CM1B Ch13 004 iv Exam style question

[singingmyblues]

I am just wondering how the PV of liabilities is calculated? Looks like real cashflow and interest rate is used, so effectively 1.5m *a:<40>@r. But I don't know how this is converted to real values? The (1+i)^0.5 *1.025^-1 part implies we accumulate half year and divide by inflation. But doesn't a:<40> mean the cashflows are half year later?

 

[Joe Hook]

So the PV of the liabilities is (working in millions): 1.5*v^0.5 + 1.5*1.025*v^1.5 + 1.5*1.025^2*v^2.5 + …

To use a level annuity function we need to match up the powers of the (1 + inflation) and v. To do that we can rewrite the above as:

1.5 * v^0-.5 * 1.025^-1 * (1.025*v + 1.025^2*v^2 + …)

That bit in brackets is an annuity where V = 1.025/(1+i) and so i’ = (1+i)/1.025 – 1 ie column B.

So we can write the overall expression as 1.5 * (1 + i)^0.5 * 1.025 ^-1 * a:<40> @ i’ .

Sorry this doesn’t read the best but hopefully it helps you to make sense of it.

Thanks
Joe