Question

Your grandfather has offered you a choice of one of the three following alternatives: $6,500 now; $1,750 a year for seven years; or $27,000 at the end of seven years.

Required:
a. Assuming you could earn 10 percent annually, compute the present value of each alternative.
b. Which alternative should you choose?

1. $27,000 received at end of seven years
2. $1,750 received each year for seven years
3. $6,500 received now

c. If you could earn 11 percent annually, compute the present value of each alternative.
d. Which alternative should you choose?

1. $27,000 received at end of seven years
2. $1,750 received each year for seven years
3. $6,500 received now

Answer 1

a. Present Value at 10%

1. $27,000 received at end of seven years

Present Value = 27,000 / ( 1 + 10%)^7

= $13,855.27

2. $1,750 received each year for seven years

This is an annuity.

Present Value = 1,750 * Present value interest factor of annuity , 7 years , 10%

= 1,750 * 4.8684

= $‭8,519.7‬0

3. $6,500 received now

It is received now so the present value is $6,500.

b. $27,000 received at end of seven years.

This has the highest present value at $13,855.27

c. Present Value at 11%

1. $27,000 received at end of seven years

Present Value = 27,000 / ( 1 + 11%)^7

= $13,004.78

2. $1,750 received each year for seven years

This is still an annuity.

Present Value = 1,750 * Present value interest factor of annuity , 7 years , 11%

= 1,750 * 4.7122

= $‭8,246.35‬

3. $6,500 received now

It is received now so the present value is still $6,500

d. Still $27,000 received at end of seven years .

Still has the highest Present Value