Question

9-59 Two equipment investments are estimated as follows: Year A в -$15,000$18,000 0 5,000 1 6,500 5,000 2 6,500 5,000 6,500 4 5,000 6,500 5 6,500 5,000 Which investment has the better discounted payback period if i 14%?

Answer 1

For finding a discounted payback period we need to find the present value of future revenue and then find Cumulative cash flow (CCF), we need to find the year in which CCF turns positive

We will use formula P = F/(1+i)^t to find the present value of future cash flows

Discounted payback period = Year bef CCF turns positive + (Absolute value of CCF bef it turns positive/Present value of cash flow in the year in which CCF turns positive)

using excel

		Project A			Project B
year	Discount factor	Net cash Flow	Present value of cash flow	Cumulative Cash flow	Net cash Flow	Present value of cash flow	Cumulative Cash flow
0	1.00000	-15000	-15,000.00	-15,000.00	-18000	-18,000.00	-18,000.00
1	0.87719	5000	4,385.96	-10,614.04	6500	5,701.75	-12,298.25
2	0.76947	5000	3,847.34	-6,766.70	6500	5,001.54	-7,296.71
3	0.67497	5000	3,374.86	-3,391.84	6500	4,387.31	-2,909.39
4	0.59208	5000	2,960.40	-431.44	6500	3,848.52	939.13
5	0.51937	5000	2,596.84	2,165.40	6500	3,375.90	4,315.03

Payback of A = 4 + 431.44 / 2596.84 = 4.17 yrs

Payback of B = 3 + 2909.39 / 3848.52 = 3.76 yrs

As payback of B is less, it should be selected.

Showing formula in excel

		Project A			Project B
year	Discount factor	Net cash Flow	Present value of cash flow	Cumulative Cash flow	Net cash Flow	Present value of cash flow	Cumulative Cash flow
0	=1/(1+0.14)^A88	-15000	=B88*C88	=D88	-18000	=B88*F88	=G88
1	=1/(1+0.14)^A89	5000	=B89*C89	=E88+D89	6500	=B89*F89	=H88+G89
2	=1/(1+0.14)^A90	5000	=B90*C90	=E89+D90	6500	=B90*F90	=H89+G90
3	=1/(1+0.14)^A91	5000	=B91*C91	=E90+D91	6500	=B91*F91	=H90+G91
4	=1/(1+0.14)^A92	5000	=B92*C92	=E91+D92	6500	=B92*F92	=H91+G92
5	=1/(1+0.14)^A93	5000	=B93*C93	=E92+D93	6500	=B93*F93	=H92+G93