cash Flow	-6000	-3000	0	3000	5000

Payback period = 2 years

Cumulative Net Cash Flows in Option B

Year	0	1	2	3	4
Cash Outflow	-1500	-1500	0	0	-1000
Cash Inflow	0	3000	3000	3000	3000
Net Cash Flow	-1500	1500	3000	3000	2000
Cumulative Net Cash Flow	-1500	0	3000	6000	8000

Payback period = 1 year

Based on the payback criterion, we will choose Option B because it has a lesser payback period.

(b) To make a choice between Option A and B based on the Present Worth criterion we prepare the Net Cash Flow table for both the options:

Net Cash Flows in Option A

Present Worth in Option A = -6000 + 3000/(0.10)^1 + 3000/(0.10)^2 + 3000/(0.10)^3 + 2000/(0.10)^4 = 2826.58

Net Cash Flows in Option B

Present Worth in Option B = -1500 + 1500/(0.10)^1 + 3000/(0.10)^2 + 3000/(0.10)^3 + 2000/(0.10)^4 = 5962.95

Based on the Present Worth criterion, we will choose Option B because it has a higher Present Worth.