FIN222 Week 2 T

Sarah wants to buy a car that costs $25,000 in 4 years. If she can earn 6% annual interest on her savings, how much should she deposit today to reach her goal?

• FV = C(1+r)ⁿ

• PV = C / (1 + r)ⁿ

• PV =

  C/r [1 - 1/(1 + r)ⁿ]

• PV = C / (r - g)

Answer explanation

Correct formula is

PV = C/(1+r)ⁿ

PV=25,000/(1.06)⁴

=$19,802.38

Sarah needs to deposit $19,802.38 today to reach her goal of $25,000 in 4 years.

Du plans to save $500 at the end of each month for the next 10 years. If his investment account earns 8% annually (compounded monthly), what will be the total value of her savings at the end of 10 years?

• FV = C(1+r)ⁿ

• FV = C/r [(1 + r)ⁿ - 1)]

• PV = C/r

• PV = C/(r-g)

Answer explanation

CFs are in annuity and FV of annuity needs to be computed.

Correct formula is FV = C/r [(1 + r)ⁿ - 1)]

FV = 500/(0.08/12)[(1+ 0.08/12)^10x12 -1)]

FV=$91,473.02

Jennifer inherits a bond that pays $1,200 every year forever. If the required rate of return is 9%, what is the maximum amount she should be willing to pay for this bond today?

• PV=C/(1+r)ⁿ

• PV=C/r [1-1/(1+r)ⁿ]

• PV= C/r

• PV = C/(r-g)

Answer explanation

CFs are in perpetuity. PV of Perpetuity needs to be computed.

PV= C/r

=1200/0.09 = $13,333.33

A company expects to receive $15,000 at the end of each year for the next 8 years from a new contract. If the discount rate is 12%, what is the present value of these future cash flows?

• PV = C /(1+r)ⁿ

• PV=C/r [1-1/(1+r)ⁿ]

• PV= C/r

• PV = C/(r-g)

Answer explanation

CFs are in annuity and PV of Annuity needs to be computed.

PV=C/r [1-1/(1+r)ⁿ]

PV=15,000/0.12[1-1/(1.12)⁸]

=$74,514.64

ABC Corporation's dividend is expected to be $2.50 next year and is projected to grow at 4% annually forever. If investors require a 10% return, what should be the current stock price?

• PV= C/(1+r)ⁿ

• PV= C/r [1-1/(1+r)ⁿ]

• PV = C/r

• PV= C/(r-g)

Answer explanation

CFs are in growing perpetuity.

PV = C /(r-g)

PV = 2.5/(0.1-0.04)

=$41.67