R38 Case study Exhibit 12 question

CFA Level III
#1

Hi guys,

I need your help. I am struggling to figure out how Jessica and Paul’s PV of annuity due is calculated.

Can anyone help?

Thanks

#2

Your easiest bet is to do it in Excel.

For Paul, the first payment is €66,440 today. Subsequent annual payments will increase by 2%. Do that for 20 years of payments, then discount them at 3%, and tot them up.

Note that you can do it on your calculator. The discount rate would be 1.03 / 1.02 − 1 = 0.9804%.

#3

Thanks, S2000magician

Actually I was able to calculate Paul’s with adj discount rate of 0.9804%, but not Jessica’s.Jessica’s Growth rate is higher than Discount rate 3%.

In this case, is there any way to do it on calculator?

Appreciate your help

#4

Mimic the calculation I did, above, using Jessica’s growth rate. It should work equally well.

Note: I tried it and it didn’t work. I’m not exactly certain why. I’ll have to think about it.

Note2: When I remember to set my calculator to BEGIN, it works, as it should.

#5

For Paul, you can just use an interest rate of (0.03 - 0.02)/1.02 = 0.9804% as set out above. For Jessica, I think you can solve it as a geometric series and there must be an elegant simplified expression. I’ll let S2000magician work his magic on it. :+1:

If there aren’t a lot of payments, you could use the CF worksheet to enter the nominal payments and discount them in the NPV worksheet. The only downside is the time to enter all the numbers without making a mistake.