Question

Luca Lucchesi has $10 million today and is setting up a trust fund for his 2 children.

If r=4%, how much should the fund pay each child next year?

Mr. Lucchesi is also thinking that his children need to learn to make their own mark in the financial world. So he is thinking of withholding the trust fund payments until 5 years (i.e. t=5). Determine the perpetual annual payments that could be supported in such a scenario.

Answer 1

Luca Lucchesi has $10 million today and is setting up a trust fund for his 2 children.

If r=4%, how much should the fund pay each child next year?

We can assume a perpetual payment which is an equal amount of payment with periodic interval for indefinite time.

Present value of a perpetuity = C/ r

Where,

Present value of a perpetuity = $10 million

Total Annual payment C =?

Interest rate r = 4%

Therefore,

$10 million = C /4%

OR C = $10,000,000 * 4% = $400,000

Therefore each child will get C/2 = $400,000/2 = $200,000 next year from this perpetuity.

Mr. Lucchesi is also thinking that his children need to learn to make their own mark in the financial world. So he is thinking of withholding the trust fund payments until 5 years (i.e. t=5). Determine the perpetual annual payments that could be supported in such a scenario.

First we have to calculate the value of initial fund after 5 years (t=5) at 4% interest rate

PV5 = PV0 * (1+r %) ^t

Where,

PV5 is Present value of perpetuity after 5 years =?

PV0 is Present value of perpetuity today = $10 million

Interest rate r =4% per year

Time period t = 5 years

Therefore,

PV5 = $10,000,000 * (1+4%) ^5

= $12,166,529.02

We can calculate perpetual payment in following manner-

Present value of perpetuity after 5 years = C/ r

Where,

Present value of perpetuity after 5 years = $12,166,529.02

Total Annual payment C =?

Interest rate r = 4%

Therefore,

$12,166,529.02 = C /4%

OR C = $12,166,529.02* 4% = $486,661.16

Therefore each child will get C/2 = $486,661.16/2 = $243,330.58 each year from this perpetuity.