2) NPV AND DVD RELEASE TIMING Until recently, a film was released on DVD many months after it was released in theatres. The longer the film plays in the theatre, the larger is the box office revenue, but the more delayed is the DVD revenue. Then again, the sooner the film is released on DVD, the more movie fans switch from theatre viewing to DVD viewing, and if fans know the DVD is coming out soon, then they're more likely to wait and watch on DVD. Thus, the timing of the DVD launch is an interesting optimization problem. Consider a 4-month period with times t=0,1,2,3 (for April, May, June, July). Suppose that the theatrical release of your movie is always April but you can choose whether to release the DVD in Simultaneously in April, with a Slight Delay in May, or with a Long Delay in June. Using the series of cash flows shown below, find the net present value maximizing DVD release date for these three discount rates: r = 0.08, r=0.1, and r = 0.12. E.g., if you release the DVD in April, then you'll make 150 selling tickets and 260 selling DVDs for an April total of 410, and you can plug these numbers into NPV. TIP: Find NPV[red April case], NPV [purple May case], and NPV [blue June case] for r = 0.08, then repeat for 10% and 12%. TIP: The Theatre Box Office and DVD Sales are all expressed in dollars. Month "Simultaneous" APRIL MAY JUNE JULY t=0 | 2 "Slight Delay" " Long Delay " 3 APRIL MAY JUNE JULY t=0 APRIL MAY JUNE JULY 2 3 t=0 2 3 Theatre Box office ($): 150 30 0 DVD Sales ($): 260 100 0 00 180 58 0 0 200 100 0 0 0 240 100 0 0 0 200 100 Time Period
2) NPV AND DVD RELEASE TIMING Until recently, a film was released on DVD many months after it was released in theatres. The longer the film plays in the theatre, the larger is the box office revenue, but the more delayed is the DVD revenue. Then again, the sooner the film is released on DVD, the more movie fans switch from theatre viewing to DVD viewing, and if fans know the DVD is coming out soon, then they're more likely to wait and watch on DVD. Thus, the timing of the DVD launch is an interesting optimization problem. Consider a 4-month period with times t=0,1,2,3 (for April, May, June, July). Suppose that the theatrical release of your movie is always April but you can choose whether to release the DVD in Simultaneously in April, with a Slight Delay in May, or with a Long Delay in June. Using the series of cash flows shown below, find the net present value maximizing DVD release date for these three discount rates: r = 0.08, r=0.1, and r = 0.12. E.g., if you release the DVD in April, then you'll make 150 selling tickets and 260 selling DVDs for an April total of 410, and you can plug these numbers into NPV. TIP: Find NPV[red April case], NPV [purple May case], and NPV [blue June case] for r = 0.08, then repeat for 10% and 12%. TIP: The Theatre Box Office and DVD Sales are all expressed in dollars. Month "Simultaneous" APRIL MAY JUNE JULY t=0 | 2 "Slight Delay" " Long Delay " 3 APRIL MAY JUNE JULY t=0 APRIL MAY JUNE JULY 2 3 t=0 2 3 Theatre Box office ($): 150 30 0 DVD Sales ($): 260 100 0 00 180 58 0 0 200 100 0 0 0 240 100 0 0 0 200 100 Time Period
Brief Principles of Macroeconomics (MindTap Course List)
8th Edition
ISBN:9781337091985
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter7: Production And Growth
Section: Chapter Questions
Problem 5CQQ
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Question
![2) NPV AND DVD RELEASE TIMING
Until recently, a film was released on DVD many months after it was released in theatres. The longer the film plays in the theatre,
the larger is the box office revenue, but the more delayed is the DVD revenue. Then again, the sooner the film is released on
DVD, the more movie fans switch from theatre viewing to DVD viewing, and if fans know the DVD is coming out soon, then
they're more likely to wait and watch on DVD. Thus, the timing of the DVD launch is an interesting optimization problem.
Consider a 4-month period with times t=0,1,2,3 (for April, May, June, July). Suppose that the theatrical release of your movie is
always April but you can choose whether to release the DVD in Simultaneously in April, with a Slight Delay in May, or with a
Long Delay in June. Using the series of cash flows shown below, find the net present value maximizing DVD release date
for these three discount rates: r = 0.08, r=0.1, and r = 0.12. E.g., if you release the DVD in April, then you'll make 150
selling tickets and 260 selling DVDs for an April total of 410, and you can plug these numbers into NPV.
TIP: Find NPV[red April case], NPV [purple May case], and NPV [blue June case] for r = 0.08, then repeat for 10% and 12%.
TIP: The Theatre Box Office and DVD Sales are all expressed in dollars.
Month
"Simultaneous"
APRIL MAY JUNE JULY
t=0 | 2
"Slight Delay"
" Long Delay "
3
APRIL MAY JUNE JULY
t=0
APRIL
MAY JUNE JULY
2
3
t=0
2
3
Theatre Box office ($):
150 30 0
DVD Sales ($):
260 100 0
00
180 58 0
0
200 100 0 0
0 240 100
0
0
0
200 100
Time Period](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6871a655-6df9-491d-9e6a-d916a0d3d66e%2F2676a6dd-0639-4576-8a21-bb2b21566069%2Fgf2eq7g_processed.png&w=3840&q=75)
Transcribed Image Text:2) NPV AND DVD RELEASE TIMING
Until recently, a film was released on DVD many months after it was released in theatres. The longer the film plays in the theatre,
the larger is the box office revenue, but the more delayed is the DVD revenue. Then again, the sooner the film is released on
DVD, the more movie fans switch from theatre viewing to DVD viewing, and if fans know the DVD is coming out soon, then
they're more likely to wait and watch on DVD. Thus, the timing of the DVD launch is an interesting optimization problem.
Consider a 4-month period with times t=0,1,2,3 (for April, May, June, July). Suppose that the theatrical release of your movie is
always April but you can choose whether to release the DVD in Simultaneously in April, with a Slight Delay in May, or with a
Long Delay in June. Using the series of cash flows shown below, find the net present value maximizing DVD release date
for these three discount rates: r = 0.08, r=0.1, and r = 0.12. E.g., if you release the DVD in April, then you'll make 150
selling tickets and 260 selling DVDs for an April total of 410, and you can plug these numbers into NPV.
TIP: Find NPV[red April case], NPV [purple May case], and NPV [blue June case] for r = 0.08, then repeat for 10% and 12%.
TIP: The Theatre Box Office and DVD Sales are all expressed in dollars.
Month
"Simultaneous"
APRIL MAY JUNE JULY
t=0 | 2
"Slight Delay"
" Long Delay "
3
APRIL MAY JUNE JULY
t=0
APRIL
MAY JUNE JULY
2
3
t=0
2
3
Theatre Box office ($):
150 30 0
DVD Sales ($):
260 100 0
00
180 58 0
0
200 100 0 0
0 240 100
0
0
0
200 100
Time Period
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