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 10 percent.

  

Year	Board Game			DVD
0	–$	850		–$	2,000
1		620			1,400
2		550			1,050
3		140			450

  

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.)

  

	Payback period
Board game	years
DVD	years

    

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.)

  

	NPV
Board game	$
DVD	$

  

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.)

  

	IRR
Board game	%
DVD	%

    

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.)

  

Incremental IRR

%

Answer 1

a) Payback period

For Board game

Statement hsowing cummulative cash flow

Year	Cash flow	Cummulative cash flow
1	620	620
2	550	1170
3	140	1310

Using interpolation we can find payback period

Year	Cummulative cash flow
1	620.00
2	1170.00
1	550.00
?	230.00

=230/550

=0.42

Thus payback period = 1 + 0.42 = 1.42 years

For DVD

Statement hsowing cummulative cash flow

Year	Cash flow	Cummulative cash flow
1	1400	1400
2	1050	2450
3	450	2900

Using interpolation we can find payback period

Year	Cummulative cash flow
1	1400.00
2	2450.00
1	1050.00
?	600.00

=600/1050

= 0.57

Thus payback period = 1+0.57 = 1.57 years

b) NPV

For Board game

Statement showing NPV

Year	Cash flow	PVIF @ 10%	PV
	A	B	A x B
1	620	0.9091	563.64
2	550	0.8264	454.55
3	140	0.7513	105.18
Total of PV of cash inflow	1123.37
Less: Initial investment	850.00
NPV	273.37

Thus NPV = $ 273.37

For For DVD

Statement showing NPV

Year	Cash flow	PVIF @ 10%	PV
	A	B	A x B
1	1400	0.9091	1272.73
2	1050	0.8264	867.77
3	450	0.7513	338.09
Total of PV of cash inflow	2478.59
Less: Initial investment	2000.00
NPV	478.59

Thus NPV = $ 478.59

c) IRR

For Board game

IRR is the rate at which NPV is 0,

if r = 31% then NPV =

Year	Cash flow	PVIF @ 31%	PV
	A	B	A x B
1	620	0.7634	473.28
2	550	0.5827	320.49
3	140	0.4448	62.28
Total of PV of cash inflow	856.05
Less: Initial investment	850.00
NPV	6.05

if r = 32% then NPV =

Year	Cash flow	PVIF @ 32%	PV
	A	B	A x B
1	620	0.7576	469.70
2	550	0.5739	315.66
3	140	0.4348	60.87
Total of PV of cash inflow	846.22
Less: Initial investment	850.00
NPV	-3.78

Now using interpolation method we can find IRR

Rate	Cummulative cash flow
31%	6.05
32%	-3.78
1%	9.83
?	6.05

= 6.05/9.83

= 0.6155

Thus IRR = 31% + 0.6155%

=31.6155%

i,e 31.62%

For For DVD

IRR is the rate at which NPV is 0,

if r = 25% then NPV =

Year	Cash flow	PVIF @ 25%	PV
	A	B	A x B
1	1400	0.8000	1120.00
2	1050	0.6400	672.00
3	450	0.5120	230.40
Total of PV of cash inflow	2022.40
Less: Initial investment	2000.00
NPV	22.40

if r = 26% then NPV =

Year	Cash flow	PVIF @ 26%	PV
	A	B	A x B
1	1400	0.7937	1111.11
2	1050	0.6299	661.38
3	450	0.4999	224.96
Total of PV of cash inflow	1997.44
Less: Initial investment	2000.00
NPV	-2.56

Now using interpolation method we can find IRR

Rate	Cummulative cash flow
25%	22.40
26%	-2.56
1%	24.96
?	22.40

= 22.40/24.96

= 0.90

Thus IRR = 25% + 0.90%

= 25.90%

d) Incremental IRR = Let us assume that project DVD is selected over  Board game

Thus statement showing incremental cash flow

Year	Incremental Cash flow
0	-1150
1	780
2	500
3	310

IRR is rate at which NPV is 0

Assume r = 21% then NPV

Year	Incremental Cash flow	PVIF @ 21%	PV
	A	B	A x B
1	780	0.8264	644.63
2	500	0.6830	341.51
3	310	0.5645	174.99
Total of PV of cash inflow	1161.12
Less: Incremental Initial investment	1150.00
NPV	11.12

Assume r = 22% then NPV

Year	Incremental Cash flow	PVIF @ 22%	PV
	A	B	A x B
1	780	0.8197	639.34
2	500	0.6719	335.93
3	310	0.5507	170.72
Total of PV of cash inflow	1145.99
Less: Incremental Initial investment	1150.00
NPV	-4.01

Now using interpolation method we can find IRR

Rate	Cummulative cash flow
21%	11.12
22%	-4.01
1%	15.13
?	11.12

=11.12/15.13

=0.73

Thus Incremental IRR = 21% + 0.73% = 21.73%