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.)
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.
To calculate the payback period, we need to determine when the cumulative cash inflows equal or surpass the initial investment. Let's calculate the payback period step-by-step:
1. Subtract the upfront cost from the annual cash inflows for each year:
Year 1: $4.1 million - $10.4 million = -$6.3 million (negative value)
Year 2: $2.1 million
Year 3: $2.1 million
Year 4: $2.1 million
Year 5: $2.1 million
2. Determine the cumulative cash inflows for each year:
Year 1: -$6.3 million
Year 2: -$6.3 million + $2.1 million = -$4.2 million
Year 3: -$4.2 million + $2.1 million = -$2.1 million
Year 4: -$2.1 million + $2.1 million = $0 million (breakeven point)
Year 5: $0 million + $2.1 million = $2.1 million
From the calculation above, we can see that the breakeven point is reached in Year 4. Therefore, the payback period is 4 years.
To determine if the movie has a positive NPV with a required payback period of two years and a cost of capital of 10.2%, we need to calculate the net present value (NPV) first:
1. Calculate the present value of the cash inflows:
Year 1: $4.1 million / (1 + 0.102) = $3.71 million
Year 2: $2.1 million / (1 + 0.102)^2 = $1.77 million
Year 3: $2.1 million / (1 + 0.102)^3 = $1.55 million
Year 4: $2.1 million / (1 + 0.102)^4 = $1.34 million
Year 5: $2.1 million / (1 + 0.102)^5 = $1.16 million
2. Calculate the present value of the initial investment (outflow):
$10.4 million / (1 + 0.102)^1 = $9.43 million
3. Calculate the NPV by summing the present values of cash inflows and subtracting the present value of the initial investment:
NPV = $3.71 million + $1.77 million + $1.55 million + $1.34 million + $1.16 million - $9.43 million = -$0.9 million
The NPV is negative, indicating that the movie does not have a positive NPV. Therefore, if you require a payback period of two years and the cost of capital is 10.2%, you should not make the movie.