Question

Assume all cash flows occur at the end of the period

1. You have a rich Aunt Ernestine, who recently passed on. In her will, she stipulated you would receive $1,000 a year through age 25; then you will receive $2,500 a year through age 30, then you are to get $5,000 a year through 40 years of age, at which time your payments will cease. You just had your twentieth birthday today (hint: your first cash flow occurs one year from now on your twenty-first birthday). At your twentieth birthday party, a woman offered you $30,000 for the right to your inherited cash flow. Assuming an opportunity cost of eight percent, what is the difference between the amount the woman offers you and the present value of your cash flows? Should you take the offer?

Answer 1

Here you will be receiving the folliwing cash flows-

1.$1000 Per year for the next 5 year [21 yr to 25 th yr]

2.$2500 per year for 5 years after 5 years [26th yr to 30th year]

3.$5000 per year for 10 year after 10 years.[31st Yr to 40th year]

(I) Calculation Present value of cash flows $1000 Per year for the next 5 year-

Present value of annuity =

A = annual cash flow = $1000

i = opportunity cost or interest = 8% or 0.08

n = time = 5 year

hence PV of cash flows $1000 Per year for the next 5 year=

=>PV of cash flows $1000 Per year for the next 5 year = $3992.71.

(II) Calculation of PV of cashflows $2500 per year for 5 years after 5 years

Here first we have to calculate the PV of the $2500 per year [ from 26th to 30th birthday] at the end of next 5 year [25th birthday].

Then we have to discount value at 25 th birthday to present date.

hence the Formula will be =

PV of cashflows $2500 per year for 5 years after 5 years =

=>PV of cashflows $2500 per year for 5 years after 5 years=

=>PV of cashflows $2500 per year for 5 years to be received after 5 years= $6793.43.

(III)Calculation of PV of cashflows $5000 per year for 10 year after 10 years

Here first we have to calculate the PV of the $5000 per year [ from 31st to 40th birthday] at the end of next 10 year [30th birthday].

Then we have to discount value at 30th birthday to present date.

hence the Formula will be =

PV of cashflows $5000 per year for 10 year after 10 years =

=>PV of cashflows $5000 per year for 10 year to be received after 10 years=$15540.33.

Total pv of the cash flows = $3992.71+$6793.43+$15540.33= $26326.47

Amount offered = $30000

Difference between the amount the woman offers you and the present value of your cash flows = $30000-$26326.47= $3673.53

As the amlunt offered is more than the PV of the total cash flow, hence the offer should be accepted.