Consider the following alternatives: i. $100 received in one year ii. $240 recei

Question

Consider the following alternatives: i. $100 received in one year ii. $240 received in five years ili $340 received in 10 years a. Rank the alternatives from most valuable to least valuable if the interest rate is 12% per year. b. What is your ranking if the interest rate is 5% per year? C. What is your ranking if the interest rate is 17% per year? a. Rank the alternatives from most valuable to least valuable if the interest rate is 12% per year First calculate the present value (PV) of each alternative: The PV of $100 received in one year if the interest rate is 12% per year is $ (Round to the nearest cent) The PV of $240 received in 5 years if the interest rate is 12% per year is $ (Round to the nearest cent) The PV of $340 received in 10 years if the interest rate is 12% per year is $ 1 (Round to the nearest cent) Next, rank the choices by their PV. (Select the best choice below.) O A. The ranking of the projects is: option ii > option i > option ii O B. The ranking of the projects is: option ii >option ii> option i. O C. The ranking of the projects is: option i> option ii> option ii O D. The ranking of the projects is: option ii >option ii >option i. b. What is your ranking if the interest rate is only 5% per year?

Explanation / Answer

PV and FV are related as:

PV = FV/ (1+r)n

Where r is rate of discount and n is the no. of period

a. r = 12 % or 0.12

i)PV of $ 100 received in one year = $ 100/ (1+0.12) = $ 100/1.12 = $ 89.29

ii) PV of $ 240 received in five year = $ 240/ (1+0.12)5 = $ 240/ (1.12)5 = $ 240/ = $ 136.18

iii) PV of $ 340 received in ten year = $ 340/ (1+0.12)10 = $ 340/ (1.12)10 = $ 340/ = $ 109.47

    Ranking:

      $ 136.18 > $ 109.47 > $ 89.29

Correct answer:

D. The ranking of projects is: option ii > option iii > option i

b. r = 5 % or 0.05

i)PV of $ 100 received in one year = $ 100/ (1+0.05) = $ 100/1.05 = $ 95.24

ii) PV of $ 240 received in five year = $ 240/ (1+0.05)5 = $ 240/ (1.05)5 = $ 240/ = $ 188.05

iii) PV of $ 340 received in ten year = $ 340/ (1+0.05)10 = $ 340/ (1.05)10 = $ 340/ = $ 208.73

    Ranking:

      $ 208.73 > $ 188.05 > $ 95.24

Correct answer:

B. The ranking of projects is: option iii > option ii > option i

c. r = 17 % or 0.17

i)PV of $ 100 received in one year = $ 100/ (1+0.017) = $ 100/1.17 = $ 85.47

ii) PV of $ 240 received in five year = $ 240/ (1+0.17)5 = $ 240/ (1.17)5 = $ 240/ = $ 109.47

iii) PV of $ 340 received in ten year = $ 340/ (1+0.17)10 = $ 340/ (1.17)10 = $ 340/ = $ 70.73

    Ranking:

      $ 109.47 > $ 85.47 > $ 70.73

Correct answer:

A. The ranking of projects is: option ii > option i > option iii

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