Question

In light of the impact of the coronavirus pandemic, Katherine Mutual Bank in the Northern Territory, would like to set up a reserve fund. The fund will earn an interest rate of 4.7% per annum. If the fund pays a fixed amount of $11 million to the bank annually for an infinite period, starting three years from today, how much does the bank need in the fund today? Select one: a. $213.5 million b. $234.0 million c. $223.5 million d. $186.0 million

Answer 1

Answer: a. $213.50

Explanation:

We need to calculate present value of perpetuity= cash flow/r

Where; cash flow = 11,000,000

r=4.7%=0.047

Present value of perpetuity= 11000000/0.047=234,042,553.19

But this value is worth 3 years hence as perpetuity will start after 3 years, as such we will discount it for present value:

Present value= 234,042,553.19/[(1+0.047)^2]

Please note that we have taken time at 2 year instead of 3 years because in present value of perpetuity, amount starts after one year as such we will reduce one year here.

=234042553.19/1.096209

= 213501762

=$213.50 million

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