Question

you just received an inheritance and are trying to decide between 3 options. your required return is 10.4%. please find the present value for each option. which option should you choose?

A. $7,700 per year forever
B. one payment of $32,000 today and one payment of $55,000 in 3 years.
C. 102 weekly payments of $800, with the first payment to be made today. Assume there are 52 weeks in a year.

Answer 1

Required rate of return = 10.4%

Option A

7700 per year forever

This is an example of a perpetuity where Cashflow = C = 7700 and r = 10.4%

The formula to calculate the present value of a perpetuity is:

PV_perpetuity = C/r = 7700/0.104 = 74038.46154

Option 2

One payment of 32000 today, and one payment of 55000 in 3 years

Present value is calculated using the formula:

PV = C_n/(1+r)ⁿ where C_n is the cashflow in the nth period

PV of C₀ = 32000

PV of cashflow C₃ = 55000/(1.104)³ = 40874.783872

Period	0	1	2	3
Cashflow	32000			55000
Present Value	32000			40874.78

The total value of present values = 32000 + 40874.783872 = 72874.78

Option C

102 weekly payments of $800, with the first payment to be made today. Assume there are 52 weeks in a year

Interest rate = 10.4%

Weekly interest rate = r = 10.4%/52 = 0.2%

No. of periods = n = 102

Present value = C + [C/(1+r)] + [C/(1+r)²] +.......+ [C/(1+r)^n-1]

This is an example of an Annuity Due

Present value of an annuity due is calculated using the formula:

PV_{Annuity Due} = C/r*[1-(1+r)^-n]*(1+r)

C = 800, n = 102, r = 0.2% or 0.002

PV_{annuity due} = (800/0.002) * [1-1.002^-102] * (1.002) = 73896.0888

Option	Present Values
A	74038.46
B	72874.78
C	73896.09

We can see that the present value of the cashflows in Option A is the maximum. So, Option A should be chosen

Answer -> Choose Option A