Please show work for full rating Bryce Wayne has recently inherited $90 million
ID: 2817615 • Letter: P
Question
Please show work for full rating
Bryce Wayne has recently inherited $90 million dollars. He estimates that his monthly living expenses will be $100,000 per month for thirty years. He also plans to make the following one-time future expenditures. 1) He wishes to purchase a mansion next year for four million dollars. 2) He wishes to purchase and remodel a cave to use as his laboratory and fortress. He plans to purchase the cave in 5 years, and forecasts that the cost will be ten million dollars. Bryce would also like to fund his favorite charity, by giving monthly contributions to the Society for the Prevention of Cruelty to Bats. He would donate a fixed amount of money per month (starting next month) in perpetuity. How much could Bryce donate per month, while making sure he has enough money to cover his expenses and planned expenditures? The appropriate interest rate is 0.33% monthly.Explanation / Answer
Answer:
Amount inherited = $90,000,000
First we need to calculate Present value (PV) of the recurring and one time expenditures:
To get PV of monthly living expense of $100,000 per month for 30 years,
We use excel function PV:
PMT = $100,000
nper = 30 years = 30*12 =360months
Rate = 0.33% monthly
PV(rate,nper,pmt,fv,type)
PV(0.33%,360,-100000,0,0)
=$21,047,663.15
PV of $4,000,000 next year with which he plans to purchase mansion:
Here,
Rate = 0.33%
FV = $4,000,000
nper = one year = 12 months
PV(0.33%,12,0,-4000000,0)
= $3,844,946
PV of $10,000,000 he needs to purchase cave in 5 years
Here,
FV = $10,000,000
nper = 5 years = 5*12 =60 months
PV(0.33%,60,0,-10000000,0)
=$8,206,373.23
Balance amount in $90 million after considering PV of monthly expenses, one time payments for mansion and cave = $90,000,000 - $21,047,663.15 - $3,844,946 - $8,206,373.23
=$56,901,117.62
He wants to give fixed monthly contributions for charity starting next month perpetually
Rate of interest = 0.33%
Balance amount available = $56,901,117.62
As the charity has to be done monthly for fixed amount in perpetuity, hence the maximum monthly contribution will be amount of interest he will earn on balance amount = $56,901,117.62* 0.33%
= $187,773.69