Homework 2 (DCF ch 6.1-3)

Trish receives $450 on the first of each month. Josh receives $450 on the last day of each month. Both Trish and Josh will receive payments for the next four years. At a discount rate of 9.5 percent, what is the difference in the present value of these two sets of payments?

Josh: Time 1: 450*1.095= 492.75 Time 2: (450+492.75)*1.095 ... continue through time 4 or PV = C[ (1 - 1/(1+r)^t) / r ] = 450[( 1 - 1/(1.007916)^48) / .007916) = $17,911.776 Trish: Time 0: 450*1.095= 492.75 Time 1: (450+492.75)*1.095 ... continue through time 4 => $17,911.776 Annuity due = ordinary annuity*(1+r) r= .095/12= .007916 = 17,911.776(1.007916) = $18,053.577 18,053.577 - 17,911.776 = $141.80

Assume you work for an employer who will contribute $60 a week for the next 20 years into a retirement plan for your benefit. At a discount rate of 9 percent, what is this employee benefit worth to you today?

PV = C[( 1 - 1/(1+r)^t) / r ] C= 60 t= 20*52= 1040 r= .09/52= 0.173% = 60[ 1 - (1/(1.00173)^1040) / .00173 ] = $28927.38

Southern Tours is considering acquiring Holiday Vacations, management believes Holiday Vacations can generate cash flows of $218,000, $224,000, $238,000 over the next three years, respectively. After that time, they feel the business will be worthless. If the desired rate of return is 14.5 percent, what is the maximum Southern Tours should pay today to acquire Holiday vacations?

PV = FV/(1+r)^t 218,000/1.145 + 224,000/1.145^2 + 238,000/1.145^3 = $519,799.59

You want to start a business that you believe can produce cash flows of $5600, $48200, and $125,000 at the end of each of the next three years, resepctively. At the end of three years you think you can sell the business for $250,000. At a discount rate of 16% what is the business worth today?

PV = FV/(1+r)^t 5600/1.16 + 48200/1.16^2 + 125000/1.16^3 + 250000/1.16^3 = $280,894.67

Which one of the following statements related to annuities and perpetuities is correct? a. An ordinary annuity is worth more than an annuity due given equal annual cash flows for 10 years at 7 percent interest, compounded annually b. A perpetuity comprised of $100 monthly payments is worth more than an annuity of $100 monthly payments provided the discount rates are equal c. Most loans are a form of a perpetuity d. The present value of perpetuity cannot be computed but the future value can e. Perpetuities are finite but annuities are not

b. A perpetuity comprised of $100 monthly payments is worth more than an annuity of $100 monthly payments provided the discount rates are equal

An ordinary annuity is best defined as a. increasing payments paid for a definitive period of time b. increasing payments paid forever c. equal payments paid at the end of regular intervals over a stated time period d. equal payments paid at the beginning of regular intervals for a limited time period e. equal payments that occur at set intervals for an unlimited period of time

c. equal payments paid at the end of regular intervals over a stated time period

You are comparing two investment options that each pay 6 percent interest, compounded annually. Both options will provide you with $12,000 of income. Option A pays $2,000 the first year followed by two annual payments of $5000 each. Option B pays three annual payments of $4000 each. Which of the following statements is correct given these two investment options? Assume a positive discount rate. a. Both options are of equal value since the both provide 12,000 of income b. option A has the higher future value at the end of year 3 c. option B has a higher present value at Time 0 d. option B is a perpetuity e. option A is an annuity

c. option B has a higher present value at Time 0

A perpetuity is defined as: a. a limited number of equal payments paid in even time increments b. payments of equal amounts that are paid irregularly but indefinitely c. varying amounts that are paid at even intervals forever d. unending equal payments paid at equal time intervals e. unending equal payments paid at either equal or unequal time intervals

d. unending equal payments paid at equal time intervals

You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional guaranteed $70,000 two years from today. If the applicable discount rate is 11.5% which offer should you accept and why? a. You should accept the 89,500 today because it has the higher net present value b. you should accept the 89,500 today because it has a lower future value c. You should accept the first offer as it is a lump sum payment d. you should accept the second offer because it has the larger net present value e. it does not matter, they are equally valuable

d. you should accept the second offer because it has the larger net present value FV = PV(1+r)^t 1. PV = 89500 2. PV = 35000 + 70,000/(1.115)^2 = $91,305.17

Which of the following statements correctly defines a time value of money relationship? a. time and future values are inversely related, all else held constant b. interest rates and time are positively related, all else held constant c. an increase in a positive discount rate increases the present value d. an increase in time increases the future value given a zero rate of interest e. time and present value are inversely related, all else held constant

e. time and present value are inversely related, all else held constant