Question

Time value of money:
Consider the following three alternatives.
105 in one year, 120 in 5 years, and 135 in 10 years. Rank the alternatives from most to least valuable if the interest rate is; (i) 1%, (ii) 3%, and (iii) 5%.

Answer 1

Answer:

Ranking from Most to least

(i) 1%,

1. 135 in 10 years = 122.21

2. 120 in 5 years = 114.18

3. 105 in one year = 103.96

(ii) 3%

1. 120 in 5 years = 103.51

2. 105 in one year = 101.94

3. 135 in 10 years = 100.45

(iii) 5%

1. 105 in one year = 100.00

2. 120 in 5 years = 94.02

3. 135 in 10 years = 82.88

Explanation:

(i) 1%,

105 in one year

PV = 105 x ((1+0.01)^-1) = 103.96

120 in 5 years

PV = 120 x ((1+0.01)^-5) = 114.18

135 in 10 years

PV = 135 x ((1+0.01)^-10) = 122.21

(ii) 3%

105 in one year

PV = 105 x ((1+0.03)^-1) = 101.94

120 in 5 years

PV = 120 x ((1+0.03)^-5) = 103.51

135 in 10 years

PV = 135 x ((1+0.03)^-10) = 100.45

(iii) 5%

105 in one year

PV = 105 x ((1+0.05)^-1) = 100.00

120 in 5 years

PV = 120 x ((1+0.05)^-5) = 94.02

135 in 10 years

PV = 135 x ((1+0.05)^-10) = 82.88