To analyze this investment, let's solve the following parts:

Step 1: Calculate the NPV of the movie

Given:

• Initial investment: $C_0 = -\$10.8$ million
• Cash flows over 5 years:
  • Year 1: $C_1 = 4.7$ million
  • Years 2 to 5: $C_2 = C_3 = C_4 = C_5 = 1.6$ million each
• Cost of capital $r = 10.1\%$

The NPV formula is: $\text{NPV} = \sum_{t=1}^{5} \frac{C_t}{(1 + r)^t} - C_0$

Breaking down the cash flows:

1. Year 1: $\frac{4.7}{(1 + 0.101)^1}$
2. Years 2 to 5: Sum of $\frac{1.6}{(1 + 0.101)^t}$ for each year

Step 2: Solve for each year’s discounted cash flow and add them

Let's calculate this step by step:

1. Year 1 Discounted Cash Flow: $\frac{4.7}{1.101} = 4.27 \text{ million}$

2. Year 2 Discounted Cash Flow: $\frac{1.6}{(1.101)^2} = 1.32 \text{ million}$

3. Year 3 Discounted Cash Flow: $\frac{1.6}{(1.101)^3} = 1.20 \text{ million}$

4. Year 4 Discounted Cash Flow: $\frac{1.6}{(1.101)^4} = 1.09 \text{ million}$

5. Year 5 Discounted Cash Flow: $\frac{1.6}{(1.101)^5} = 0.99 \text{ million}$

Summing these:

$\text{Total Discounted Cash Flow} = 4.27 + 1.32 + 1.20 + 1.09 + 0.99 = 8.87 \text{ million}$

Now, subtract the initial investment to find the NPV:

$\text{NPV} = 8.87 - 10.8 = -1.93 \text{ million}$

So, with a cost of capital of 10.1%, the NPV is negative at -$1.93 million. This suggests the movie would not have a positive NPV at this cost of capital.

Step 3: Payback Period

The payback period is the time it takes to recover the initial investment from cumulative cash flows.

• Year 1 cumulative cash flow: $4.7 million
• Year 2 cumulative cash flow: $4.7 + 1.6 = 6.3$ million
• Year 3 cumulative cash flow: $6.3 + 1.6 = 7.9$ million
• Year 4 cumulative cash flow: $7.9 + 1.6 = 9.5$ million
• Year 5 cumulative cash flow: $9.5 + 1.6 = 11.1$ million

The initial investment of $10.8 million is recovered between Year 4 and Year 5, so the payback period is just over 4 years.

Since the payback period is greater than the required 2 years, you would not make the movie based on the payback period criterion.

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Would you like further details on each calculation or have other questions?

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Follow-up Questions

1. How would changing the cost of capital affect the NPV?
2. What is the impact of extending the movie's revenue period by two years on NPV?
3. How could a higher initial investment influence the payback period?
4. What is the effect of increasing cash flows in the later years on the investment's profitability?
5. How does using IRR (Internal Rate of Return) compare to the payback period method for this project?

Tip: The NPV method considers the time value of money, making it more accurate for long-term investments than the payback period.