Question

Assume the following:

• An average movie ticket costs $12.13 today (Suppose today is 5/1/2020).

• The effective monthly nominal interest rate is 0.5%. If I save in a bank, this is the nominal

  interest rate I am going to earn.

• CPI rises by about 3% every year in the U.S. This is the pace at which the price of a movie ticket

  rises.

• Perpetuities of money and movie tickets are valuable to you because others can inherit them

  from you.

• Expand your cell to show 4 decimal places (e.g., $12.4567).

1. Taking inflation into account, what is the expected nominal price of a movie ticket in 5/1/2030?

2. How much do I have to save in the bank today, so that my bank account in 5/1/2030 is exactly enough to offer 10 tickets?

3. The movie theatre offers you a super ticket, which allows you to get a movie ticket every May 1st starting from today (5/1/2020) until 2030. So you will receive 11 tickets in total. What is the fair value of this super ticket today?

4. The movie theatre also offers you a saving plan, which gives you $20 every May 1st starting from today (5/1/2020) until 2030. So you will receive 11 payments in total. What is the fair value of this saving plan today?

Answer 1

Cost today = 12.13

inflation = 3%

Nominal price of ticket in 5/1/2030

time = 10 years

Nominal price = 12.13*(1+3%)^10 = $16.3017

How much I have to save in bank to buy 10 tickets

Cost of 10 tickets = 16.3017*10 = 163.0170

Let the amount put in bank today = A

A*(1+0.5%)^10 = 163.0170

A = $155.0859

Let FV be the fair value of super ticket

FV = 16.3017+16.3017*(1+3%)/(1+0.5%)+16.3017*((1+3%)/(1+0.5%))^2+....+16.3017*((1+3%)/(1+0.5%))^10

FV = 16.3017*(((1+3%)/(1+0.5%))^11 - 1)/((1+3%)/(1+0.5%)-1) = $203.3722

Let the fair value of saving plan be X

X = 20+20/((1+0.5%)*(1+3%))^1+20/((1+0.5%)*(1+3%))^2+....+20/((1+0.5%)*(1+3%))^10

X = 20*(1 - 1/((1+0.5%)*(1+3%))^11)/(1 - 1/((1+0.5%)*(1+3%)))

X = 186.2064