Question

You are considering making a movie. The movie is expected to cost $10.4 million up front and take a year to produce. After that, it is expected to make $4.1 million in the year it is released and $2.1 million for the following four years. What is the payback period of this investment? If you require a payback period of two your the the movie have positive NPV if the cost of capital is 10.2% ? What is the payback period of this investment? The payback period is years. (Round to one decimal place.) If you require a payback period of two years, will you make the movie? (Select from the drop-down menu.) Does the movie have positive NPV if the cost of capital is 10.2% ? If the cost of capital is 10.2%, the NPV is $ million. (Round to two decimal places.)

Answer 1

To calculate the payback period, we need to determine when the cumulative cash flow equals or exceeds the initial investment.

The cash flows for the movie are as follows:
Year 0: -$10.4 million (initial investment)
Year 1: $4.1 million
Year 2: $2.1 million
Year 3: $2.1 million
Year 4: $2.1 million
Year 5: $2.1 million

To calculate the cumulative cash flow for each year:
Year 1: $4.1 million
Year 2: ($10.4 million - $4.1 million) + $2.1 million = -$2.3 million
Year 3: ($10.4 million - $2.3 million) + $2.1 million = -$0.2 million
Year 4: ($10.4 million - $0.2 million) + $2.1 million = $1.5 million
Year 5: ($10.4 million - $1.5 million) + $2.1 million = $0.2 million

The payback period is the point at which the cumulative cash flow becomes positive, which occurs at the end of Year 4. Therefore, the payback period is 4 years.

To determine if the movie has a positive net present value (NPV) at a cost of capital of 10.2%, we need to discount the cash flows and subtract the initial investment.
Applying a discount rate of 10.2%, the discounted cash flows are as follows:
Year 0: -$10.4 million
Year 1: $4.1 million / (1+0.102)^1 = $3.71 million
Year 2: $2.1 million / (1+0.102)^2 = $1.80 million
Year 3: $2.1 million / (1+0.102)^3 = $1.62 million
Year 4: $2.1 million / (1+0.102)^4 = $1.46 million
Year 5: $2.1 million / (1+0.102)^5 = $1.31 million

The discounted cash flows are as follows:
Year 0: -$10.4 million
Year 1: $3.71 million
Year 2: $1.80 million
Year 3: $1.62 million
Year 4: $1.46 million
Year 5: $1.31 million

Now, we sum up the discounted cash flows:
NPV = -$10.4 million + $3.71 million + $1.80 million + $1.62 million + $1.46 million + $1.31 million = $0.50 million

The NPV at a cost of capital of 10.2% is $0.50 million.

Since the payback period of this investment is 4 years (less than the required 2-year payback period), you should make the movie.

However, since the NPV at a cost of capital of 10.2% is $0.50 million (greater than zero), the movie has a positive NPV.