Please answer all or none! Thank You. 1 a. You believe you must withdraw $12,000

Question

Please answer all or none! Thank You.

1

a. You believe you must withdraw $12,000 per month during retirement. You plan to be retired for 30 years. Assuming your money will earn 4.5% during retirement and also assuming that you will not adjust your withdrawals for inflation, how much money will you need to have on hand on the day you retire, in order to fund your retirement?

b. A project has the following cash flows: Investment amount: $80,000 Year 1--$18,000 Year 2--$32,000 Year 3--$40,000 Year 4--$12,000. Calculate the IRR.

c. You own a business which generates $200,000 in profit per year. Someone has offered to buy it from you. Based on a 5 year projection and a belief that you could earn 9% annually if you had the money today, how much do you believe the business is worth today?

Explanation / Answer

1.

PV of annuity = P*[(1-(1+r)^(-n)) / r]

P - Periodic payment = 12000

r - rate per period = 0.045/12

n - number of periods = 30*12=360

PV of annuity = 12000*((1-(1+0.045/12)^(-360)) /0.045/12) = 2368333.91

Amount required at the time of retirement = $2368333.91

b.

IRR is the rate at which NPV = 0

NPV is calculated by discounting the cashflows

PV = C/(1+r)^n

C - Cashflow

r - Discount rate

n - years to the cashflow

NPV = -80000 + 18000/(1+IRR)^1 + 32000/(1+IRR)^2 + 40000/(1+IRR)^3 + 12000/(1+IRR)^4 = 0

By trail and error, IRR = 10.61%

c.

FInd the NPV of the cashflows

NPV = 200000/(1+0.09)^1 + 200000/(1+0.09)^2 + 200000/(1+0.09)^3 + 200000/(1+0.09)^4 + 200000/(1+0.09)^5 = $777930.25

Present worth = $777930.25

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