Equivalent Rates - Valuation Mathematics

[logicandtruth]

Hi all

I am currently working on questions focusing on valuation mathematics. A question on equivalent rates is perplexing me. The first question is straightforward, but I get stuck on the second question.

Q1. What is the value of the right to receive £100,000 annually in advance in perpetuity assuming a discount rate of 10%?

A1. £1,100,000

The formula below is for a level annuity that is received in perpetuity and in advance. Here in the UK typically commercial property leases are structured so tenants pay rents four times spread evenly over a year.

View attachment 8408

Q2. What is the value of the right to receive £100,000 per annum quarterly in advance in perpetuity assuming an annual nominal rate of 10%?

A. £1,062,344

I tried various iterations of the formula, but can't get the above answer. Any help would be much appreciated

 

[Wilmer]

Q2. What is the value of the right to receive £100,000 per annum quarterly
in advance in perpetuity assuming an annual nominal rate of 10%?

A. £1,062,344

Rate needs to be converted to the quarterly rate
that results in 10% annual; that rate is ~2.41%:
1.0241^4 = 1.10, so 10% effective.

Bank tatement will look like:

QUARTER PAYMENT INTEREST  BALANCE
     0                   1,062,344
     0  -25,000       0  1,037,344
     1  -25,000  25,000  1,037,344 : 1037344*.0241= 25000
     2  -25,000  25,000  1,037,344
...and so on till death do you part!

Sooooo...using formula:
PMT/r + PMT = 25000/.0241 + 25000 = 1,062,344

HOKAY?

 

[logicandtruth]

I see where I went wrong, I was incorrectly converting the interest to a quarter rate:

Quarterly rate = (1 + annual rate )(1/4) – 1

Thank you, understood.