Question

otal PV = $16,936.06 + $6,416.88 = $23,352.94 . Practice question 2.27 Homework • Unanswered An asset is projected to generate annual cash flows of $5,000 for the first 15 years starting one year from today followed by a final cash flow of $10,000 in the 16th year. If the discount rate is 8%, how much is this asset worth today? Round to the nearest cent. Numeric Answer: Cannot be empty Your Answer 59221.59 Answered - Incorrect 1 attempt left Resubmit [ Fullscr

Answer 1

Here we need to calculate the present value of the annual cash inflows and present value of final cash inflow in 16th year,

Present value of annual cash inflows of $5000 for first 15 years:

Here, the cash inflows will be same every year, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity, P is the periodical amount = $5000, r is the rate of interest = 8% and n is the time period = 15

Present value of cash inflows = Present value of annuity of $5000 at 8% for 15 years

Now, putting these values in the above formula, we get,

PVA = $5000 * (1 - (1 + 8%)^-15 / 8%)

PVA = $5000 * (1 - ( 1+ 0.08)^-15 / 0.08)

PVA = $5000 * (1 - ( 1.08)^-15 / 0.08)

PVA = $5000 * (1 - 0.31524170496) / 0.08)

PVA = $5000 * (0.68475829504 / 0.08)

PVA = $5000 * 8.559478688

PVA = $42797.39

Next, we will calculate present value of final cash inflow in 16th year as below:

Present value of final cash inflow of $10000:

Here we will use the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value = $10000, PV = Present value, r = rate of interest = 8%, n= time period = 16

now, putting theses values in the above equation, we get,

PV = $10000 / (1 + 8%)¹⁶

PV = $10000 / (1 + 0.08)¹⁶

PV = $10000 / (1.08)¹⁶

PV = $10000 / 3.42594264333

PV = $2918.90

Present value of cash inflows = Present value of annual cash inflows of $5000 + Present value of final cash inflow of $10000 in 16th year

Present value of cash inflows = $42797.39 + $2918.90 = $45716.29

So, the asset is worth $45716.29 today.