Calculate the Value of a Portfolio: Annuity and Perpetuity Calculation

C

The value of the perpetuity is 300/0.09 = 3,333. The annuity is worth (250/0.09)*(1-1/(1.09^6)) = 1,121 The portfolio is thus worth 1,121 + 3,333 = 4,454

To calculate the present value of the portfolio, we need to discount the future cash flows using the given discount rate of 9% per year.

Let's break down the problem step by step:

Step 1: Calculate the present value of the annuity.

The annuity is a six-year annuity paying $250 a year. The formula to calculate the present value of an annuity is:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where: PV = Present value C = Cash flow per period r = Discount rate per period n = Number of periods

Using the given values, we have: C = $250 r = 9% = 0.09 (as a decimal) n = 6

Plugging the values into the formula, we get:

PV_annuity = $250 * [(1 - (1 + 0.09)^(-6)) / 0.09] = $250 * [(1 - 0.5626821) / 0.09] = $250 * (0.4373179 / 0.09) = $250 * 4.8590757 = $1,214.77 (rounded to the nearest cent)

Step 2: Calculate the present value of the perpetuity.

The perpetuity pays $300 a year indefinitely. The formula to calculate the present value of a perpetuity is:

PV = C / r

Where: PV = Present value C = Cash flow per period r = Discount rate per period

Using the given values, we have: C = $300 r = 9% = 0.09 (as a decimal)

Plugging the values into the formula, we get:

PV_perpetuity = $300 / 0.09 = $3,333.33 (rounded to the nearest cent)

Step 3: Calculate the total present value of the portfolio.

To calculate the total present value of the portfolio, we sum the present values of the annuity and perpetuity:

Total PV = PV_annuity + PV_perpetuity = $1,214.77 + $3,333.33 = $4,548.10 (rounded to the nearest cent)

Therefore, the portfolio is worth approximately $4,548.10. Among the given answer choices, the closest value is C. $4,454.