Question

Assume there is index of the vacation cruise industry. Assume further that its value decreased due to the COVID-19 to $1800 per share, which represents about 30% of its end of 2019 value. The industry is not expected to fully recover this year and expected FCF per share will be -$80 in 2020, $140 in 2021 and grows at a constant annual rate of 5% thereafter. The appropriate discount rate to value the index is 12%. a) should an investor long or short this index? Show work. b) what minimum growth rate in FCF beyond 2021 would warranty longing this index?

Answer 1

a]

Value of stock = present value of next 2 years FCF + present value of terminal value at end of 2 years

Terminal value at end of 2 years = Year 2 FCF * (1 + growth rate after 2 years) / (discount rate - growth rate after 2 years)

Present value = future value / (1 + required return)^{number of years}

Value of index today = $1,714.29

An investor should short the index as the actual market value is higher than the value calculated above.

b]

To long the index, the value calculated above should be higher than the market value of $1,800.

We use GoalSeek in Excel to find the growth rate at which the value of the index is at least $1,801.

To warrant longing the index, the minimum growth rate should be 5.32%