Question

Consider the following​ alternatives: i. $ 100 received in one year ii. $ 230 received in five years iii. $ 300 received in 10 years a. Rank the alternatives from most valuable to least valuable if the interest rate is 9 % per year. b. What is your ranking if the interest rate is 1 % per​ year? c. What is your ranking if the interest rate is 14 % per​ year? a. Rank the alternatives from most valuable to least valuable if the interest rate is 9 % per year. First calculate the present value​ (PV) of each​ alternative: The PV of $ 100 received in one year if the interest rate is 9 % per year is ​$ nothing. ​(Round to the nearest​ cent.) The PV of $ 230 received in 5 years if the interest rate is 9 % per year is ​$ nothing. ​(Round to the nearest​ cent.) The PV of $ 300 received in 10 years if the interest rate is 9 % per year is ​$ nothing. ​(Round to the nearest​ cent.) ​Next, rank the choices by their​ PV:  ​(Select the best choice​ below.)

A. The ranking of the projects​ is: option iii ​> option ii ​> option i. B. The ranking of the projects​ is: option i ​> option iii ​> option ii. C. The ranking of the projects​ is: option ii ​> option iii ​> option i. D. The ranking of the projects​ is: option ii ​> option i ​> option iii.

b. What is your ranking if the interest rate is only 1 % per​ year? First calculate the present value​ (PV) of each​ alternative: The PV of $ 100 received in one year if the interest rate is 1 % per year is ​$ nothing. ​(Round to the nearest​ cent.) The PV of $ 230 received in 5 years if the interest rate is 1 % per year is ​$ nothing. ​(Round to the nearest​ cent.) The PV of $ 300 received in 10 years if the interest rate is 1 % per year is ​$ nothing. ​(Round to the nearest​ cent.) Next rank the choices by their​ PV:  ​(Select the best choice​ below.) A. The ranking of the projects​ is: option iii ​> option i ​> option ii. B. The ranking of the projects​ is: option i ​> option ii ​> option iii. C. The ranking of the projects​ is: option ii ​> option iii ​> option i. D. The ranking of the projects​ is: option iii ​> option ii ​> option i.

c. What is your ranking if the interest rate is 14 % per​ year? First calculate the present value​ (PV) of each​ alternative: The PV of $ 100 received in one year if the interest rate is 14 % per year is ​$ nothing. ​(Round to the nearest​ cent.) The PV of $ 230 received in 5 years if the interest rate is 14 % per year is ​$ nothing. ​(Round to the nearest​ cent.) The PV of $ 300 received in 10 years if the interest rate is 14 % per year is ​$ nothing. ​(Round to the nearest​ cent.) Next rank the choices by their​ PV: ​(Select the best choice​ below.)

A. The ranking of the projects​ is: option ii ​> option i ​> option iii. B. The ranking of the projects​ is: option iii ​> option i ​> option ii. C. The ranking of the projects​ is: option i ​> option ii ​> option iii. D. The ranking of the projects​ is: option ii ​> option iii ​> option i.

Click to select your answer(s).

Answer 1

Net Present Value = Cash Flow / (1+i)ⁿ

a) interest rate = 9%

i) PV of $100 in one year = 100/(1+0.09)¹ = $91.74

ii) PV of $230 in 5 years = 230/(1 + 1.09)⁵ = $149.48

iii) PV of $300 in 10 years = 300/(1 + 1.09)¹⁰ = $126.72

therefore ranking : ii>iii>i

b) interest rate = 1%

i) PV of $100 in one year = 100/(1+0.09)¹ = $99.01

ii) PV of $230 in 5 years = 230/(1 + 1.09)⁵ = $218.84

iii) PV of $300 in 10 years = 300/(1 + 1.09)¹⁰ = $271.59

therefore ranking : iii>ii>i

c) interest rate = 14%

i) PV of $100 in one year = 100/(1+0.09)¹ = $87.72

ii) PV of $230 in 5 years = 230/(1 + 1.09)⁵ = $119.45

iii) PV of $300 in 10 years = 300/(1 + 1.09)¹⁰ = $80.92

therefore ranking : ii>i>iii