Question

In: Finance

Consider the following​ alternatives: i. $ 150 received in one year ii. $ 210 received in...

Consider the following​ alternatives: i. $ 150 received in one year ii. $ 210 received in five years iii. $ 350 received in 10 years

a. Rank the alternatives from most valuable to least valuable if the interest rate is 8 % per year.

b. What is your ranking if the interest rate is 3 % 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 8 % per year. First calculate the present value​ (PV) of each​ alternative: The PV of $ 150 received in one year if the interest rate is 8 % per year is ​$ ___. ​(Round to the nearest​ cent.)

The PV of $ 210 received in 5 years if the interest rate is 8 % per year is ​$___. ​(Round to the nearest​ cent.) The PV of $ 350 received in 10 years if the interest rate is 8 % per year is ​$ __. ​(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 ii ​> option iii ​> option i.

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

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

b. What is your ranking if the interest rate is only 3 % per​ year? First calculate the present value​ (PV) of each​ alternative: The PV of $ 150 received in one year if the interest rate is 3 % per year is ​$ __. ​(Round to the nearest​ cent.) The PV of $ 210 received in 5 years if the interest rate is 3 % per year is ​$ __. ​(Round to the nearest​ cent.)

The PV of $ 350 received in 10 years if the interest rate is 3 % per year is ​$ __. ​(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 i ​> option ii ​> option iii.

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

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

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

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 $ 150 received in one year if the interest rate is 14 % per year is ​$ nothing. ​(Round to the nearest​ cent.) The PV of $ 210 received in 5 years if the interest rate is 14 % per year is ​$ nothing. ​(Round to the nearest​ cent.) The PV of $ 350 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 i ​> option ii ​> option iii.

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

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

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

Solutions

Expert Solution

PV is calculated using the formula below:

where FV is the future value, r is the interest rate and n is the time period

Case 1: Interest rate = r = 8%

i. $ 150 received in one year

FV = 150, r = 8%, n = 1

PV = 150/(1+0.08)1 = 150/1.08 = 138.8889

ii. $ 210 received in five years

FV = 210, r = 8%, n = 5

PV = 210/(1.08)5 = 142.9225

Present value of 210 received after 5 years = 142.9225

iii. $ 350 received in 10 years

FV = 350, r = 8%, n = 10

Present value of 350 received after 10 years = 350/(1.08)10 = 162.1177

The PV of $ 150 received in one year if the interest rate is 8 % per year is ​$138.89 ​(Round to the nearest​ cent.)

The PV of $ 210 received in 5 years if the interest rate is 8 % per year is ​$142.92 The PV of $ 350 received in 10 years if the interest rate is 8 % per year is ​$162.12

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

Case 2: Interest rate = r = 3%

i. $ 150 received in one year

FV = 150, r = 3%, n = 1

PV = 150/(1+0.03)1 = 150/1.03 = 145.6311

ii. $ 210 received in five years

FV = 210, r = 3%, n = 5

PV = 210/(1.03)5 = 181.1478

iii. $ 350 received in 10 years

FV = 350, r = 3%, n = 10

Present value of 350 received after 10 years = 350/(1.03)10 = 260.4329

The PV of $ 150 received in one year if the interest rate is 3 % per year is ​$145.63 ​(Round to the nearest​ cent.) The PV of $ 210 received in 5 years if the interest rate is 3 % per year is ​$181.15

The PV of $ 350 received in 10 years if the interest rate is 3 % per year is ​$260.43

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

Case 3: Interest rate = r = 14%

i. $ 150 received in one year

FV = 150, r = 14%, n = 1

PV = 150/(1+0.14)1 = 150/1.14 = 131.5789

ii. $ 210 received in five years

FV = 210, r = 14%, n = 5

PV = 210/(1.14)5 = 109.0674

iii. $ 350 received in 10 years

FV = 350, r = 14%, n = 10

Present value of 350 received after 10 years = 350/(1.14)10 = 94.41033

The PV of $ 150 received in one year if the interest rate is 14 % per year is ​$131.58 The PV of $ 210 received in 5 years if the interest rate is 14 % per year is ​$109.07. The PV of $ 350 received in 10 years if the interest rate is 14 % per year is ​$94.41

The ranking of the projects​ is: option i ​> option ii ​> option iii​​​​​​​

jeff jeffy answered 1 year ago
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