Topic 5 - TVM

What is the present value of an ordinary annuity with the payments of $500 for 3 years if the discount rate is 10%? $1,243.43 $1,367.77 $1,655.00 $1,820.55

1,243.43 PVAordinary = PMT [(1-{1/(1+r)n})/r] = 500 [(1-{1/(1.10)3})/0.10] = $1,243.43 [Calculator: 500 PMT, 10 I/Y, 3 N, compute PV].

Today is your 30th birthday. As luck would have it, you also welcome a new baby into your home as your birthday present. You desire to provide some financial support for your baby in 18 years and a lump sum of money when you retire at the age of 60. Four years of college tuition costs a total of $21,657 in today's dollars. Additionally, you desire to have purchasing power of $1,000,000 (at today's value) when you retire. If the average inflation rate is 2% and you can earn 8% on your account, how much do you need in your account today to cover your baby's future college tuition and your retirement goal? (allow $5 rounding error)

Answer: $187,749· Step 1: $21657 in 18 years = FV = PV(1+r)t = 21657(1+0.02)18 = $30931.53· Step 2: $1,000,000 in 30 years = FV = PV(1+r)t = 1000000(1+0.02)30 = $1,811,362· Step 3: Discount tuition for 18 years = FV = PV(1+r)t = 30931.53/(1+0.08)18 = $7741· Step 4: Discount retirement for 30 years = PV = FV/(1+r)t = 1811362/(1+0.08)30 = $180,008Step 5: Add PVs together; Total amount needed today = $7741 + 180008 = $187,749.

You just turned 25 and graduated from a university. You are already thinking about your retirement. You want to have $500,000 in today's dollar value when you retire. You have a lot of savings today and you were wondering if the savings may be enough if you invest wisely. You are anticipating an average inflation rate of 2% and you can earn 10% return on average. If you retire 40 years from now, how much savings do you need to have today to reach your goal?

Answer: $24,393First, you need to find the future value of $500,000 with the inflation rate. Then you need to find how much you need today if you can earn 10% a year for 40 years.Step 1: FV = PV(1+r)t = 500000(1+0.02)40 = $1,104,020[calculator: 500000 PV, 2 I/Y, 40 N, compute FV]Step 2: PV = FV/(1+r)t = 1104020/(1+0.10)40 = $24,393[calculator: 1104020 FV, 10 I/Y, 40 N, compute PV]

You have a 5 year old son. You want to provide financial help when he goes to college in 13 years. You are planning to give him $20,000 a year at the beginning of each year during his 4 years of college. How much do you have to set aside today if you can earn annual interest of 5% in an account you deposit the money? $24,904 $39,490 $42,426 $37,610

Answer: $39,490Step 1:PV: ($74,464.96)FV: 0PMT 20000N: 4I: 5%Mode: 1 (Begin) Step 2:PV: ($39,490.36)FV: $74,464.96PMT: 0N: 13I: 5%Mode: 0

What is the present value of an ordinary annuity with the payment of $300 for 5 years if the discount rate is 10%? $1,530.30 $1,228.53 $1,137.24 $1,831.53

Correct Answer: $1,137.24 PVAordinary = PMT [(1-{1/(1+r)n})/r] = 300 [(1-{1/(1.10)5})/0.10] = 1,137.24

What is the future value of an ordinary annuity with payments of $300 for 5 years if the discount rate is 10%? $1,831.53 $1,228.53 $1,530.30 $1,137.24

Correct Answer: $1,831.53 FVAordinary = PMT [({1+r}n - 1)/r] = 300 [({1.10}5 - 1)/0.10] = 1831.53 [Calculator: 300 PMT, 5 N, 10 I/Y, compute FV]

You calculated the present value of an ordinary annuity to be $10,000. The discount rate is 10%. Which of the following is the most likely solution for the present value of an annuity due with the same cash flows? $9,500 $9,000 $11,000 $10,000

Correct Answer: $11,000 If the stream of cash flows are the same between ordinary annuities and annuities due, then the present value of an annuity due must be higher. (The annuity due method shifts payments closer to time 0 which means the cash flows are discounted less).

Your grandparents decided to give you $3,500 a year at the beginning of each year for 4 years while you are in college. If instead they were to give you an equivalent single sum today, how much would they have to give you today? Assume that the discount rate is 6%. $12,127.87 $16,229.83 $15,311.16 $12,855.54

Correct Answer: $12,855.54 PV: ($12,855.54) FV: 0 PMT: 3500 N: 4 I: 6% Mode: 1 (Begin)

During all 4 years of your college life, you save $3,000 a year at the end of each year. If you can earn a 6% annual return on your investment, how much will you have when you graduate in 4 years? $12,000 $10,395 $13,124 $13,911

Correct Answer: $13,124 PV: 0 FV: $13,123.85 PMT: -3000 N: 4 I: 6% Mode: 0(End)

Starting on your child's 10th birthday, you plan to make annual contributions of $1,994.70 to an account that earns a 5% annual return. Your final contribution will be on your child's 17th birthday. How much will your child have in the account when they start college on their 18th birthday? $20,000 $21,995 $19,048 $23,094

Correct Answer: $20,000 PV: 0 FV: ($20,000) PMT: 1,994.70 N: 8 I: 5% Mode: 1 (Begin)

Your friend will retire a year from today and she is hoping to have enough in her retirement account for her to withdraw $50,000 each year for 15 years with the first withdrawal coming on the day she retires (i.e., one year from today). She does not plan to contribute any money during her final year before retirement. She has been earning 7% return on her retirement account and is assuming that will continue in the future. How much should she have today in her account? $467,883 $437,273 $487,273 $455,396

Correct Answer: $455,396 PV: ($455,395.70) FV: 0 PMT: 50000 N: 15 I: 7% Mode: 0

You just turned 20 years old today and started thinking about retirement savings. If you deposit $2,000 at the end of each year into an account earning annual interest of 8%, how much will you have if you retire in 40 years? $559,562 $427,219 $518,113 $399,270

Correct Answer: $518,113 PV: 0 FV: ($518,113.04) PMT: 2000 N: 40 I: 8% Mode: 0

You are planning to go on a great vacation when you retire in 30 years. You calculated the travel expense for several potential trips. To fund the travel, you decided to save $100 a year (starting at the end of the current year) for 30 years in an account with an annual interest rate of 7.5%. You want to use all of the savings for the trip. Which of the following four countries is the choice that is both feasible and will come closest to exhausting your savings? Japan - cost of $10,000. Australia - cost of $12,000. France - cost of $11,000. Brazil - cost of $9,000.

Correct Answer: Japan - cost of $10,000. PV FV PMT N I Mode - ($10,339.94) 100.00 30 7.50% 0 (End) Calculator: PV: 0. PMT: 100, N: 30, I: 7.5%, Mode: 0, solve for FV: $10,339.94.

Cost of Capital

How much it costs the firm (in percentage terms) to finance its operations through debt and/or equity.

Your professor just talked about going on a trip when he retires in 10 years. He anticipates the cost of the trip to be $10,000. He said he will deposit some money today so that he will have $10,000 in 10 years. If he can earn an annual rate of 5% on his account, how much does he have to set aside today? $19,672 $5,847 $6,139 $21,049

Put calculator as BGN then input and CPT for PV

Discount rate formula

R = Real risk - free rate + Inflation + Risk Premium

Define Real risk - free rate Inflation and Risk Premium

Real risk - free rate = The rate earned on riskless investments with 0% inflation. Inflation = Annual decay in the purchasing power of money. Risk Premium = Compensation for bearing the risk of a particular investment.

If you were to set up a perpetual educational fund for your family which will pay $5,000 a year forever, how much do you have to set a side today? Assume the appropriate discount rate is 8%. $62,500 $65,000 $67,500 $70,000

The correct answer is $62,500. PVperpetuity = PMT/I = 5000/0.08 = $62,500

Time value money def

The process of valuing money at specific points in time.

Discount rate definition

The rate at which money is discounted or compounded.

annuity

an equally spaced series of cash flows all of the same magnitude. That is, payments of $100 at time 1, time 2, and time 3 would be a three-period, $100-per-payment annuity.

Perpetuities is a

annuity that lasts forever, associated with charitable giving

annuities due assume the payments

come at the beginning of the period.