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 8 percent. Year Board Game -$1,000 650 DVD 2,300 1,550 1,350 600 WN - 700 170 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.) Board game DVD Payback period years 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

Payback period is the time taken to recover the initial investment from the CFs of the project:

Board Game:

Year	Opening Balance	Investment	CF	Closing Balance
0		$            1,000.00		$            1,000.00
1	$              1,000.00		$                         650.00	$               350.00
2	$                  350.00		$                         700.00	$              -350.00

• Closing balance = Opening balance + investment-CF
• Opening balance = previous year's closing balance
• We can see that the closing balance of year 1 is 350 while the CF of year 2 is 700 so during 350/700 = 0.5 of year 2 the entire investment was recovered
• Payback period = 1.5 years

DVD:

Year	Opening Balance	Investment	CF	Closing Balance
0		$            2,300.00		$            2,300.00
1	$              2,300.00		$                      1,550.00	$               750.00
2	$                  750.00		$                      1,350.00	$              -600.00

• We can see that the closing balance of year 1 is 750 while the CF of year 2 is 1350 so during 750/1350= 0.555 of year 2 the entire investment was recovered
• Payback period = 1.555 years

NPV is calculated below:

Board Game:

Year	CF	Discount Factor		Discounted CF
0	$-1,000.00	1/(1+0.08)^0=	1	1*-1000=	$ -1,000.00
1	$ 650.00	1/(1+0.08)^1=	0.925925926	0.925925925925926*650=	$      601.85
2	$ 700.00	1/(1+0.08)^2=	0.85733882	0.857338820301783*700=	$      600.14
3	$ 170.00	1/(1+0.08)^3=	0.793832241	0.79383224102017*170=	$      134.95
				NPV = Sum of all Discounted CF	$      336.94

DVD:

Year	CF	Discount Factor		Discounted CF
0	$ -2,300.00	1/(1+0.08)^0=	1	1*-2300=	-2,300.00
1	$ 1,550.00	1/(1+0.08)^1=	0.925925926	0.925925925925926*1550=	1,435.19
2	$ 1,350.00	1/(1+0.08)^2=	0.85733882	0.857338820301783*1350=	1,157.41
3	$      600.00	1/(1+0.08)^3=	0.793832241	0.79383224102017*600=	476.30
				NPV = Sum of all Discounted CF	768.89

NPV of DVD is higher so it should be selected

IRR is the rate where NPV = 0. We can either use hit and trial method or we can use a financial calculator or excel's goal seek function.

Board game: IRR is 29.30% rounded to 2 decimal places

Year	CF	Discount Factor		Discounted CF
0	$-1,000.00	1/(1+0.293038324070846)^0=	1	1*-1000=	$ -1,000.00
1	$      650.00	1/(1+0.293038324070846)^1=	0.773372282	0.773372282463926*650=	$      502.69
2	$      700.00	1/(1+0.293038324070846)^2=	0.598104687	0.598104687283463*700=	$      418.67
3	$      170.00	1/(1+0.293038324070846)^3=	0.462557587	0.462557587156785*170=	$         78.63
				NPV = Sum of all Discounted CF	$           0.00

DVD: IRR is 28.73% rounded to 2 decimal places

Year	CF	Discount Factor		Discounted CF
0	$ -2,300.00	1/(1+0.287296224118931)^0=	1	1*-2300=	-2,300.00
1	$   1,550.00	1/(1+0.287296224118931)^1=	0.776821979	0.776821978705355*1550=	1,204.07
2	$   1,350.00	1/(1+0.287296224118931)^2=	0.603452387	0.603452386599703*1350=	814.66
3	$      600.00	1/(1+0.287296224118931)^3=	0.468775077	0.46877507701285*600=	281.27
				NPV = Sum of all Discounted CF	-0.00

Incremental return calculation:

We first find the incremental CF

Year	CF DVD	CF Board game	Incremental CF = CF DVD - CF Board game
0.00	$ -2,300.00	$-1,000.00	$         -1,300.00
1.00	$   1,550.00	$650.00	$              900.00
2.00	$   1,350.00	$700.00	$              650.00
3.00	$      600.00	$170.00	$              430.00

Now we can find the incremental IRR for the incremental CF: which comes to 28.29% rounded to 2 decimal places

Year	CF	Discount Factor		Discounted CF
0	$-1,300.00	1/(1+0.282976388549566)^0=	1	1*-1300=	$ -1,300.00
1	$      900.00	1/(1+0.282976388549566)^1=	0.779437571	0.779437571045655*900=	$      701.49
2	$      650.00	1/(1+0.282976388549566)^2=	0.607522927	0.60752292715755*650=	$      394.89
3	$      430.00	1/(1+0.282976388549566)^3=	0.473526195	0.473526194698227*430=	$      203.62
				NPV = Sum of all Discounted CF	$         -0.00