Baseball cards, once viewed solely as memorabilia, have evolved into a lucrative investment market. Rare and vintage cards, especially those featuring Hall of Fame players or limited editions, can fetch significant prices at auctions and through private sales. The allure of baseball cards lies in their historical significance, rarity, and potential for appreciation over time.

Case Scenario:

Imagine a prospective investor, Alex, who is considering investing in baseball cards as a long$-$term strategy. Alex has identified a collection of vintage baseball cards from the $1950$s$,$ including rookie cards of notable players like Mickey Mantle and Willie Mays. The projected cash flows from this investment are based on the following assumptions:

Initial Investment: Alex plans to purchase the collection for $$50,000.$

Projected Cash Flows:

Year $1$: $$0($investment$)$

Year $2$: $$0($investment$)$

Year $3$: $$0($investment$)$

Year $4$: $$0($investment$)$

Year $5$: $$75,000($projected sale price$)$

The projected sale price in year $5$ reflects a conservative estimate of the collection's value based on historical appreciation rates of similar items.

Discount Rates:

The risk associated with investing in baseball cards is evaluated using variable discount rates: $10\%$ for moderate risk $($base case scenario$)$

$15\%$ for high risk $($worst$-$case scenario$)$

Time Horizon: The analysis focuses on a $5-$year time horizon, aligning with the typical holding period for such investments before revaluation.

Tasks:

$1.$ Calculate the net cash flows over the $5-$year period, considering the initial investment and the expected cash inflow from the sale of the baseball card collection.

$2.$ Apply the discount rates $(10\%$ and $15\%)$ to discount the projected cash flows back to their present value. This step allows students to assess the present value of future cash flows under different risk scenarios.

$3.$ Conduct sensitivity analysis by varying the discount rates to determine how changes in risk perception affect the investment's net present value $($NPV$)$ and internal rate of return $($IRR$).$

$4.$ Based on the analysis, advise Alex on the feasibility of investing in the baseball card collection. Consider factors such as risk tolerance, market trends, and potential for appreciation in the collectibles market