You are building a new movie theater in Atlantic Station, and have two options.

Question

You are building a new movie theater in Atlantic Station, and have two options. The first is to build a large theater for $1.7 million that will generate $350,000 in profit a year. The other option is to build a smaller theater for $800,000 that will generate S160,000 in profit a year. Assume that revenue is equally distributed over the year Using the payback method without discounting future cash flows, which option would you choose? Using the discounted payback method at an interest rate of 3% per year, which option would you choose?

Explanation / Answer

The payback period of an investment is number of years required to recover our initial investment based on the project's expected cash flows.

(A) Decision using payback method without discounting future cash flows

For the theater project -1 : The initial investment is $1.7 million and profit is $0.35 million per year.

For the theater project -2 : The initial investment is $0.8 million and profit is $0.16 million per year.

Assuming that revenue is equally distributed over the year, payback period for project 1 -

PBP1 = 1.7/0.35 =4.86 years

Similarly payback period for project 2 will be-

PBP2 = 0.8/0.16 =5 years

Here we can see that PBP1 < PBP2, hence theater project with investment of $1.7 million should be chosen over theater project of $0.8 million.

(B) Decision using payback method after discounting future cash flows at internal rate of return of 3% per annum

For theater project 1, the initial cash outflow is $1.7 million and future cash inflow is $0.35 million per annum.

Taking discount rate of 3% per annum, the payback period for the project would be the time in which discounted cash flow stream or net present value of the future profits would be equal to $1,700,000.

or say, 1700000 = 350000*[ (1- {1/(1.03)n}/0.03], where n is number of years (payback period)

Solving this equation for 'n':

1- {1/(1.03)n}/0.03= 1700000/350000

or say 1- {1/(1.03)n}/0.03= 4.86

or say 1- {1/(1.03)n} = 4.86*0.03

or say 1- {1/(1.03)n} = 0.146

or say  1/(1.03)n = 1 - 0.146

or say 1/(1.03)n = 0.854

or say n(ln 1.03)= ln 0.854

'ln' refers to natural logarithms.

or say n = ln 0.854 / ln 1.03 = 5.34 Years

Hence PBP1 = 5.34 Years

Similarly for Project 2 we calculate PBP2 as follows.

800000 = 160000*[ (1- {1/(1.03)n}/0.03], where n is number of years (payback period)

Solving this equation for 'n':

1- {1/(1.03)n}/0.03= 800000/160000

or say 1- {1/(1.03)n}/0.03= 5

or say 1- {1/(1.03)n} = 5*0.03

or say 1- {1/(1.03)n} = 0.15

or say  1/(1.03)n = 1 - 0.15

or say 1/(1.03)n = 0.85

or say n(ln 1.03)= ln 0.85

'ln' refers to natural logarithms.

or say n = ln 0.85 / ln 1.03 = 5.5 Years

Hence PBP2 = 5.5 Years

Here again we can see that PBP1 < PBP2, hence theater project with investment of $1.7 million should be chosen over theater project of $0.8 million.

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