Question

You are considering making a movie. The movie is expected to cost $ 10.3 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 $ 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 10.6 %​?

Answer 1

a) Calculation of Payback Period

Year	Cash Flows	Cumulative Cash flows
0	$(10,300,000)	$(10,300,000)
1	$4,100,000	$(6,200,000)
2	$1,900,000	$(4,300,000)
3	$1,900,000	$(2,400,000)
4	$1,900,000	$(500,000)
5	$1,900,000	$1,400,000

Step 1 : Calculate the Cumulative net cash flow.

Step 2 : Calculation of Pay back Period  

Payback Period = A +B/C

where,
A is the last period number in which cash flow is negative or 0 (i.e..., 4)
B is the absolute cumulative net cash flow (ignoring negative sign) at the end of the period A (i.e..., 500,000)
C is the total cash inflow during the period next to period A  (i.e..., 1900,000)

Payback Period = 4 + 500,000/ 1900,000
Payback Period = 4 + 0.2631579
Payback Period = 4.26 years

Decision: Desired payback period of the project is 2 years. However, the Payback period calculated comes to 4.26 years which is higher. Therefore ,we should not accept the project.

b) Calculation of NPV if the cost of capital is 10.6 %

NPV = Present Value of Cash Inflows - Present Value of Cash Outflows

Year	Cash Flows	[email protected]%	Present Value
0	$(10,300,000)	1	($10,300,000.00)
1	$4,100,000	0.904159132	$3,707,052.44
2	$1,900,000	0.817503736	$1,553,257.10
3	$1,900,000	0.739153468	$1,404,391.59
4	$1,900,000	0.668312358	$1,269,793.48
5	$1,900,000	0.604260722	$1,148,095.37
		NPV	($1,217,410.02)

NPV if the cost of capital is 10.6 % is negative

Note :
PVF(r,t) = (1/(1+r))^n