7. One year ago, you purchased a rare Indian-head penny for $14,000. Because of the
recession and the need to generate current income, you plan to sell the coin and
invest in Treasury bills. The Treasury bill yield now stands at 8 percent, although it
was 7 percent one year ago. A coin dealer has offered to pay you $12,800 for the
coin. Compute the holding period return on this investment.
To compute the holding period return on this investment, you need to calculate the percentage change in value over the holding period, which is one year in this case. Here are the steps to follow:
Step 1: Calculate the initial value of the investment.
The initial value is the purchase price of the rare Indian-head penny, which is $14,000.
Step 2: Calculate the final value of the investment.
The final value is the amount the coin dealer is offering to pay you for the coin, which is $12,800.
Step 3: Calculate the income received from the investment.
Since you plan to invest the proceeds from selling the coin in Treasury bills, and the Treasury bill yield is 8 percent, you can calculate the income received as follows:
Income = Initial value * Treasury bill yield
Income = $14,000 * 8% = $1,120
Step 4: Compute the holding period return.
Holding Period Return = (Final value + Income - Initial value) / Initial value * 100
Holding Period Return = ($12,800 + $1,120 - $14,000) / $14,000 * 100
Holding Period Return = -$80 / $14,000 * 100
Holding Period Return = -0.57%
The holding period return on this investment is -0.57%.
To compute the holding period return on this investment, we need to calculate the total return and divide it by the initial investment.
First, let's calculate the total return. It is given by the formula:
Total Return = (Ending Value - Beginning Value + Income) / Beginning Value
Beginning Value = $14,000 (the purchase price of the coin)
Ending Value = $12,800 (the selling price offered by the dealer)
Income = $14,000 x (8% - 7%) = $140 (the interest earned from investing in Treasury bills)
Total Return = ($12,800 - $14,000 + $140) / $14,000
Now, let's calculate the holding period return.
Holding Period Return = Total Return / Beginning Value
Holding Period Return = [($12,800 - $14,000 + $140) / $14,000] / $14,000
Simplifying the expression:
Holding Period Return = ($12,800 - $14,000 + $140) / ($14,000 x $14,000)
Holding Period Return = -$60 / ($14,000 x $14,000)
Holding Period Return = -0.000030612
Therefore, the holding period return on this investment is approximately -0.000030612.