Solve for the unknown number of years in each of the following (Do not round int

Question

Solve for the unknown number of years in each of the following (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)): Present Value Years Interest Rate Future Value Imprudential, Inc. has an unfunded pension liability of $565 million that must be paid in 15 years. To assess the value of the firm?s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 5.8 percent, what is the present value of this liability? (Enter your answer in dollars not in millions. Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Present value $ value: Bob bought some land costing $15,990. Today, that same land is valued at $46,017. How long has Bob owned this land if the price of land has been increasing at 5 percent per year? 23.85 years 13.70 years 22.71 years 14.39 years 21.67 years

Explanation / Answer

1) We need to find the time period(N) in which the initial investment of $15,990(PV) compounded to $46,017(FV) when the interest rate is 5%(I/Y).

Solving for N using the formula: FV = PV * (1 + I/Y)N

$46,017 = $15,990 * (1.05)N

2.8779 = (1.05)N

N = 21.67 years is the time period since Bob has owned this land.

2) We need to find the PV of the unfunded liability of $565,000,000(FV) which much be paid in 15 years(N) when the interest rate is 5.8%(I/Y).

Solving for PV using the formula: PV = FV / (1 + I/Y)N

PV = $565,000,000 / (1.058)15

PV = $565,000,000 / 2.3296

PV = $242,528,863.39 is the PV of the unfunded liability which must be paid in 15 years.

3) As we know: FV = PV * (1 + I/Y)N

Where FV = Future value of the investment.

PV = Present value of the investment

I/Y = Interest rate per period

N = Number of compounding periods

a) Solving for N when PV = $640, FV = $1,886 and I/Y = 10%

$1,886 = $640 * (1.10)N

N = 11.34 years.

b) Solving for N when PV = $890, FV = $2,349 and I/Y = 11%

$2,349 = $890 * (1.11)N

N = 9.30 years.

c) Solving for N when PV = $19,200, FV = $292,799 and I/Y = 16%

$292,799 = $19,200 * (1.16)N

N = 18.36 years.

d) Solving for N when PV = $22,300, FV = $337,837 and I/Y = 13%

$337,837 = $22,300 * (1.13)N

N = 22.24 years.

We can also solve the above problem using a financial calculator entering thr PV amount as a negative amount(as it is a cash outflow), entering the FV amount as a positive amount(as it is a cash inflow) and finally entering the interest rate and compute for N which will be the time period.

I hope my solution solves your query.

Regards.

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