Question

Suppose today is Dec 31st, 2020, and as always, today is time t=0. Prithu wants to buy a $20 million yacht. The dealer is offering the following scheme. Pay $2 million as down payment today and borrow $18 million from the dealership at 18% per year and payoff the loan in 4 yearly installments, the first installment is due one year from now, meaning December 31, 2021. If he agrees to the scheme, he will receive the delivery of the brand-new luxury yacht, exactly 2 years from today, meaning on December 31, 2022. Prithu also estimates that dockage charges, crew salary, insurance, fuel and general maintenance of the yacht that cost $1.2 million per year today will escalate by 3% per year. He takes the deal.

a) Suppose it is December 31, 2025 now. Looking back, how much in total will he have spent on the yacht over the last 5 years? (Hint: In other words, what is the simple sum of all the amounts he has spent toward the yacht in these 5 years?)

b) Realizing that he ended up spending way more than he had budgeted, he now wants to sell the yacht on December 31, 2025. The yacht can be rented out on a monthly basis starting January 2026, with the first rent accruing on Jan-31, 2026. He estimates that he can rent out the yacht at $300,000 per month, which grows at 5% per month, for a total of 60 months (after which the yacht needs to be scrapped at a salvage value of $500,000). If the rate of interest is still 18% per year, what is the price he can expect to sell the yacht for on December 31, 2025?

Answer 1

Annual payment towards debt servicing = PMT (Rate, Nper, PV, FV) = PMT (18%, 4, -18, 0) = $ 6.69 million

Part (a)

Hence, the total spent on the yacht over the last 5 years = Own contribution + Annual payment x number of payment + Yacht operating costs in year 3 + Yacht operating costs in year 4 + Yacht operating costs in year 5 = 2 + 6.69 x 4 + 1.2 x (1 + 3%)³ + 1.2 x (1 + 3%)⁴ + 1.2 x (1 + 3%)⁵​​​​​​​ = $ 32.82 million (= $ 32,818,196.17, if you want the figures in $ and cents)

Part (b)

Interest rate per month = 18%/12 = 1.5%

Price = PV of growing annuity

Hence, price = 300,000 / (1.5% - 5%) x [1 - {(1 + 5%)/(1 + 1.5%)}⁶⁰] = $  56,959,846.70