Question

please show formulas

g.    At a cost of capital of 12%, what is the discounted payback period for these two projects?
WACC   =	12%
Project A
	Time period	0	1	2	3	4	5	6	7
	Cash flow	-$375	-$300	-$200	-$100	$600	$600	$926	-$200
	Disc. cash flow
	Disc. cum. cash flow
Intermediate calculation for payback
Payback using intermediate calculations
Project B
	Time period	0	1	2	3	4	5	6	7
	Cash flow	-$575	$190	$190	$190	$190	$190	$190	$0
	Disc. cash flow
	Disc. cum. cash flow
Intermediate calculation for payback
Payback using intermediate calculations
	Discounted Payback using PERCENTRANK		Ok because cash flows follow normal pattern.
h.   What is the profitability index for each project if the cost of capital is 12%?
PV of future cash flows for A:
PI of A:
PV of future cash flows for B:
PI of B:

Answer 1

Discounted Payback Period - PROEJCT A

Year	Cash Flows ($)	PVIF at 12%	Discounted Cash Flow ($)	Discounted Cumulative Cash Flow ($)
0	-375.00	1.00000	-375.00	-375.00
1	-300.00	0.89286	-267.86	-642.86
2	-200.00	0.79719	-159.44	-802.30
3	-100.00	0.71178	-71.18	-873.47
4	600.00	0.63552	381.31	-492.16
5	600.00	0.56743	340.46	-151.71
6	926.00	0.50663	469.14	317.43
7	200.00	0.45235	90.47	407.90

Discounted Payback = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 5 Year + ($151.71 / $469.14)

= 5 Year + 0.32 Years

= 5.32 Years

Discounted Payback Period - PROEJCT B

Year	Cash Flows ($)	PVIF at 12%	Discounted Cash Flow ($)	Discounted Cumulative Cash Flow ($)
0	-575.00	1.00000	-575.00	-575.00
1	190.00	0.89286	169.64	-405.36
2	190.00	0.79719	151.47	-253.89
3	190.00	0.71178	135.24	-118.65
4	190.00	0.63552	120.75	2.10
5	190.00	0.56743	107.81	109.91
6	190.00	0.50663	96.26	206.17
7	0	0.45235	0	206.17

Discounted Payback = Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year)

= 3 Year + ($118.65 / $120.75)

= 3 Year + 0.98 Years

= 3.98 Years

Profitability Index (PI)

Profitability Index (PI) – PROJECT A

Profitability Index (PI) = PV of future cash flows for A / Initial Outflow

= [-$267.86 - $159.44 - $71.18 + $381.31 + $340.46 + $469.14 + $90.47] / $375

= $782.90 / $375

= 2.09

Profitability Index (PI) – PROJECT B

Profitability Index (PI) = PV of future cash flows for B / Initial Outflow

= [$169.64 + 151.47 + 135.24 + 120.75 + 107.81 + 96.26 + 0] / $575

= $781.17 / $575

= 1.36