Question

You are assessing the viability of operating an amusement park. The nominal revenues from ticket sales at the end of Year 1 will be $554176. They will increase by 4% per year in real terms. The only annual cost will be to lease the whole operation for $118845 per year. The leasing costs are nominal and will start at the end of Year 1. They will stay fixed in nominal terms.

Assume the inflation rate is 5% and the real discount rate is 10%. All cash flows occur at year-end. The company will not pay any taxes. The business will continue into perpetuity.

What is the NPV of the project?

Select one:

a. $6921840

b. $8029703

c. $9139137

d. $8940472

e. $8267772

Answer 1

Feel free to comment back in case of any query in solution.

The question clearly states that,

Growth rate = 4% (Real)

Inflation rate = 5%

Discount Rate = 10% (Real)

Revenue per year = $554176

Lease rent per year = $118845

Gross Profit Per Year = 554176 – 118845 = $435331

Taxes = 0

Net Profit per year = 435331 – 0 = $435331

We know that, By Fisher’s rule,

(1+Nominal rate) = (1+Real rate) x (1+Inflation)

(1+N) = (1+0.04) X (1+0.05)

N = 0.092 = 9.2% = Nominal Growth rate

Also, for discount rate,

(1+Nominal rate) = (1+Real rate) x (1+Inflation)

(1+D) = (1+0.1) x (1+0.05)

D = 0.155 = 15.5% = Nominal Discount Rate

Now, this is a problem of growing perpetuity where the cash flow annually is C = $435331,

Growth rate = g = 9.2% and Discount rate = R = 15.5%

The present value (PV) of growing perpetuity is = PV = C/(R-g)

PV = 435331/ (0.155-0.092) = $6,910,016              (Close to OPTION A)