Question

Answer all questions and show your work:

1. What is the value of a financial instrument that provides constant income for 40 years of $1,500 per year? Assume a 5% discount rate.

2. What is the value of a financial instrument that provides constant income for 40 years of $4,000 per year and has costs that are $2,500 per year? Assume a 5% discount rate.

3. What is the value of a financial instrument that provides constant income forever of $1,500 per year? Assume a 5% discount rate.

4. What is the value of a financial instrument that provides constant income for 15 years of $1,500 per year? Assume a 5% discount rate.

5. What is the value of a financial instrument that provides constant income for 15 years of $1,500 per year? Assume a 15% discount rate.

6. Explain how present value differs from net present value.

7. Explain how net present value differs from an annuity.

8. Explain how net present value differs from a perpetuity.

9. Explain how a present value differs from an annuity.

Answer 1

Formula for PV of annuity is:

PV = P x [1 - (1+r) -n]/r

P = Periodic cash flow

r = Required rate

n = Number of periods

1)

P = $ 1,500, r = 0.05, n = 40

PV = $ 1,500 x [ 1 – (1+0.05)-40]/0.05]

      = $ 1,500 x [ 1 – (1.05)-40]/0.05]

      = $ 1,500 x [(1 – 0.142045682300278)/0.05]

      = $ 1,500 x (0.857954317699722/0.05)

      = $ 1,500 x 17.1590863539944

      = $ 25,738.6295309917 or $ 25,738.63

2)

Net annual cash flow = Annual income – Annual cost = $ 4,000 - $ 2,500 = $ 1,500

P = $ 1,500, r = 0.05, n = 40

PV = $ 1,500 x [ 1 – (1+0.05)-40]/0.05]

      = $ 1,500 x [ 1 – (1.05)-40]/0.05]

      = $ 1,500 x [(1 – 0.142045682300278)/0.05]

      = $ 1,500 x (0.857954317699722/0.05)

      = $ 1,500 x 17.1590863539944

      = $ 25,738.6295309917 or $ 25,738.63

3)

Formula for PV of perpetuity is:

PV = P/r

P = Periodic cash payment = $ 1,500

r = Required rate = 0.05

PV = $ 1,500/0.05 = $ 30,000

4)

P = $ 1,500, r = 0.05, n = 15

PV = $ 1,500 x [ 1 – (1+0.05)-15]/0.05]

      = $ 1,500 x [ 1 – (1.05)-15]/0.05]

      = $ 1,500 x [(1 – 0.48101709809097)/0.05]

      = $ 1,500 x (0.51898290190903/0.05)

      = $ 1,500 x 10.3796580381806

      = $ 15,569.4870572709 or $ 15,569.49

5)

P = $ 1,500, r = 0.15, n = 40

PV = $ 1,500 x [ 1 – (1+0.15)-15]/0.15]

      = $ 1,500 x [ 1 – (1.15)-15]/0.15]

      = $ 1,500 x [(1 – 0.122894485205336)/0.15]

      = $ 1,500 x (0.877105514794664/0.15)

      = $ 1,500 x 5.84737009863109

      = $ 8771.05514794663 or $ 8,771.06

6)

Present value is the current value of series of future payments or a single amount discounted at a specific rate whereas net present value is the difference between present value of future cash inflows and present value of cash outflow over a period and specific rate of return.

7)

Net present value is the difference between present value of future cash inflows and present value of cash outflow over a period and specific rate of return whereas annuity is a constant stream of cash flows over a period.

8)

Net present value is the difference between present value of future cash inflows and present value of cash outflow over a period and specific rate of return whereas perpetuity is a series of cash flows lasting forever.

9)

Present value is the current value of series of future payments or a single amount discounted at a specific rate whereas annuity is a constant stream of cash flows over a period.