Question

Wii Brothers, a game manufacturer, has a new idea for an adventure game. It can market the game either as a traditional board game or as an interactive DVD, but not both. Consider the following cash flows of the two mutually exclusive projects for the company. Assume the discount rate is 12 percent.

  

Year	Board Game			DVD
0	–$	1,200		–$	2,700
1		690			1,750
2		950			1,570
3		210			800

  

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
Board game
Year	Cash flow stream	Cumulative cash flow
0	-1200	-1200
1	690	-510
2	950	440
3	210	650
Payback period is the time by which undiscounted cashflow cover the intial investment outlay
this is happening between year 1 and 2
therefore by interpolation payback period = 1 + (0-(-510))/(440-(-510))
1.54 Years
DVD
Year	Cash flow stream	Cumulative cash flow
0	-2700	-2700
1	1750	-950
2	1570	620
3	800	1420
Payback period is the time by which undiscounted cashflow cover the intial investment outlay
this is happening between year 1 and 2
therefore by interpolation payback period = 1 + (0-(-950))/(620-(-950))
1.61 Years
b
Board game
Discount rate	12.00%
Year	0	1	2	3
Cash flow stream	-1200	690	950	210
Discounting factor	1	1.12	1.2544	1.404928
Discounted cash flows project	-1200	616.0714	757.3342	149.4739
NPV = Sum of discounted cash flows
NPV Board game =	322.88
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
DVD
Discount rate	0.12
Year	0.00%	1	2	3
Cash flow stream	-2700	1750	1570	800
Discounting factor	100.00%	1.12	1.2544	1.404928
Discounted cash flows project	-2700	1562.5	1251.594	569.4242
NPV = Sum of discounted cash flows
NPV DVD =	683.52
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
c
Board game
IRR is the rate at which NPV =0
IRR	0.292355493
Year	0	1	2	3
Cash flow stream	-1200	690	950	210
Discounting factor	1	1.292355	1.670183	2.15847
Discounted cash flows project	-1200	533.9088	568.8	97.29115
NPV = Sum of discounted cash flows
NPV Board game =	9.22626E-06
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	29.24%
DVD
IRR is the rate at which NPV =0
IRR	0.282001791
Year	0	1	2	3
Cash flow stream	-2700	1750	1570	800
Discounting factor	1	1.282002	1.643529	2.107007
Discounted cash flows project	-2700	1365.053	955.2618	379.6856
NPV = Sum of discounted cash flows
NPV DVD =	1.64114E-05
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	28.20%
d
DVD-Board game Cash flow values are as follows
Year	Cash flow stream
0	-1500
1	1060
2	620
3	590
Incremental IRR is calculated based on difference of the cash flow of the two projects
Incremental CF
IRR is the rate at which NPV =0
IRR	0.273658989
Year	0	1	2	3
Cash flow stream	-1500	1060	620	590
Discounting factor	1	1.273659	1.622207	2.066139
Discounted cash flows project	-1500	832.2479	382.1953	285.5568
NPV = Sum of discounted cash flows
NPV Incremental CF =	7.37606E-06
Where
Discounting factor =	(1 + IRR)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
IRR=	27.37%