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Consider the following​ alternatives: i. $130 received in one year ii. $240 received in 5 years iii. $340 received in 10 years a. Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year. b. What is your ranking if the interest rate is only 6% per​ year? c. What is your ranking if the interest rate is 19% per​ year?

Question

Consider the following​ alternatives:

i. 130receivedinoneyearii.130 received in one year ii. 240 received in 5 years iii. $340 received in 10 years a. Rank the alternatives from most valuable to least valuable if the interest rate is 10% per year. b. What is your ranking if the interest rate is only 6% per​ year? c. What is your ranking if the interest rate is 19% per​ year?

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Solution

a. To rank the alternatives based on their present value, we need to discount the future cash flows to the present using the given interest rate. The formula to calculate the present value (PV) is:

PV = FV / (1 + r)^n

where: FV = Future Value r = Interest Rate n = Number of Years

i. PV of 130receivedinoneyear=130 received in one year = 130 / (1 + 0.10)^1 = 118.18ii.PVof118.18 ii. PV of 240 received in 5 years = 240/(1+0.10)5=240 / (1 + 0.10)^5 = 149.91 iii. PV of 340receivedin10years=340 received in 10 years = 340 / (1 + 0.10)^10 = $130.85

So, the ranking from most valuable to least valuable at 10% interest rate is: ii, iii, i.

b. If the interest rate is 6% per year, the present values are:

i. PV of 130receivedinoneyear=130 received in one year = 130 / (1 + 0.06)^1 = 122.64ii.PVof122.64 ii. PV of 240 received in 5 years = 240/(1+0.06)5=240 / (1 + 0.06)^5 = 179.08 iii. PV of 340receivedin10years=340 received in 10 years = 340 / (1 + 0.06)^10 = $190.96

So, the ranking from most valuable to least valuable at 6% interest rate is: iii, ii, i.

c. If the interest rate is 19% per year, the present values are:

i. PV of 130receivedinoneyear=130 received in one year = 130 / (1 + 0.19)^1 = 109.24ii.PVof109.24 ii. PV of 240 received in 5 years = 240/(1+0.19)5=240 / (1 + 0.19)^5 = 94.56 iii. PV of 340receivedin10years=340 received in 10 years = 340 / (1 + 0.19)^10 = $65.99

So, the ranking from most valuable to least valuable at 19% interest rate is: i, ii, iii.

This problem has been solved

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