Question

Mario Brothers, a game manufacturer, has a new idea for an adventure game. It can either market the game as a traditional board game or as a PC game, but not both. Consider the following cash flows of the two mutually exclusive projects. Assume the discount rate for both projects is 9 percent.

Year	Board Game			PC
0	−$	1,550		−$	3,400
1		760			2,100
2		1,300			1,640
3		280			1,150

a.	What is the payback period for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
b.	What is the NPV for each project? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
c.	What is the IRR for each project? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
d.	What is the incremental IRR? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a. Payback period:

Payback period is the period in which initial investment is recovered.

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
If Actual PBP > Expected PBP - Project will be rejected
Actual PBP </= Expected PBP - Project will be accepted

Board Game

Year	Opening Balance	Cash Flow	Closing Balance
1	$            1,550.00	$            760.00	$             790.00
2	$               790.00	$         1,300.00	$           -510.00

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 1 Years + [ $ 790 / $ 1300 ]
= 1 Years + 0.61 Years
= 1.61 Years

Payback Period is 1.61 Years

PBP Refer Payback Period

PC Game

Year	Opening Balance	Cash Flow	Closing Balance
1	$            3,400.00	$         2,100.00	$          1,300.00
2	$            1,300.00	$         1,640.00	$           -340.00

PBP = Year in which least +ve Closing Balance + [ Closing balance at that year / Cash flow in Next Year ]
= 1 Years + [ $ 1300 / $ 1640 ]
= 1 Years + 0.79 Years
= 1.79 Years

Payback Period is 1.79 Years

PBP Refer Payback Period

b. NPV

NPV :
NPV = PV of Cash Inflows - PV of Cash Outflows
If NPV > 0 , Project can be accepted
NPV = 0 , Indifference point. Project can be accepted/ Rejected.
NPV < 0 , Project will be rejected.

Board Game :

Cash Flows for 3 Years
Year	CF	PVF @9 %	Disc CF
0	$         -1,550.00	1.0000	$         -1,550.00
1	$             760.00	0.9174	$             697.25
2	$          1,300.00	0.8417	$          1,094.18
3	$             280.00	0.7722	$             216.21
NPV			$             457.64

PC Game:

Cash Flows for 3 Years
Year	CF	PVF @9 %	Disc CF
0	$         -3,400.00	1.0000	$         -3,400.00
1	$          2,100.00	0.9174	$          1,926.61
2	$          1,640.00	0.8417	$          1,380.36
3	$          1,150.00	0.7722	$             888.01
NPV			$             794.97

C. IRR

IRR :
IRR is the Rate at which PV of Cash Inflows are equal to PV of Cash Outflows.
It assumes that intermediary Cfs are reinvested at IRR only.

IRR = Rate at which least +ve NPV + [ NPV at that Rate / Change in NPV due to 1% inc in disc rate ] * 1%

If IRR > Cost of Capital - Project can be accepted
IRR = Cost of Capital - Indifferebce Point - Project will be accepted / Rejected
IRR < Cost of Capital - Project will be erejected

Year	CF	PVF @26 %	Disc CF	PVF @27 %	Disc CF
0	$         -1,550.00	1.0000	$         -1,550.00	1.0000	$         -1,550.00
1	$             760.00	0.7937	$             603.17	0.7874	$             598.43
2	$          1,300.00	0.6299	$             818.85	0.6200	$             806.00
3	$             280.00	0.4999	$             139.97	0.4882	$             136.69
NPV			$                11.99		$                -8.88

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 26 % + [ 11.99 / ( 11.99 - ( -8.88) ) ] * 1 %
= 26 % + [ 11.99 / ( 20.87) ] * 1 %
= 26 % + [ 0.57 ] * 1 %
= 26 % + 0.57 %
= 26.57 %

PC Game :

Year	CF	PVF @23 %	Disc CF	PVF @24 %	Disc CF
0	$         -3,400.00	1.0000	$         -3,400.00	1.0000	$         -3,400.00
1	$          2,100.00	0.8130	$          1,707.32	0.8065	$          1,693.55
2	$          1,640.00	0.6610	$          1,084.01	0.6504	$          1,066.60
3	$          1,150.00	0.5374	$             617.99	0.5245	$             603.16
NPV			$                  9.32		$              -36.69

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 23 % + [ 9.32 / ( 9.32 - ( -36.69) ) ] * 1 %
= 23 % + [ 9.32 / ( 46.01) ] * 1 %
= 23 % + [ 0.2 ] * 1 %
= 23 % + 0.2 %
= 23.2 %

d. Incremental IRR:

Year	CF (PC Game)	CF (Board Game)	Incremental CF	PVF @20 %	Disc CF	PVF @21 %	Disc CF
0	$    -3,400.00	$          -1,550.00	$         -1,850.00	1.0000	$         -1,850.00	1.0000	$         -1,850.00
1	$     2,100.00	$               760.00	$          1,340.00	0.8333	$          1,116.67	0.8264	$          1,107.44
2	$     1,640.00	$            1,300.00	$             340.00	0.6944	$             236.11	0.6830	$             232.22
3	$     1,150.00	$               280.00	$             870.00	0.5787	$             503.47	0.5645	$             491.09
NPV					$                  6.25		$              -19.25

IRR = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 20 % + [ 6.25 / ( 6.25 - ( -19.25) ) ] * 1 %
= 20 % + [ 6.25 / ( 25.5) ] * 1 %
= 20 % + [ 0.25 ] * 1 %
= 20 % + 0.25 %
= 20.25 %

Pls do rate, if the answer is correct and comment, if any further assistance is required.