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.

---

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.