You are considering making a movie. The movie is expected to cost ​$10.1 million up front and take a year to produce. After​ that, it is expected to make ​$4.5 million in the year it is released and ​$1.9 million for the following four years. What is the payback period of this​ investment? If you require a payback period of two​ years, will you make the​ movie? Does the movie have positive NPV if the cost of capital is 10.2 %​?

Let's address each part of this question systematically.

### Step 1: Calculate the Payback Period

The **payback period** is the time it takes to recover the initial investment of $10.1 million through the cash inflows generated by the movie.

#### Cash Flows:
- Initial Investment (Year 0): **$10.1 million** (outflow)
- Year 1: **$4.5 million**
- Year 2: **$1.9 million**
- Year 3: **$1.9 million**
- Year 4: **$1.9 million**
- Year 5: **$1.9 million**

#### Cumulative Cash Flows
Let's calculate cumulative cash flows year-by-year to determine when the initial investment is fully recovered.

1. **Year 1**: $4.5 million  
   Cumulative: $4.5 million

2. **Year 2**: $4.5 million + $1.9 million = $6.4 million  
   Cumulative: $6.4 million

3. **Year 3**: $6.4 million + $1.9 million = $8.3 million  
   Cumulative: $8.3 million

4. **Year 4**: $8.3 million + $1.9 million = $10.2 million  
   Cumulative: $10.2 million

By the end of Year 4, the cumulative cash inflow ($10.2 million) slightly exceeds the initial investment of $10.1 million. Therefore, the **payback period** is just under **4 years**.

#### Decision on the Payback Requirement
Since the required payback period is 2 years, and our payback period is around 4 years, we **would not make the movie** based on this criterion.

### Step 2: Calculate the NPV (Net Present Value)

The NPV is calculated by discounting each cash flow back to present value using the cost of capital (10.2%) and then summing these present values.

The formula for NPV is:
\[
\text{NPV} = \sum \frac{\text{Cash Flow in Year t}}{(1 + r)^t} - \text{Initial Investment}
\]
where $ r = 10.2\% = 0.102 $.

#### NPV Calculation
1. **Initial Investment** (Year 0): $-10.1$ million (already a present value)
2. **Year 1**: $ \frac{4.5}{(1 + 0.102)^1} = \frac{4.5}{1.102} = 4.0844 $
3. **Year 2**: $ \frac{1.9}{(1 + 0.102)^2} = \frac{1.9}{1.215604} = 1.5633 $
4. **Year 3**: $ \frac{1.9}{(1 + 0.102)^3} = \frac{1.9}{1.339504} = 1.4186 $
5. **Year 4**: $ \frac{1.9}{(1 + 0.102)^4} = \frac{1.9}{1.476455} = 1.2869 $
6. **Year 5**: $ \frac{1.9}{(1 + 0.102)^5} = \frac{1.9}{1.629158} = 1.1665 $

Now, sum these values:

\[
\text{NPV} = -10.1 + 4.0844 + 1.5633 + 1.4186 + 1.2869 + 1.1665 = -0.5803 \text{ million}
\]

### Conclusion
1. **Payback Period**: Approximately 4 years. Since this exceeds the required 2 years, we would not make the movie based on payback period criteria.
2. **NPV**: $-0.5803$ million, or $-\$580,300$, which is negative. A negative NPV means the project does not add value, so we would not proceed with the movie based on NPV either.

**Summary**: The movie does not meet the required payback period and has a negative NPV. Therefore, it would be rejected on both financial criteria.

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Would you like further details on any part of this solution? Here are some related questions to consider:

1. What factors could improve the payback period or NPV in this scenario?
2. How does the choice of discount rate affect the NPV calculation?
3. What are alternative metrics to evaluate project viability?
4. What are the limitations of using the payback period as a decision criterion?
5. How would an increase in expected cash flows affect both the payback period and NPV?

**Tip**: NPV is often preferred over the payback period because it accounts for the time value of money, while the payback period simply measures time without discounting.

You are considering making a movie. The movie is expected to cost $10.1 million up front and take a year to produce. After that, it is expected to make $4.5 million in the year it is released and $1.9 million for the following four years. What is the payback period of this investment? If you require a payback period of two years, will you make the movie? Does the movie have positive NPV if the cost of capital is 10.2%?

Analyze a movie investment with an initial cost of $10.1 million, expected revenue over five years, and a 10.2% discount rate. Learn how to calculate the payback period and determine if the investment meets a two-year requirement. Includes a step-by-step NPV calculation.

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