Question

Q1) Daniel is an investor and he should choose between these options.

a. Offers $12,000 in 5 annual payments of $2,500 each.

b. Offers $14,000 in 4 annual payments of $2,000 each and then one payment of $6,000 in year 5.

Compare the present value of each option for each of the following required rates of return 5%, 10% and 20%. What is your advice in each case?

Answer 1

If required return is 5%:

Option 1:

Present Value = $2,500/1.05 + $2,500/1.05^2 + $2,500/1.05^3 + $2,500/1.05^4 + $2,500/1.05^5
Present Value = $10,823.69

Option 2:

Present Value = $2,000/1.05 + $2,000/1.05^2 + $2,000/1.05^3 + $2,000/1.05^4 + $6,000/1.05^5
Present Value = $11,793.06

Daniel should choose Option 2 as its present value is higher.

If required return is 10%:

Option 1:

Present Value = $2,500/1.10 + $2,500/1.10^2 + $2,500/1.10^3 + $2,500/1.10^4 + $2,500/1.10^5
Present Value = $9,476.97

Option 2:

Present Value = $2,000/1.10 + $2,000/1.10^2 + $2,000/1.10^3 + $2,000/1.10^4 + $6,000/1.10^5
Present Value = $10,065.26

Daniel should choose Option 2 as its present value is higher.

If required return is 20%:

Option 1:

Present Value = $2,500/1.20 + $2,500/1.20^2 + $2,500/1.20^3 + $2,500/1.20^4 + $2,500/1.20^5
Present Value = $7,476.53

Option 2:

Present Value = $2,000/1.20 + $2,000/1.20^2 + $2,000/1.20^3 + $2,000/1.20^4 + $6,000/1.20^5
Present Value = $7,588.73

Daniel should choose Option 2 as its present value is higher.